young's double slit experiment applications

27.3 Young’s Double Slit Experiment

Learning objectives.

By the end of this section, you will be able to:

• Explain the phenomena of interference.
• Define constructive interference for a double slit and destructive interference for a double slit.

Although Christiaan Huygens thought that light was a wave, Isaac Newton did not. Newton felt that there were other explanations for color, and for the interference and diffraction effects that were observable at the time. Owing to Newton’s tremendous stature, his view generally prevailed. The fact that Huygens’s principle worked was not considered evidence that was direct enough to prove that light is a wave. The acceptance of the wave character of light came many years later when, in 1801, the English physicist and physician Thomas Young (1773–1829) did his now-classic double slit experiment (see Figure 27.10 ).

Why do we not ordinarily observe wave behavior for light, such as observed in Young’s double slit experiment? First, light must interact with something small, such as the closely spaced slits used by Young, to show pronounced wave effects. Furthermore, Young first passed light from a single source (the Sun) through a single slit to make the light somewhat coherent. By coherent , we mean waves are in phase or have a definite phase relationship. Incoherent means the waves have random phase relationships. Why did Young then pass the light through a double slit? The answer to this question is that two slits provide two coherent light sources that then interfere constructively or destructively. Young used sunlight, where each wavelength forms its own pattern, making the effect more difficult to see. We illustrate the double slit experiment with monochromatic (single λ λ ) light to clarify the effect. Figure 27.11 shows the pure constructive and destructive interference of two waves having the same wavelength and amplitude.

When light passes through narrow slits, it is diffracted into semicircular waves, as shown in Figure 27.12 (a). Pure constructive interference occurs where the waves are crest to crest or trough to trough. Pure destructive interference occurs where they are crest to trough. The light must fall on a screen and be scattered into our eyes for us to see the pattern. An analogous pattern for water waves is shown in Figure 27.12 (b). Note that regions of constructive and destructive interference move out from the slits at well-defined angles to the original beam. These angles depend on wavelength and the distance between the slits, as we shall see below.

To understand the double slit interference pattern, we consider how two waves travel from the slits to the screen, as illustrated in Figure 27.13 . Each slit is a different distance from a given point on the screen. Thus different numbers of wavelengths fit into each path. Waves start out from the slits in phase (crest to crest), but they may end up out of phase (crest to trough) at the screen if the paths differ in length by half a wavelength, interfering destructively as shown in Figure 27.13 (a). If the paths differ by a whole wavelength, then the waves arrive in phase (crest to crest) at the screen, interfering constructively as shown in Figure 27.13 (b). More generally, if the paths taken by the two waves differ by any half-integral number of wavelengths [ ( 1 / 2 ) λ ( 1 / 2 ) λ , ( 3 / 2 ) λ ( 3 / 2 ) λ , ( 5 / 2 ) λ ( 5 / 2 ) λ , etc.], then destructive interference occurs. Similarly, if the paths taken by the two waves differ by any integral number of wavelengths ( λ λ , 2 λ 2 λ , 3 λ 3 λ , etc.), then constructive interference occurs.

Take-Home Experiment: Using Fingers as Slits

Look at a light, such as a street lamp or incandescent bulb, through the narrow gap between two fingers held close together. What type of pattern do you see? How does it change when you allow the fingers to move a little farther apart? Is it more distinct for a monochromatic source, such as the yellow light from a sodium vapor lamp, than for an incandescent bulb?

Figure 27.14 shows how to determine the path length difference for waves traveling from two slits to a common point on a screen. If the screen is a large distance away compared with the distance between the slits, then the angle θ θ between the path and a line from the slits to the screen (see the figure) is nearly the same for each path. The difference between the paths is shown in the figure; simple trigonometry shows it to be d sin θ d sin θ , where d d is the distance between the slits. To obtain constructive interference for a double slit , the path length difference must be an integral multiple of the wavelength, or

Similarly, to obtain destructive interference for a double slit , the path length difference must be a half-integral multiple of the wavelength, or

where λ λ is the wavelength of the light, d d is the distance between slits, and θ θ is the angle from the original direction of the beam as discussed above. We call m m the order of the interference. For example, m = 4 m = 4 is fourth-order interference.

The equations for double slit interference imply that a series of bright and dark lines are formed. For vertical slits, the light spreads out horizontally on either side of the incident beam into a pattern called interference fringes, illustrated in Figure 27.15 . The intensity of the bright fringes falls off on either side, being brightest at the center. The closer the slits are, the more is the spreading of the bright fringes. We can see this by examining the equation

For fixed λ λ and m m , the smaller d d is, the larger θ θ must be, since sin θ = mλ / d sin θ = mλ / d . This is consistent with our contention that wave effects are most noticeable when the object the wave encounters (here, slits a distance d d apart) is small. Small d d gives large θ θ , hence a large effect.

Example 27.1

Finding a wavelength from an interference pattern.

Suppose you pass light from a He-Ne laser through two slits separated by 0.0100 mm and find that the third bright line on a screen is formed at an angle of 10 . 95º 10 . 95º relative to the incident beam. What is the wavelength of the light?

The third bright line is due to third-order constructive interference, which means that m = 3 m = 3 . We are given d = 0 . 0100 mm d = 0 . 0100 mm and θ = 10 . 95º θ = 10 . 95º . The wavelength can thus be found using the equation d sin θ = mλ d sin θ = mλ for constructive interference.

The equation is d sin θ = mλ d sin θ = mλ . Solving for the wavelength λ λ gives

Substituting known values yields

To three digits, this is the wavelength of light emitted by the common He-Ne laser. Not by coincidence, this red color is similar to that emitted by neon lights. More important, however, is the fact that interference patterns can be used to measure wavelength. Young did this for visible wavelengths. This analytical technique is still widely used to measure electromagnetic spectra. For a given order, the angle for constructive interference increases with λ λ , so that spectra (measurements of intensity versus wavelength) can be obtained.

Example 27.2

Calculating highest order possible.

Interference patterns do not have an infinite number of lines, since there is a limit to how big m m can be. What is the highest-order constructive interference possible with the system described in the preceding example?

Strategy and Concept

The equation d sin θ = mλ (for m = 0, 1, − 1, 2, − 2, … ) d sin θ = mλ (for m = 0, 1, − 1, 2, − 2, … ) describes constructive interference. For fixed values of d d and λ λ , the larger m m is, the larger sin θ sin θ is. However, the maximum value that sin θ sin θ can have is 1, for an angle of 90º 90º . (Larger angles imply that light goes backward and does not reach the screen at all.) Let us find which m m corresponds to this maximum diffraction angle.

Solving the equation d sin θ = mλ d sin θ = mλ  for  m m gives

Taking sin θ = 1 sin θ = 1 and substituting the values of d d and λ λ from the preceding example gives

Therefore, the largest integer m m can be is 15, or

The number of fringes depends on the wavelength and slit separation. The number of fringes will be very large for large slit separations. However, if the slit separation becomes much greater than the wavelength, the intensity of the interference pattern changes so that the screen has two bright lines cast by the slits, as expected when light behaves like a ray. We also note that the fringes get fainter further away from the center. Consequently, not all 15 fringes may be observable.

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154 Young’s Double Slit Experiment

[latexpage]

Learning Objectives

• Explain the phenomena of interference.
• Define constructive interference for a double slit and destructive interference for a double slit.

Although Christiaan Huygens thought that light was a wave, Isaac Newton did not. Newton felt that there were other explanations for color, and for the interference and diffraction effects that were observable at the time. Owing to Newton’s tremendous stature, his view generally prevailed. The fact that Huygens’s principle worked was not considered evidence that was direct enough to prove that light is a wave. The acceptance of the wave character of light came many years later when, in 1801, the English physicist and physician Thomas Young (1773–1829) did his now-classic double slit experiment (see (Figure) ).

Why do we not ordinarily observe wave behavior for light, such as observed in Young’s double slit experiment? First, light must interact with something small, such as the closely spaced slits used by Young, to show pronounced wave effects. Furthermore, Young first passed light from a single source (the Sun) through a single slit to make the light somewhat coherent. By coherent , we mean waves are in phase or have a definite phase relationship. Incoherent means the waves have random phase relationships. Why did Young then pass the light through a double slit? The answer to this question is that two slits provide two coherent light sources that then interfere constructively or destructively. Young used sunlight, where each wavelength forms its own pattern, making the effect more difficult to see. We illustrate the double slit experiment with monochromatic (single \(\lambda \)) light to clarify the effect. (Figure) shows the pure constructive and destructive interference of two waves having the same wavelength and amplitude.

When light passes through narrow slits, it is diffracted into semicircular waves, as shown in (Figure) (a). Pure constructive interference occurs where the waves are crest to crest or trough to trough. Pure destructive interference occurs where they are crest to trough. The light must fall on a screen and be scattered into our eyes for us to see the pattern. An analogous pattern for water waves is shown in (Figure) (b). Note that regions of constructive and destructive interference move out from the slits at well-defined angles to the original beam. These angles depend on wavelength and the distance between the slits, as we shall see below.

To understand the double slit interference pattern, we consider how two waves travel from the slits to the screen, as illustrated in (Figure) . Each slit is a different distance from a given point on the screen. Thus different numbers of wavelengths fit into each path. Waves start out from the slits in phase (crest to crest), but they may end up out of phase (crest to trough) at the screen if the paths differ in length by half a wavelength, interfering destructively as shown in (Figure) (a). If the paths differ by a whole wavelength, then the waves arrive in phase (crest to crest) at the screen, interfering constructively as shown in (Figure) (b). More generally, if the paths taken by the two waves differ by any half-integral number of wavelengths [\(\left(1/2\right)\lambda \), \(\left(3/2\right)\lambda \), \(\left(5/2\right)\lambda \), etc.], then destructive interference occurs. Similarly, if the paths taken by the two waves differ by any integral number of wavelengths (\(\lambda \), \(2\lambda \), \(3\lambda \), etc.), then constructive interference occurs.

Look at a light, such as a street lamp or incandescent bulb, through the narrow gap between two fingers held close together. What type of pattern do you see? How does it change when you allow the fingers to move a little farther apart? Is it more distinct for a monochromatic source, such as the yellow light from a sodium vapor lamp, than for an incandescent bulb?

(Figure) shows how to determine the path length difference for waves traveling from two slits to a common point on a screen. If the screen is a large distance away compared with the distance between the slits, then the angle \(\theta \) between the path and a line from the slits to the screen (see the figure) is nearly the same for each path. The difference between the paths is shown in the figure; simple trigonometry shows it to be \(d\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}\theta \), where \(d\) is the distance between the slits. To obtain constructive interference for a double slit , the path length difference must be an integral multiple of the wavelength, or

Similarly, to obtain destructive interference for a double slit , the path length difference must be a half-integral multiple of the wavelength, or

where \(\lambda \) is the wavelength of the light, \(d\) is the distance between slits, and \(\theta \) is the angle from the original direction of the beam as discussed above. We call \(m\) the order of the interference. For example, \(m=4\) is fourth-order interference.

The equations for double slit interference imply that a series of bright and dark lines are formed. For vertical slits, the light spreads out horizontally on either side of the incident beam into a pattern called interference fringes, illustrated in (Figure) . The intensity of the bright fringes falls off on either side, being brightest at the center. The closer the slits are, the more is the spreading of the bright fringes. We can see this by examining the equation

For fixed \(\lambda \) and \(m\), the smaller \(d\) is, the larger \(\theta \) must be, since \(\text{sin}\phantom{\rule{0.25em}{0ex}}\theta =\mathrm{m\lambda }/d\). This is consistent with our contention that wave effects are most noticeable when the object the wave encounters (here, slits a distance \(d\) apart) is small. Small \(d\) gives large \(\theta \), hence a large effect.

Suppose you pass light from a He-Ne laser through two slits separated by 0.0100 mm and find that the third bright line on a screen is formed at an angle of \(\text{10}\text{.}\text{95º}\) relative to the incident beam. What is the wavelength of the light?

The third bright line is due to third-order constructive interference, which means that \(m=3\). We are given \(d=0\text{.}\text{0100}\phantom{\rule{0.25em}{0ex}}\text{mm}\) and \(\theta =\text{10}\text{.}\text{95º}\). The wavelength can thus be found using the equation \(d\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}\theta =\mathrm{m\lambda }\) for constructive interference.

The equation is \(d\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}\theta =\mathrm{m\lambda }\). Solving for the wavelength \(\lambda \) gives

Substituting known values yields

To three digits, this is the wavelength of light emitted by the common He-Ne laser. Not by coincidence, this red color is similar to that emitted by neon lights. More important, however, is the fact that interference patterns can be used to measure wavelength. Young did this for visible wavelengths. This analytical technique is still widely used to measure electromagnetic spectra. For a given order, the angle for constructive interference increases with \(\lambda \), so that spectra (measurements of intensity versus wavelength) can be obtained.

Interference patterns do not have an infinite number of lines, since there is a limit to how big \(m\) can be. What is the highest-order constructive interference possible with the system described in the preceding example?

Strategy and Concept

The equation \(d\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}\theta =\mathrm{m\lambda }\phantom{\rule{0.25em}{0ex}}\text{(for}\phantom{\rule{0.25em}{0ex}}m=0,\phantom{\rule{0.25em}{0ex}}1,\phantom{\rule{0.25em}{0ex}}-1,\phantom{\rule{0.25em}{0ex}}2,\phantom{\rule{0.25em}{0ex}}-2,\phantom{\rule{0.25em}{0ex}}\dots \right)\) describes constructive interference. For fixed values of \(d\) and \(\lambda \), the larger \(m\) is, the larger \(\text{sin}\phantom{\rule{0.25em}{0ex}}\theta \) is. However, the maximum value that \(\text{sin}\phantom{\rule{0.25em}{0ex}}\theta \) can have is 1, for an angle of \(\text{90º}\). (Larger angles imply that light goes backward and does not reach the screen at all.) Let us find which \(m\) corresponds to this maximum diffraction angle.

Solving the equation \(d\text{sin}\phantom{\rule{0.25em}{0ex}}\theta =\mathrm{m\lambda }\) for \(m\) gives

Taking \(\text{sin}\phantom{\rule{0.25em}{0ex}}\theta =1\) and substituting the values of \(d\) and \(\lambda \) from the preceding example gives

Therefore, the largest integer \(m\) can be is 15, or

The number of fringes depends on the wavelength and slit separation. The number of fringes will be very large for large slit separations. However, if the slit separation becomes much greater than the wavelength, the intensity of the interference pattern changes so that the screen has two bright lines cast by the slits, as expected when light behaves like a ray. We also note that the fringes get fainter further away from the center. Consequently, not all 15 fringes may be observable.

Section Summary

• Young’s double slit experiment gave definitive proof of the wave character of light.
• An interference pattern is obtained by the superposition of light from two slits.
• There is constructive interference when \(d\text{sin}\phantom{\rule{0.25em}{0ex}}\theta =\mathrm{m\lambda }\phantom{\rule{0.25em}{0ex}}\text{(for}\phantom{\rule{0.25em}{0ex}}m=0,\phantom{\rule{0.25em}{0ex}}1,\phantom{\rule{0.25em}{0ex}}-1,\phantom{\rule{0.25em}{0ex}}2,\phantom{\rule{0.25em}{0ex}}-2,\phantom{\rule{0.25em}{0ex}}\dots \right)\), where \(d\) is the distance between the slits, \(\theta \) is the angle relative to the incident direction, and \(m\) is the order of the interference.
• There is destructive interference when \(d\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}\theta =\left(m+\frac{1}{2}\right)\lambda \phantom{\rule{0.25em}{0ex}}\text{(for}\phantom{\rule{0.5em}{0ex}}m=0,\phantom{\rule{0.25em}{0ex}}1,\phantom{\rule{0.25em}{0ex}}-1,\phantom{\rule{0.25em}{0ex}}2,\phantom{\rule{0.25em}{0ex}}-2,\phantom{\rule{0.25em}{0ex}}\dots \right)\).

Conceptual Questions

Young’s double slit experiment breaks a single light beam into two sources. Would the same pattern be obtained for two independent sources of light, such as the headlights of a distant car? Explain.

Suppose you use the same double slit to perform Young’s double slit experiment in air and then repeat the experiment in water. Do the angles to the same parts of the interference pattern get larger or smaller? Does the color of the light change? Explain.

Is it possible to create a situation in which there is only destructive interference? Explain.

(Figure) shows the central part of the interference pattern for a pure wavelength of red light projected onto a double slit. The pattern is actually a combination of single slit and double slit interference. Note that the bright spots are evenly spaced. Is this a double slit or single slit characteristic? Note that some of the bright spots are dim on either side of the center. Is this a single slit or double slit characteristic? Which is smaller, the slit width or the separation between slits? Explain your responses.

Problems & Exercises

At what angle is the first-order maximum for 450-nm wavelength blue light falling on double slits separated by 0.0500 mm?

\(0\text{.}\text{516º}\)

Calculate the angle for the third-order maximum of 580-nm wavelength yellow light falling on double slits separated by 0.100 mm.

What is the separation between two slits for which 610-nm orange light has its first maximum at an angle of \(\text{30}\text{.}0º\)?

\(1\text{.}\text{22}×{\text{10}}^{-6}\phantom{\rule{0.25em}{0ex}}\text{m}\)

Find the distance between two slits that produces the first minimum for 410-nm violet light at an angle of \(\text{45}\text{.}0º\).

Calculate the wavelength of light that has its third minimum at an angle of \(\text{30}\text{.}0º\) when falling on double slits separated by \(3\text{.}\text{00}\phantom{\rule{0.25em}{0ex}}\text{μm}\). Explicitly, show how you follow the steps in Problem-Solving Strategies for Wave Optics .

What is the wavelength of light falling on double slits separated by \(2\text{.}\text{00}\phantom{\rule{0.25em}{0ex}}\text{μm}\) if the third-order maximum is at an angle of \(\text{60}\text{.}0º\)?

At what angle is the fourth-order maximum for the situation in (Figure) ?

\(2\text{.}\text{06º}\)

What is the highest-order maximum for 400-nm light falling on double slits separated by \(\text{25}\text{.}0\phantom{\rule{0.25em}{0ex}}\text{μm}\)?

Find the largest wavelength of light falling on double slits separated by \(1\text{.}\text{20}\phantom{\rule{0.25em}{0ex}}\text{μm}\) for which there is a first-order maximum. Is this in the visible part of the spectrum?

1200 nm (not visible)

What is the smallest separation between two slits that will produce a second-order maximum for 720-nm red light?

(a) What is the smallest separation between two slits that will produce a second-order maximum for any visible light? (b) For all visible light?

(b) 1520 nm

(a) If the first-order maximum for pure-wavelength light falling on a double slit is at an angle of \(\text{10}\text{.}0º\), at what angle is the second-order maximum? (b) What is the angle of the first minimum? (c) What is the highest-order maximum possible here?

(Figure) shows a double slit located a distance \(x\) from a screen, with the distance from the center of the screen given by \(y\). When the distance \(d\) between the slits is relatively large, there will be numerous bright spots, called fringes. Show that, for small angles (where \(\text{sin}\phantom{\rule{0.25em}{0ex}}\theta \approx \theta \), with \(\theta \) in radians), the distance between fringes is given by \(\text{Δ}y=\mathrm{x\lambda }/d\).

For small angles \(\text{sin}\phantom{\rule{0.25em}{0ex}}\theta -\text{tan}\phantom{\rule{0.25em}{0ex}}\theta \approx \theta \phantom{\rule{0.25em}{0ex}}\left(\text{in radians}\right)\).

For two adjacent fringes we have,

Subtracting these equations gives

Using the result of the problem above, calculate the distance between fringes for 633-nm light falling on double slits separated by 0.0800 mm, located 3.00 m from a screen as in (Figure) .

Using the result of the problem two problems prior, find the wavelength of light that produces fringes 7.50 mm apart on a screen 2.00 m from double slits separated by 0.120 mm (see (Figure) ).

ISP209: The Mystery of the Physical World Copyright © 2012 by OSCRiceUniversity is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

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• Quantum mechanics
• Opinion and reviews

The double-slit experiment

This article is an extended version of the article “The double-slit experiment” that appeared in the September 2002 issue of Physics World (p15). It has been further extended to include three letters about the history of the double-slit experiment with single electrons that were published in the May 2003 issue of the magazine.

What is the most beautiful experiment in physics? This is the question that Robert Crease asked Physics World readers in May – and more than 200 replied with suggestions as diverse as Schrödinger’s cat and the Trinity nuclear test in 1945. The top five included classic experiments by Galileo, Millikan, Newton and Thomas Young. But uniquely among the top 10, the most beautiful experiment in physics – Young’s double-slit experiment applied to the interference of single electrons – does not have a name associated with it.

Most discussions of double-slit experiments with particles refer to Feynman’s quote in his lectures: “We choose to examine a phenomenon which is impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery.” Feynman went on to add: “We should say right away that you should not try to set up this experiment. This experiment has never been done in just this way. The trouble is that the apparatus would have to be made on an impossibly small scale to show the effects we are interested in. We are doing a “thought experiment”, which we have chosen because it is easy to think about. We know the results that would be obtained because there are many experiments that have been done, in which the scale and the proportions have been chosen to show the effects we shall describe”.

It is not clear that Feynman was aware that the first double-slit experiment with electrons had been carried out in 1961, the year he started his lectures (which were published in 1963). More surprisingly, perhaps, Feynman did not stress that an interference pattern would build up even if there was just one electron in the apparatus at a time. (This lack of emphasis was unusual because in the same lecture Feynman describes the electron experiment – and other double-slit experiments with water waves and bullets – in considerable detail).

So who actually carried out the first double-slit experiment with single electrons? Not surprisingly many thought or gedanken experiments are named after theorists – such as the Aharonov-Bohm effect, Bell’s inequality, the Casimir force, the Einstein-Podolsky-Rosen paradox, Schrödinger’s cat and so on – and these names rightly remain even when the experiment has been performed by others in the laboratory. However, it seems remarkable that no name whatsoever is attached to the double-slit experiment with electrons. Standard reference books are silent on this question but a study of the literature reveals several unsung experimental heroes.

Back to Young

Young carried out his original double-slit experiment with light some time in the first decade of the 1800s, showing that the waves of light from the two slits interfered to produce a characteristic fringe pattern on a screen. In 1909 Geoffrey Ingram (G I) Taylor conducted an experiment in which he showed that even the feeblest light source – equivalent to “a candle burning at a distance slightly exceeding a mile” – could lead to interference fringes. This led to Dirac’s famous statement that “each photon then interferes only with itself”.

In 1927 Clinton Davisson and Lester Germer observed the diffraction of electron beams from a nickel crystal – demonstrating the wave-like properties of particles for the first time – and George (G P) Thompson did the same with thin films of celluloid and other materials shortly afterwards. Davisson and Thomson shared the 1937 Nobel prize for “discovery of the interference phenomena arising when crystals are exposed to electronic beams”, but neither performed a double-slit experiment with electrons.

In the early 1950s Ladislaus Laszlo Marton of the US National Bureau of Standards (now NIST) in Washington, DC demonstrated electron interference but this was in a Mach-Zehnder rather than a double-slit geometry. These were the early days of the electron microscope and physicists were keen to exploit the very short de Broglie wavelength of electrons to study objects that were too small to be studied with visible light. Doing gedanken or thought experiments in the laboratory was further down their list of priorities.

A few years later Gottfried Möllenstedt and Heinrich Düker of the University of Tübingen in Germany used an electron biprism – essentially a very thin conducting wire at right angles to the beam – to split an electron beam into two components and observe interference between them. (Möllenstedt made the wires by coating fibres from spiders’ webs with gold – indeed, it is said that he kept spiders in the laboratory for this purpose). The electron biprism was to become widely used in the development of electron holography and also in other experiments, including the first measurement of the Aharonov-Bohm effect by Bob Chambers at Bristol University in the UK in 1960.

But in 1961 Claus Jönsson of Tübingen, who had been one of Möllenstedt’s students, finally performed an actual double-slit experiment with electrons for the first time ( Zeitschrift für Physik 161 454). Indeed, he demonstrated interference with up to five slits. The next milestone – an experiment in which there was just one electron in the apparatus at any one time – was reached by Akira Tonomura and co-workers at Hitachi in 1989 when they observed the build up of the fringe pattern with a very weak electron source and an electron biprism ( American Journal of Physics 57 117-120). Whereas Jönsson’s experiment was analogous to Young’s original experiment, Tonomura’s was similar to G I Taylor’s. (Note added on 7 May: Pier Giorgio Merli, Giulio Pozzi and GianFranco Missiroli carried out double-slit interference experiments with single electrons in Bologna in the 1970s; see Merli et al. in Further reading and the letters from Steeds, Merli et al. , and Tonomura at the end of this article.)

Since then particle interference has been demonstrated with neutrons, atoms and molecules as large as carbon-60 and carbon-70. And earlier this year another famous experiment in optics – the Hanbury Brown and Twiss experiment – was performed with electrons for the first time (again at Tübingen!). However, the results are profoundly different this time because electrons are fermions – and therefore obey the Pauli exclusion principle – whereas photons are bosons and do not.

Credit where it’s due

So why are Jönsson, Tonomura and the other pioneers of the double-slit experiment not well known? One obvious reason is that Jönsson’s results were first published in German in a German journal. Another reason might be that there was little incentive to perform the ultimate thought experiment in the lab, and little recognition for doing so. When Jönsson’s paper was translated into English 13 years later and published in the American Journal of Physics in 1974 (volume 42, pp4-11), the journal’s editors, Anthony (A P) French and Edwin Taylor, described it as a “great experiment”, but added that there are “few professional rewards” for performing what they describe as “real, pedagogically clean fundamental experiments.”

It is worth noting that the first double-slit experiment with single electrons by Tonomura and co-workers was also published in the American Journal of Physics , which publishes articles on the educational and cultural aspects of physics, rather than being a research journal. Indeed, the journal’s information for contributors states: “We particularly encourage manuscripts on already published contemporary research that can be used directly or indirectly in the classroom. We specifically do not publish articles announcing new theories or experimental results.”

French and Taylor’s editorial also confirms how little known Jönsson’s experiment was at the time: “For decades two-slit electron interference has been presented as a thought experiment whose predicted results are justified by their remote and somewhat obscure relation to real experiments in which electrons are diffracted by crystals. Few such recent presentations acknowledge that the two-slit electron interference experiment has now been done and that the results agree with the expectation of quantum physics in all detail.”

However, it should be noted that the history of physics is complicated and that events are rarely as clear-cut as we might like. For instance, it is widely claimed that Young performed his double-slit experiment in 1801 but he did not publish any account of it until his Lectures on Natural Philosophy in 1807. It also appears as if Davisson and a young collaborator called Charles Kunsman observed electron diffraction in 1923 – four years before Davisson and Germer – without realising it.

Final thoughts

Gedanken or thought experiments have played an important role in the history of quantum physics. It is unlikely that the whole area of quantum information would be as lively as it is today – both theoretically and experimentally – if a small band of physicists had not persevered and actually demonstrated quantum phenomena with individual particles.

At one time the Casimir force, which has yet to be measured with an accuracy of better than 15% in the geometry first proposed by Hendrik Casimir in 1948, might also have been viewed as purely a pedagogical experiment – a gedanken experiment with little relevance to real experimental physics. However, it is now clear that applications as varied as nanotechnology and experimental tests of theories of “large” extra dimensions require a detailed knowledge of the Casimir force .

The need for “real, pedagogically clean fundamental experiments” is clearly as great as ever.

This is a longer version of the article “The double-slit experiment” that appeared in the print version of the September issue of Physics World, on page 15. Three letters that appeared in the May 2003 issue of the magazine have been added to the end of this version of the article.

T Young 1802 On the theory of light and colours (The 1801 Bakerian Lecture) Philosophical Transactions of the Royal Society of London 92 12-48

T Young 1804 Experiments and calculations relative to physical optics (The 1803 Bakerian Lecture) Philosophical Transactions of the Royal Society of London 94 1-16

T Young 1807 A Course of Lectures on Natural Philosophy and the Mechanical Arts (J Johnson, London)

G I Taylor 1909 Interference fringes with feeble light Proceedings of the Cambridge Philosophical Society 15 114-115

P A M Dirac 1958 The Principles of Quantum Mechanics (Oxford University Press) 4th edn p9

R P Feynman, R B Leighton and M Sands 1963 The Feynman Lecture on Physics (Addison-Wesley) vol 3 ch 37 (Quantum behaviour)

A Howie and J E Fowcs Williams (eds) 2002 Interference: 200 years after Thomas Young’s discoveries Philosophical Transactions of the Royal Society of London 360 803-1069

R P Crease 2002 The most beautiful experiment Physics World September pp19-20. This article contains the results of Crease’s survey for Physics World ; the first article about the survey appeared on page 17 of the May 2002 issue.

Electron interference experiments

Visit www.nobel.se/physics/laureates/1937/index.html for details of the Nobel prize awarded to Clinton Davisson and George Thomson

L Marton 1952 Electron interferometer Physical Review 85 1057-1058

L Marton, J Arol Simpson and J A Suddeth 1953 Electron beam interferometer Physical Review 90 490-491

L Marton, J Arol Simpson and J A Suddeth 1954 An electron interferometer Reviews of Scientific Instruments 25 1099-1104

G Möllenstedt and H Düker 1955 Naturwissenschaften 42 41

G Möllenstedt and H Düker 1956 Zeitschrift für Physik 145 377-397

G Möllenstedt and C Jönsson 1959 Zeitschrift für Physik 155 472-474

R G Chambers 1960 Shift of an electron interference pattern by enclosed magnetic flux Physical Review Letters 5 3-5

C Jönsson 1961 Zeitschrift für Physik 161 454-474

C Jönsson 1974 Electron diffraction at multiple slits American Journal of Physics 42 4-11

A P French and E F Taylor 1974 The pedagogically clean, fundamental experiment American Journal of Physics 42 3

P G Merli, G F Missiroli and G Pozzi 1976 On the statistical aspect of electron interference phenomena American Journal of Physics 44 306-7

A Tonomura, J Endo, T Matsuda, T Kawasaki and H Ezawa 1989 Demonstration of single-electron build-up of an interference pattern American Journal of Physics 57 117-120

H Kiesel, A Renz and F Hasselbach 2002 Observation of Hanbury Brown-Twiss anticorrelations for free electrons Nature 418 392-394

Atoms and molecules

O Carnal and J Mlynek 1991 Young’s double-slit experiment with atoms: a simple atom interferometer Physical Review Letters 66 2689-2692

D W Keith, C R Ekstrom, Q A Turchette and D E Pritchard 1991 An interferometer for atoms Physical Review Letters 66 2693-2696

M W Noel and C R Stroud Jr 1995 Young’s double-slit interferometry within an atom Physical Review Letters 75 1252-1255

M Arndt, O Nairz, J Vos-Andreae, C Keller, G van der Zouw and A Zeilinger 1999 Wave-particle duality of C 60 molecules Nature 401 680-682

B Brezger, L Hackermüller, S Uttenthaler, J Petschinka, M Arndt and A Zeilinger 2002 Matter-wave interferometer for large molecules Physical Review Letters 88 100404

Review articles and books

G F Missiroli, G Pozzi and U Valdrè 1981 Electron interferometry and interference electron microscopy Journal of Physics E 14 649-671. This review covers early work on electron interferometry by groups in Bologna, Toulouse, Tübingen and elsewhere.

A Zeilinger, R Gähler, C G Shull, W Treimer and W Mampe 1988 Single- and double-slit diffraction of neutrons Reviews of Modern Physics 60 1067-1073

A Tonomura 1993 Electron Holography (Springer-Verlag, Berlin/New York)

H Rauch and S A Werner 2000 Neutron Interferometry: Lessons in Experimental Quantum Mechanics (Oxford Science Publications)

The double-slit experiment with single electrons

The article “A brief history of the double-slit experiment” (September 2002 p15; correction October p17) describes how Claus Jönsson of the University of Tübingen performed the first double-slit interference experiment with electrons in 1961. It then goes on to say: “The next milestone – an experiment in which there was just one electron in the apparatus at any one time – was reached by Akira Tonomura and co-workers at Hitachi in 1989 when they observed the build up of the fringe pattern with a very weak electron source and an electron biprism ( Am. J. Phys. 57 117-120)”.

In fact, I believe that “the first double-slit experiment with single electrons” was performed by Pier Giorgio Merli, GianFranco Missiroli and Giulio Pozzi in Bologna in 1974 – some 15 years before the Hitachi experiment. Moreover, the Bologna experiment was performed under very difficult experimental conditions: the intrinsic coherence of the thermionic electron source used by the Bologna group was considerably lower than that of the field-emission source used in the Hitachi experiment.

The Bologna experiment is reported in a film called “Electron Interference” that received the award in the physics category at the International Festival on Scientific Cinematography in Brussels in 1976. A selection of six frames from the film ( see figure ) was also used for a short paper, “On the statistical aspect of electron interference phenomena”, that was submitted for publication in May 1974 and published two years later (P G Merli, G F Missiroli and G Pozzi 1976 Am. J. Phys. 44 306-7).

John Steeds Department of Physics, University of Bristol [email protected]

The history of science is not restricted to the achievements of big scientists or big scientific institutions. Contributions can also be made by researchers with the necessary background, curiosity and enthusiasm. In the period 1973-1974 we were investigating practical applications of electron interferometry with a Siemens Elmiskop 101 electron microscope that had been carefully calibrated at the CNR-LAMEL laboratory in Bologna, where one of us (PGM) was based ( J. Phys. E7 729-32).

These experiments followed earlier work at the Istituto di Fisica in 1972-73 in which the electron biprism was inserted in a Siemens Elmiskop IA and then used both for didactic ( Am. J. Phys. 41 639-644) and research experiments ( J. Microscopie 18 103-108). We used the Elmiskop 101 for many experiments including, for instance, the observation of the electrostatic field associated with p-n junctions ( J. Microscopie 21 11-20).

During this period we learnt that Professors Angelo and Aurelio Bairati in the Institute of Anatomy at the University of Milan had bought an image intensifier that could be used with the Elmiskop 101. Out of curiosity, and also realizing the conceptual importance of interference experiments with single photons or electrons, we asked if we could attempt to perform an interference experiment with single electrons in the Milan laboratory. Our results formed the basis of the film “Electron interference” and were also published in 1976 ( Am. J. Phys. 44 306-7).

Following the publication of the paper by Tonomura and co-workers in 1989, which did not refer to our 1976 paper (although it did contain an incorrect reference to our film), the American Journal of Physics published a letter from Greyson Gilson of Submicron Structures Inc. The letter stated: “Tonomura et al. seem to believe that they were the first to perform a successful two-slit interference experiment using electrons and also that they were the first to observe the cumulative build-up of the resulting electron interference pattern. Although their demonstration is very admirable, reports of similar work have appeared in this Journal for about 30 years (see, for examples, Refs. 2-7.) It seems inappropriate to permit the widespread misconception that such experiments have not been performed and perhaps cannot be performed to continue.” (G Gilson 1989 Am. J. Phys. 57 680). Three of the seven papers that Gilson refers to were from our group in Bologna.

The main subject of our 1976 paper and the 1989 paper from the Hitachi group are the same: the single-electron build-up of the interference pattern and the statistical aspect of the phenomena. Obviously the electron-detection system used by the Hitachi group in 1989 was more sophisticated than the one we used in 1974. However, the sentence on page 118 of the paper by Tonomura et al. , which states that in our film we “showed the electron arrival in each frame without recording the cumulative arrivals”, is not correct: this can be seen by watching the film and looking at figure 1 of our 1976 paper (a version of which is shown here ).

Finally, it is also worth noting that the first double-slit experiment with single electrons was actually a by-product of research into the practical applications of electron interferometry.

Pier Giorgio Merli LAMEL, CNR Bologna, Italy [email protected] Giulio Pozzi Department of Physics, University of Bologna [email protected] GianFranco Missiroli Department of Physics, University of Bologna [email protected]

The Bologna group photographed the monitor of a sensitive TV camera as they changed the intensity of an electron beam. They observed that a few light flashes of electrons appeared at low intensities, and that interference fringes were formed at high intensities. They also mentioned that they were able to increase the storage time up to “values of minutes”. Historically, they are the first to report such experiments concerning the formation of interference patterns as far as I know.

Later, similar experiments were conducted by Hannes Lichte, then at Tübingen and now at Dresden. Important experiments on electron interference were also carried out by Valentin Fabrikant and co-workers at the Moscow Institute for Energetics in 1949 and later by Takeo Ichinokawa of Waseda University in Tokyo.

Our experiments at Hitachi (A Tonomura, J Endo, T Matsuda, T Kawasaki and H Ezawa 1989 Demonstration of single-electron buildup of an interference pattern Am. J. Phys. 57 117–120) differed from these experiments in the following respects:

(a) Our experiments were carried out from beginning to end with constant and extremely low electron intensities – fewer than 1000 electrons per second – so there was no chance of finding two or more electrons in the apparatus at the same time. This removed any possibility that the fringes might be due to interactions between the electrons, as had been suspected by some physicists, such as Sin-Itiro Tomonaga.

(b) We developed a position-sensitive electron-counting system that was modified from the photon-counting image acquisition system produced by Hamamatsu Photonics. In this system, the formation of fringes could be observed as a time series; the electrons were accumulated over time to gradually form an interference pattern on the monitor (similar to a long exposure with a photographic film). The electrons arrived at random positions on the detector only once in a while and it took more than 20 minutes for the interference pattern to form (see figure). To film the build-up process, the electron source, the electron biprism and the rest of the experiment therefore had to be extremely stable: if the interference pattern had drifted by a fraction of fringe spacing over the exposure time, the whole fringe pattern would have disappeared.

(c) The electrons arriving at the detector were detected with almost 100% efficiency. Counting losses and noise in conventional TV cameras mean that it is difficult to know if each flash of the screen really corresponds to an individual electron. Therefore, the detection error in our experiment was limited to less than 1%.

We believe that we carried out the first experiment in which the build-up process of an interference pattern from single-electron events could be seen in real time as in Feynman’s famous double-slit Gedanken experiment under the condition, we emphasize, that there was no chance of finding two or more electrons in the apparatus.

Akira Tonomura Hitachi Advanced Research Laboratory, Saitama, Japan [email protected]

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Double-slit diffraction – en

Double-slit diffraction, also known as the double-slit interference or Young’s double-slit experiment, is a phenomenon in which light waves pass through two closely spaced slits and interfere with each other, creating a pattern of alternating bright and dark fringes on a screen placed some distance away from the slits. This experiment, first conducted by Thomas Young in 1801, provided strong evidence for the wave theory of light and laid the groundwork for understanding other wave phenomena.

When light passes through the two slits, each slit acts as a new source of light waves. The waves emerging from the slits overlap and interfere with each other, leading to constructive interference at some points and destructive interference at others. The constructive interference results in bright fringes, while the destructive interference leads to dark fringes.

The positions of the bright fringes in the interference pattern can be determined using the following formula:

y = (L * λ * n) / d

• y is the distance from the central maximum to the nth bright fringe
• L is the distance between the double-slit and the screen
• λ is the wavelength of the light
• n is an integer representing the order of the bright fringe (0 for the central maximum, 1 for the first bright fringe, and so on)
• d is the distance between the two slits

The double-slit diffraction experiment not only demonstrates the wave nature of light but also serves as a basis for understanding other wave phenomena, such as single-slit diffraction, diffraction gratings, and the behavior of other types of waves (e.g., sound waves and electrons). Moreover, this experiment has played a significant role in the development of quantum mechanics, as it revealed the wave-particle duality concept that emerged from studying the interference patterns and behavior of particles like electrons in similar experimental setups.

Applications of double-slit diffraction principles include:

• Diffraction gratings: These are optical components consisting of many closely spaced slits or lines that diffract light into specific angles, creating a spectrum. Diffraction gratings are used in spectrometers, monochromators, and other devices for separating and analyzing light wavelengths.
• Optical devices: Interference filters, beam splitters, and other optical devices rely on the principles of interference and diffraction to manipulate light.
• Quantum mechanics: The double-slit experiment has been adapted to study the behavior of particles like electrons, which exhibit both wave-like and particle-like characteristics, leading to advancements in quantum mechanics.
• Holography: The interference and diffraction principles used in the double-slit experiment are also essential for understanding and creating holograms, which record and reconstruct three-dimensional images using the wave nature of light.

Understanding the principles of double-slit diffraction is crucial for the design and analysis of various optical systems and devices that rely on the manipulation of light through interference and diffraction.

Diffraction

Diffraction is a phenomenon that occurs when electromagnetic waves, such as light, encounter an obstacle or pass through an aperture (opening) in their path. As the waves interact with the obstacle or aperture, they bend, spread out, and interfere with each other, creating a new wave pattern that deviates from their original propagation direction. Diffraction is a consequence of the wave nature of electromagnetic radiation and is governed by the principle of superposition.

The extent of diffraction depends on the wavelength of the electromagnetic wave and the size of the obstacle or aperture relative to the wavelength. When the size of the obstacle or aperture is comparable to or larger than the wavelength, significant diffraction occurs, leading to a noticeable spreading and bending of the waves.

Some examples and applications of diffraction in electromagnetic waves include:

• Single-slit diffraction : When a light wave passes through a narrow single slit and strikes a screen, a diffraction pattern is formed. The pattern consists of a central bright fringe (maximum) surrounded by alternating bright and dark fringes (maxima and minima). The intensity of the fringes decreases as the distance from the central maximum increases. This pattern arises due to the interference of light waves diffracted from different parts of the slit.
• Double-slit diffraction : In Young’s double-slit experiment, light passes through two closely spaced narrow slits and forms an interference pattern on a screen. The pattern consists of alternating bright and dark fringes due to the superposition of light waves diffracted from the two slits. This experiment demonstrates the wave nature of light and provides evidence for the principle of superposition.
• Diffraction gratings : A diffraction grating is an optical element consisting of a large number of equally spaced narrow slits or grooves. When light passes through the grating, it diffracts and interferes, creating a pattern of bright spots or lines on a screen. Each line corresponds to a specific wavelength of light, and the grating effectively disperses the light into its constituent wavelengths, creating a spectrum. Diffraction gratings are used in various applications, such as spectrometers and wavelength division multiplexing in fiber-optic communication systems.
• Radio wave diffraction : Diffraction also occurs with longer-wavelength electromagnetic waves, such as radio waves. Radio waves can diffract around obstacles like buildings, mountains, or the Earth’s curvature, allowing them to reach areas that are not in the direct line of sight of the transmitter. This property is useful for communication systems, especially in areas with complex topography or urban environments.
• X-ray diffraction : X-ray diffraction is a technique used to study the crystal structure of materials. When a beam of X-rays encounters a crystal, the X-rays are diffracted by the regular arrangement of atoms within the crystal lattice. The resulting diffraction pattern can be analyzed to determine the crystal structure and atomic positions within the material. This technique has been instrumental in various scientific discoveries, such as the determination of the structure of DNA by Rosalind Franklin, James Watson, and Francis Crick.

In summary, diffraction is a fundamental phenomenon in the behavior of electromagnetic waves that occurs when they encounter obstacles or apertures. It is crucial for understanding various wave patterns and has applications in a wide range of fields, from optics and spectroscopy to radio communication.

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Young’s double-slit experiment

What is young’s double-slit experiment.

Young’s Double-Slit Experiment is a classic experiment in physics that demonstrates the wave-particle duality of light. It was conducted by Thomas Young in 1801 and remains a fundamental experiment in modern physics. The experiment is a demonstration of the principle of interference, which occurs when waves of light are allowed to interact with each other.

In this experiment, a beam of light is directed towards a barrier with two slits, creating two coherent sources of light waves. The waves then interfere with each other on a screen placed behind the barrier, creating a pattern of bright and dark fringes. This pattern is an interference pattern and demonstrates the wave-like nature of light.

The experiment helped to confirm the wave theory of light and paved the way for the development of quantum mechanics, which explained the dual nature of light as both a wave and a particle.

The Setup and Procedure of the Experiment

The setup of the experiment involves a light source, a barrier with two slits, and a screen to observe the interference pattern. The light source is typically a laser or a monochromatic light source to ensure that the light waves are coherent. The barrier is placed in front of the screen, and the light is allowed to pass through the two slits, creating two coherent sources of light waves.

The procedure involves adjusting the distance between the two slits, the distance between the barrier and the screen, and the wavelength of the light source. By adjusting these parameters, the interference pattern on the screen can be altered. The pattern can be observed by either looking at the screen or by using a photographic plate to record the pattern.

The experiment can be repeated with different types of light sources, including white light, to observe the interference pattern for different wavelengths of light. It can also be repeated with different types of barriers, including metal barriers, to observe how different materials affect the interference pattern.

The Results and Implications of the Experiment

The results of the experiment show that light behaves as a wave, creating interference fringes that are characteristic of wave patterns. The experiment also demonstrates the principle of superposition, which states that waves can combine to create a single wave with a different amplitude and phase.

The implications of the experiment are far-reaching and have led to the development of quantum mechanics, which explains the wave-particle duality of light. The experiment has also been used to study other phenomena, such as the interference of electrons and the behavior of matter waves.

The experiment has been used to support the idea that light is both a wave and a particle, which has been a fundamental concept in physics for over a century. The experiment has also led to the development of new technologies, such as holography, which rely on the principles of interference and diffraction.

Example Applications of the Double-Slit Experiment

The double-slit experiment has various practical applications, including in the development of advanced optical components and techniques. The experiment has been used to develop interference filters that can selectively transmit certain wavelengths of light and reject others. The filters are used in optical instruments, such as cameras and telescopes, to improve image quality and reduce unwanted light.

The experiment has also been used in the development of holography, which is a technique for creating three-dimensional images using interference patterns. Holography uses the principles of interference and diffraction to create an image that appears to be three-dimensional.

The experiment has also been used to study the behavior of electrons and other matter waves, leading to the development of electron microscopy and other advanced imaging techniques. The study of matter waves has also led to the development of quantum computing, which relies on the principles of wave-particle duality to process information.

PHYS102: Introduction to Electromagnetism

Young's double slit experiment.

As the reading illustrates, Huygens' principle is not just a philosophical interpretation – it is also a computational tool . In particular, the idea of circular (or spherical ) elementary waves makes it relatively easy to explain how a wave can bend around corners and spread out after passing through a constriction. This is called diffraction because it allows wave energy to go around corners in directions that the rays of geometric optics (or the trajectories of classical particles) would not be permitted to go.

Read about the proof that light is a wave in this experiment Thomas Young gave using diffraction by a pair of closely spaced slits.

Although Christiaan Huygens thought that light was a wave, Isaac Newton did not. Newton felt that there were other explanations for color, and for the interference and diffraction effects that were observable at the time. Owing to Newton’s tremendous stature, his view generally prevailed. The fact that Huygens’s principle worked was not considered evidence that was direct enough to prove that light is a wave. The acceptance of the wave character of light came many years later when, in 1801, the English physicist and physician Thomas Young (1773–1829) did his now-classic double slit experiment (see Figure 27.10 ).

Figure 27.10 Young’s double slit experiment. Here pure-wavelength light sent through a pair of vertical slits is diffracted into a pattern on the screen of numerous vertical lines spread out horizontally. Without diffraction and interference, the light would simply make two lines on the screen.

Why do we not ordinarily observe wave behavior for light, such as observed in Young’s double slit experiment? First, light must interact with something small, such as the closely spaced slits used by Young, to show pronounced wave effects. Furthermore, Young first passed light from a single source (the Sun) through a single slit to make the light somewhat coherent.

By coherent , we mean waves are in phase or have a definite phase relationship. Incoherent means the waves have random phase relationships.

Figure 27.11 The amplitudes of waves add. (a) Pure constructive interference is obtained when identical waves are in phase. (b) Pure destructive interference occurs when identical waves are exactly out of phase, or shifted by half a wavelength.

When light passes through narrow slits, it is diffracted into semicircular waves, as shown in Figure 27.12 (a). Pure constructive interference occurs where the waves are crest to crest or trough to trough. Pure destructive interference occurs where they are crest to trough. The light must fall on a screen and be scattered into our eyes for us to see the pattern. An analogous pattern for water waves is shown in Figure 27.12 (b). Note that regions of constructive and destructive interference move out from the slits at well-defined angles to the original beam. These angles depend on wavelength and the distance between the slits, as we shall see below.

Figure 27.12 Double slits produce two coherent sources of waves that interfere. (a) Light spreads out (diffracts) from each slit, because the slits are narrow. These waves overlap and interfere constructively (bright lines) and destructively (dark regions). We can only see this if the light falls onto a screen and is scattered into our eyes. (b) Double slit interference pattern for water waves are nearly identical to that for light. Wave action is greatest in regions of constructive interference and least in regions of destructive interference. (c) When light that has passed through double slits falls on a screen, we see a pattern such as this. (credit: PASCO)

To understand the double slit interference pattern, we consider how two waves travel from the slits to the screen, as illustrated in Figure 27.13 . Each slit is a different distance from a given point on the screen. Thus different numbers of wavelengths fit into each path. Waves start out from the slits in phase (crest to crest), but they may end up out of phase (crest to trough) at the screen if the paths differ in length by half a wavelength, interfering destructively as shown in Figure 27.13 (a).

Take-Home Experiment: Using Fingers as Slits

Look at a light, such as a street lamp or incandescent bulb, through the narrow gap between two fingers held close together. What type of pattern do you see? How does it change when you allow the fingers to move a little farther apart? Is it more distinct for a monochromatic source, such as the yellow light from a sodium vapor lamp, than for an incandescent bulb?

Figure 27.13 Waves follow different paths from the slits to a common point on a screen. (a) Destructive interference occurs here, because one path is a half wavelength longer than the other. The waves start in phase but arrive out of phase. (b) Constructive interference occurs here because one path is a whole wavelength longer than the other. The waves start out and arrive in phase.

Similarly, to obtain destructive interference for a double slit, the path length difference must be a half-integral multiple of the wavelength, or

The equations for double slit interference imply that a series of bright and dark lines are formed. For vertical slits, the light spreads out horizontally on either side of the incident beam into a pattern called interference fringes, illustrated in Figure 27.15 . The intensity of the bright fringes falls off on either side, being brightest at the center. The closer the slits are, the more is the spreading of the bright fringes. We can see this by examining the equation

Figure 27.15 The interference pattern for a double slit has an intensity that falls off with angle. The photograph shows multiple bright and dark lines, or fringes, formed by light passing through a double slit.

Example 27.1 Finding a Wavelength from an Interference Pattern

Substituting known values yields

Example 27.2 Calculating Highest Order Possible

Strategy and concept.

The number of fringes depends on the wavelength and slit separation. The number of fringes will be very large for large slit separations. However, if the slit separation becomes much greater than the wavelength, the intensity of the interference pattern changes so that the screen has two bright lines cast by the slits, as expected when light behaves like a ray. We also note that the fringes get fainter further away from the center. Consequently, not all 15 fringes may be observable.

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Young’s double-slit experiment

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The observation of interference effects definitively indicates the presence of overlapping waves. Thomas Young postulated that light is a wave and is subject to the superposition principle; his great experimental achievement was to demonstrate the constructive and destructive interference of light (c. 1801). In a modern version of Young’s experiment, differing in its essentials only in the source of light, a laser equally illuminates two parallel slits in an otherwise opaque surface. The light passing through the two slits is observed on a distant screen. When the widths of the slits are significantly greater than the wavelength of the light, the rules of geometrical optics hold—the light casts two shadows, and there are two illuminated regions on the screen. However, as the slits are narrowed in width, the light diffracts into the geometrical shadow, and the light waves overlap on the screen. (Diffraction is itself caused by the wave nature of light, being another example of an interference effect—it is discussed in more detail below.)

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The superposition principle determines the resulting intensity pattern on the illuminated screen. Constructive interference occurs whenever the difference in paths from the two slits to a point on the screen equals an integral number of wavelengths (0, λ, 2λ,…). This path difference guarantees that crests from the two waves arrive simultaneously. Destructive interference arises from path differences that equal a half-integral number of wavelengths (λ/2, 3λ/2,…). Young used geometrical arguments to show that the superposition of the two waves results in a series of equally spaced bands, or fringes, of high intensity, corresponding to regions of constructive interference, separated by dark regions of complete destructive interference.

An important parameter in the double-slit geometry is the ratio of the wavelength of the light λ to the spacing of the slits d . If λ/ d is much smaller than 1, the spacing between consecutive interference fringes will be small, and the interference effects may not be observable. Using narrowly separated slits, Young was able to separate the interference fringes. In this way he determined the wavelengths of the colours of visible light. The very short wavelengths of visible light explain why interference effects are observed only in special circumstances—the spacing between the sources of the interfering light waves must be very small to separate regions of constructive and destructive interference.

Observing interference effects is challenging because of two other difficulties. Most light sources emit a continuous range of wavelengths, which result in many overlapping interference patterns, each with a different fringe spacing. The multiple interference patterns wash out the most pronounced interference effects, such as the regions of complete darkness. Second, for an interference pattern to be observable over any extended period of time, the two sources of light must be coherent with respect to each other. This means that the light sources must maintain a constant phase relationship. For example, two harmonic waves of the same frequency always have a fixed phase relationship at every point in space, being either in phase, out of phase, or in some intermediate relationship. However, most light sources do not emit true harmonic waves; instead, they emit waves that undergo random phase changes millions of times per second. Such light is called incoherent . Interference still occurs when light waves from two incoherent sources overlap in space, but the interference pattern fluctuates randomly as the phases of the waves shift randomly. Detectors of light, including the eye, cannot register the quickly shifting interference patterns, and only a time-averaged intensity is observed. Laser light is approximately monochromatic (consisting of a single wavelength) and is highly coherent; it is thus an ideal source for revealing interference effects.

After 1802, Young’s measurements of the wavelengths of visible light could be combined with the relatively crude determinations of the speed of light available at the time in order to calculate the approximate frequencies of light. For example, the frequency of green light is about 6 × 10 14 Hz ( hertz , or cycles per second). This frequency is many orders of magnitude larger than the frequencies of common mechanical waves. For comparison, humans can hear sound waves with frequencies up to about 2 × 10 4 Hz. Exactly what was oscillating at such a high rate remained a mystery for another 60 years.

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Chapter 27 Wave Optics

215 27.3 Young’s Double Slit Experiment

• Explain the phenomena of interference.
• Define constructive interference for a double slit and destructive interference for a double slit.

Although Christiaan Huygens thought that light was a wave, Isaac Newton did not. Newton felt that there were other explanations for color, and for the interference and diffraction effects that were observable at the time. Owing to Newton’s tremendous stature, his view generally prevailed. The fact that Huygens’s principle worked was not considered evidence that was direct enough to prove that light is a wave. The acceptance of the wave character of light came many years later when, in 1801, the English physicist and physician Thomas Young (1773–1829) did his now-classic double slit experiment (see Figure 1 ).

Why do we not ordinarily observe wave behavior for light, such as observed in Young’s double slit experiment? First, light must interact with something small, such as the closely spaced slits used by Young, to show pronounced wave effects. Furthermore, Young first passed light from a single source (the Sun) through a single slit to make the light somewhat coherent. By coherent , we mean waves are in phase or have a definite phase relationship. Incoherent means the waves have random phase relationships. Why did Young then pass the light through a double slit? The answer to this question is that two slits provide two coherent light sources that then interfere constructively or destructively. Young used sunlight, where each wavelength forms its own pattern, making the effect more difficult to see. We illustrate the double slit experiment with monochromatic (single [latex]\boldsymbol{\lambda}[/latex]) light to clarify the effect. Figure 2 shows the pure constructive and destructive interference of two waves having the same wavelength and amplitude.

When light passes through narrow slits, it is diffracted into semicircular waves, as shown in Figure 3 (a). Pure constructive interference occurs where the waves are crest to crest or trough to trough. Pure destructive interference occurs where they are crest to trough. The light must fall on a screen and be scattered into our eyes for us to see the pattern. An analogous pattern for water waves is shown in Figure 3 (b). Note that regions of constructive and destructive interference move out from the slits at well-defined angles to the original beam. These angles depend on wavelength and the distance between the slits, as we shall see below.

To understand the double slit interference pattern, we consider how two waves travel from the slits to the screen, as illustrated in Figure 4 . Each slit is a different distance from a given point on the screen. Thus different numbers of wavelengths fit into each path. Waves start out from the slits in phase (crest to crest), but they may end up out of phase (crest to trough) at the screen if the paths differ in length by half a wavelength, interfering destructively as shown in Figure 4 (a). If the paths differ by a whole wavelength, then the waves arrive in phase (crest to crest) at the screen, interfering constructively as shown in Figure 4 (b). More generally, if the paths taken by the two waves differ by any half-integral number of wavelengths [[latex]\boldsymbol{(1/2) \;\lambda}[/latex], [latex]\boldsymbol{(3/2) \;\lambda}[/latex], [latex]\boldsymbol{(5/2) \;\lambda}[/latex], etc.], then destructive interference occurs. Similarly, if the paths taken by the two waves differ by any integral number of wavelengths ([latex]\boldsymbol{\lambda}[/latex], [latex]\boldsymbol{2 \lambda}[/latex], [latex]\boldsymbol{3 \lambda}[/latex], etc.), then constructive interference occurs.

Take-Home Experiment: Using Fingers as Slits

Look at a light, such as a street lamp or incandescent bulb, through the narrow gap between two fingers held close together. What type of pattern do you see? How does it change when you allow the fingers to move a little farther apart? Is it more distinct for a monochromatic source, such as the yellow light from a sodium vapor lamp, than for an incandescent bulb?

Figure 5 shows how to determine the path length difference for waves traveling from two slits to a common point on a screen. If the screen is a large distance away compared with the distance between the slits, then the angle [latex]\boldsymbol{\theta}[/latex] between the path and a line from the slits to the screen (see the figure) is nearly the same for each path. The difference between the paths is shown in the figure; simple trigonometry shows it to be [latex]\boldsymbol{d \;\textbf{sin} \;\theta}[/latex], where [latex]\boldsymbol{d}[/latex] is the distance between the slits. To obtain constructive interference for a double slit , the path length difference must be an integral multiple of the wavelength, or

Similarly, to obtain destructive interference for a double slit , the path length difference must be a half-integral multiple of the wavelength, or

where [latex]\boldsymbol{\lambda}[/latex] is the wavelength of the light, [latex]\boldsymbol{d}[/latex] is the distance between slits, and [latex]\boldsymbol{\theta}[/latex] is the angle from the original direction of the beam as discussed above. We call [latex]\boldsymbol{m}[/latex] the order of the interference. For example, [latex]\boldsymbol{m = 4}[/latex] is fourth-order interference.

The equations for double slit interference imply that a series of bright and dark lines are formed. For vertical slits, the light spreads out horizontally on either side of the incident beam into a pattern called interference fringes, illustrated in Figure 6 . The intensity of the bright fringes falls off on either side, being brightest at the center. The closer the slits are, the more is the spreading of the bright fringes. We can see this by examining the equation

For fixed [latex]\boldsymbol{\lambda}[/latex] and [latex]\boldsymbol{m}[/latex], the smaller [latex]\boldsymbol{d}[/latex] is, the larger [latex]\boldsymbol{\theta}[/latex] must be, since [latex]\boldsymbol{\textbf{sin} \;\theta = m \lambda / d}[/latex].

This is consistent with our contention that wave effects are most noticeable when the object the wave encounters (here, slits a distance [latex]\boldsymbol{d}[/latex] apart) is small. Small [latex]\boldsymbol{d}[/latex] gives large [latex]\boldsymbol{\theta}[/latex], hence a large effect.

Example 1: Finding a Wavelength from an Interference Pattern

Suppose you pass light from a He-Ne laser through two slits separated by 0.0100 mm and find that the third bright line on a screen is formed at an angle of [latex]\boldsymbol{10.95 ^{\circ}}[/latex] relative to the incident beam. What is the wavelength of the light?

The third bright line is due to third-order constructive interference, which means that [latex]\boldsymbol{m = 3}[/latex]. We are given [latex]\boldsymbol{d = 0.0100 \;\textbf{mm}}[/latex] and [latex]\boldsymbol{\theta = 10.95^{\circ}}[/latex]. The wavelength can thus be found using the equation [latex]\boldsymbol{d \;\textbf{sin} \;\theta = m \lambda}[/latex] for constructive interference.

The equation is [latex]\boldsymbol{d \;\textbf{sin} \;\theta = m \lambda}[/latex]. Solving for the wavelength [latex]\boldsymbol{\lambda}[/latex] gives

Substituting known values yields

To three digits, this is the wavelength of light emitted by the common He-Ne laser. Not by coincidence, this red color is similar to that emitted by neon lights. More important, however, is the fact that interference patterns can be used to measure wavelength. Young did this for visible wavelengths. This analytical technique is still widely used to measure electromagnetic spectra. For a given order, the angle for constructive interference increases with [latex]\boldsymbol{\lambda}[/latex], so that spectra (measurements of intensity versus wavelength) can be obtained.

Example 2: Calculating Highest Order Possible

Interference patterns do not have an infinite number of lines, since there is a limit to how big [latex]\boldsymbol{m}[/latex] can be. What is the highest-order constructive interference possible with the system described in the preceding example?

Strategy and Concept

The equation [latex]\boldsymbol{d \;\textbf{sin} \;\theta = m \lambda \; (\textbf{for} \; m = 0, \; 1, \; -1, \; 2, \; -2, \; \dots)}[/latex] describes constructive interference. For fixed values of [latex]\boldsymbol{d}[/latex] and [latex]\boldsymbol{\lambda}[/latex], the larger [latex]\boldsymbol{m}[/latex] is, the larger [latex]\boldsymbol{\textbf{sin} \;\theta}[/latex] is. However, the maximum value that [latex]\boldsymbol{\textbf{sin} \;\theta}[/latex] can have is 1, for an angle of [latex]\boldsymbol{90 ^{\circ}}[/latex]. (Larger angles imply that light goes backward and does not reach the screen at all.) Let us find which [latex]\boldsymbol{m}[/latex] corresponds to this maximum diffraction angle.

Solving the equation [latex]\boldsymbol{d \;\textbf{sin} \;\theta = m \lambda}[/latex] for [latex]\boldsymbol{m}[/latex] gives

Taking [latex]\boldsymbol{\textbf{sin} \;\theta = 1}[/latex] and substituting the values of [latex]\boldsymbol{d}[/latex] and [latex]\boldsymbol{\lambda}[/latex] from the preceding example gives

Therefore, the largest integer [latex]\boldsymbol{m}[/latex] can be is 15, or

The number of fringes depends on the wavelength and slit separation. The number of fringes will be very large for large slit separations. However, if the slit separation becomes much greater than the wavelength, the intensity of the interference pattern changes so that the screen has two bright lines cast by the slits, as expected when light behaves like a ray. We also note that the fringes get fainter further away from the center. Consequently, not all 15 fringes may be observable.

Section Summary

• Young’s double slit experiment gave definitive proof of the wave character of light.
• An interference pattern is obtained by the superposition of light from two slits.
• There is constructive interference when [latex]\boldsymbol{d \;\textbf{sin} \;\theta = m \lambda \;(\textbf{for} \; m = 0, \; 1, \; -1, \;2, \; -2, \dots)}[/latex], where [latex]\boldsymbol{d}[/latex] is the distance between the slits, [latex]\boldsymbol{\theta}[/latex] is the angle relative to the incident direction, and [latex]\boldsymbol{m}[/latex] is the order of the interference.
• There is destructive interference when [latex]\boldsymbol{d \;\textbf{sin} \;\theta = (m+ \frac{1}{2}) \lambda}[/latex] (for [latex]\boldsymbol{m = 0, \; 1, \; -1, \; 2, \; -2, \; \dots}[/latex]).

Conceptual Questions

1: Young’s double slit experiment breaks a single light beam into two sources. Would the same pattern be obtained for two independent sources of light, such as the headlights of a distant car? Explain.

2: Suppose you use the same double slit to perform Young’s double slit experiment in air and then repeat the experiment in water. Do the angles to the same parts of the interference pattern get larger or smaller? Does the color of the light change? Explain.

3: Is it possible to create a situation in which there is only destructive interference? Explain.

4:   Figure 7 shows the central part of the interference pattern for a pure wavelength of red light projected onto a double slit. The pattern is actually a combination of single slit and double slit interference. Note that the bright spots are evenly spaced. Is this a double slit or single slit characteristic? Note that some of the bright spots are dim on either side of the center. Is this a single slit or double slit characteristic? Which is smaller, the slit width or the separation between slits? Explain your responses.

Problems & Exercises

2: Calculate the angle for the third-order maximum of 580-nm wavelength yellow light falling on double slits separated by 0.100 mm.

3: What is the separation between two slits for which 610-nm orange light has its first maximum at an angle of [latex]\boldsymbol{30.0 ^{\circ}}[/latex]?

4: Find the distance between two slits that produces the first minimum for 410-nm violet light at an angle of [latex]\boldsymbol{45.0 ^{\circ}}[/latex].

5: Calculate the wavelength of light that has its third minimum at an angle of [latex]\boldsymbol{30.0 ^{\circ}}[/latex] when falling on double slits separated by [latex]\boldsymbol{3.00 \;\mu \textbf{m}}[/latex]. Explicitly, show how you follow the steps in Chapter 27.7 Problem-Solving Strategies for Wave Optics .

6: What is the wavelength of light falling on double slits separated by [latex]\boldsymbol{2.00 \;\mu \textbf{m}}[/latex] if the third-order maximum is at an angle of [latex]\boldsymbol{60.0 ^{\circ}}[/latex]?

7: At what angle is the fourth-order maximum for the situation in Problems & Exercises 1 ?

8: What is the highest-order maximum for 400-nm light falling on double slits separated by [latex]\boldsymbol{25.0 \;\mu \textbf{m}}[/latex]?

9: Find the largest wavelength of light falling on double slits separated by [latex]\boldsymbol{1.20 \;\mu \textbf{m}}[/latex] for which there is a first-order maximum. Is this in the visible part of the spectrum?

10: What is the smallest separation between two slits that will produce a second-order maximum for 720-nm red light?

11: (a) What is the smallest separation between two slits that will produce a second-order maximum for any visible light? (b) For all visible light?

12: (a) If the first-order maximum for pure-wavelength light falling on a double slit is at an angle of [latex]\boldsymbol{10.0^{\circ}}[/latex], at what angle is the second-order maximum? (b) What is the angle of the first minimum? (c) What is the highest-order maximum possible here?

13:   Figure 8 shows a double slit located a distance [latex]\boldsymbol{x}[/latex] from a screen, with the distance from the center of the screen given by [latex]\boldsymbol{y}[/latex]. When the distance [latex]\boldsymbol{d}[/latex] between the slits is relatively large, there will be numerous bright spots, called fringes. Show that, for small angles (where [latex]\boldsymbol{\textbf{sin} \;\theta \approx \theta}[/latex], with [latex]\boldsymbol{\theta}[/latex] in radians), the distance between fringes is given by [latex]\boldsymbol{\Delta y = x \lambda /d}[/latex].

14: Using the result of the problem above, calculate the distance between fringes for 633-nm light falling on double slits separated by 0.0800 mm, located 3.00 m from a screen as in Figure 8 .

15: Using the result of the problem two problems prior, find the wavelength of light that produces fringes 7.50 mm apart on a screen 2.00 m from double slits separated by 0.120 mm (see Figure 8 ).

1:  [latex]\boldsymbol{0.516 ^{\circ}}[/latex]

3:  [latex]\boldsymbol{1.22 \times 10^{-6} \;\textbf{m}}[/latex]

7: [latex]\boldsymbol{2.06 ^{\circ}}[/latex]

9: 1200 nm (not visible)

11: (a) 760 nm

(b) 1520 nm

13: For small angles [latex]\boldsymbol{\textbf{sin} \;\theta - \;\textbf{tan} \;\theta \approx \theta}[/latex] (in radians).

For two adjacent fringes we have,

Subtracting these equations gives

College Physics: OpenStax Copyright © August 22, 2016 by OpenStax is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

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Young's Double Slit Experiment

The Original Experiment

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Throughout the nineteenth century, physicists had a consensus that light behaved like a wave, in large part thanks to the famous double slit experiment performed by Thomas Young. Driven by the insights from the experiment, and the wave properties it demonstrated, a century of physicists sought out the medium through which light was waving, the luminous ether . Though the experiment is most notable with light, the fact is that this sort of experiment can be performed with any type of wave, such as water. For the moment, however, we'll focus on the behavior of light.

What Was the Experiment?

In the early 1800s (1801 to 1805, depending on the source), Thomas Young conducted his experiment. He allowed light to pass through a slit in a barrier so it expanded out in wave fronts from that slit as a light source (under Huygens' Principle ). That light, in turn, passed through the pair of slits in another barrier (carefully placed the right distance from the original slit). Each slit, in turn, diffracted the light as if they were also individual sources of light. The light impacted an observation screen. This is shown to the right.

When a single slit was open, it merely impacted the observation screen with greater intensity at the center and then faded as you moved away from the center. There are two possible results of this experiment:

Particle interpretation: If light exists as particles, the intensity of both slits will be the sum of the intensity from the individual slits.

Wave interpretation: If light exists as waves, the light waves will have interference under the principle of superposition , creating bands of light (constructive interference) and dark (destructive interference).

When the experiment was conducted, the light waves did indeed show these interference patterns. A third image that you can view is a graph of the intensity in terms of position, which matches with the predictions from interference.

Impact of Young's Experiment

At the time, this seemed to conclusively prove that light traveled in waves, causing a revitalization in Huygen's wave theory of light, which included an invisible medium, ether , through which the waves propagated. Several experiments throughout the 1800s, most notably the famed Michelson-Morley experiment , attempted to detect the ether or its effects directly.

They all failed and a century later, Einstein's work in the photoelectric effect and relativity resulted in the ether no longer being necessary to explain the behavior of light. Again a particle theory of light took dominance.

Expanding the Double Slit Experiment

Still, once the photon theory of light came about, saying the light moved only in discrete quanta, the question became how these results were possible. Over the years, physicists have taken this basic experiment and explored it in a number of ways.

In the early 1900s, the question remained how light — which was now recognized to travel in particle-like "bundles" of quantized energy, called photons, thanks to Einstein's explanation of the photoelectric effect — could also exhibit the behavior of waves. Certainly, a bunch of water atoms (particles) when acting together form waves. Maybe this was something similar.

One Photon at a Time

It became possible to have a light source that was set up so that it emitted one photon at a time. This would be, literally, like hurling microscopic ball bearings through the slits. By setting up a screen that was sensitive enough to detect a single photon, you could determine whether there were or were not interference patterns in this case.

One way to do this is to have a sensitive film set up and run the experiment over a period of time, then look at the film to see what the pattern of light on the screen is. Just such an experiment was performed and, in fact, it matched Young's version identically — alternating light and dark bands, seemingly resulting from wave interference.

This result both confirms and bewilders the wave theory. In this case, photons are being emitted individually. There is literally no way for wave interference to take place because each photon can only go through a single slit at a time. But the wave interference is observed. How is this possible? Well, the attempt to answer that question has spawned many intriguing interpretations of  quantum physics , from the Copenhagen interpretation to the many-worlds interpretation.

It Gets Even Stranger

Now assume that you conduct the same experiment, with one change. You place a detector that can tell whether or not the photon passes through a given slit. If we know the photon passes through one slit, then it cannot pass through the other slit to interfere with itself.

It turns out that when you add the detector, the bands disappear. You perform the exact same experiment, but only add a simple measurement at an earlier phase, and the result of the experiment changes drastically.

Something about the act of measuring which slit is used removed the wave element completely. At this point, the photons acted exactly as we'd expect a particle to behave. The very uncertainty in position is related, somehow, to the manifestation of wave effects.

More Particles

Over the years, the experiment has been conducted in a number of different ways. In 1961, Claus Jonsson performed the experiment with electrons, and it conformed with Young's behavior, creating interference patterns on the observation screen. Jonsson's version of the experiment was voted "the most beautiful experiment" by  Physics World  readers in 2002.

In 1974, technology became able to perform the experiment by releasing a single electron at a time. Again, the interference patterns showed up. But when a detector is placed at the slit, the interference once again disappears. The experiment was again performed in 1989 by a Japanese team that was able to use much more refined equipment.

The experiment has been performed with photons, electrons, and atoms, and each time the same result becomes obvious — something about measuring the position of the particle at the slit removes the wave behavior. Many theories exist to explain why, but so far much of it is still conjecture.

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What Is The Double-Slit Experiment?

The double-slit experiment, observation affects reality, the various interpretations:.

The double-slit experiment shows the duality of the quantum world. A photon’s wave/particle duality is affected when it is observed.

Light has been one of the major areas of inquiry for physicists since we first began questioning the world around us. Understandably so, as it is the medium by which we see, measure and understand the world. It holds a powerful symbolism in our imaginations, is reflected in our religions and is famously quoted in our scriptures.

Rigorous science has enlightened our ignorance about Light. Until the 1800s, light was thought to be made up of particles, attested by Newtonian physics.

This came rather intuitively, as we see light traveling in a straight line, like bullets coming out of a gun.

However, nature is often weirder than our expectations and light’s weird behavior was first shown by Thomas Young in his now heavily worked upon and immortalized double-slit experiment. This experiment provides some fascinating insights into the minute workings of nature and has challenged everything we know about light, matter, and reality itself. Let’s revisit the experiment that has baffled legendary scientists – including Einstein!

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The experiment is pretty straightforward, with very few parts. There are three main components:

• A source of light or matter – photons, electrons, bullets

• Two narrow slits for the source to pass-through.

• A projection screen, where the source makes its impression. The pattern of the impression tells us if it is a wave or a particle.

The objective of the experiment is to see the underlying make-up of light and matter.

Let’s start with something familiar, bullets from a machine gun. Our gun fires bullets at regular intervals towards the range of the two slits.

Two straight lines appear on the projector. The graph pattern is that of two mountains; where the crests imply the impression points, and the troughs imply empty places.

The thing to note here is, if we close S2 and fire the gun, only one line appears. Thus, we can safely say that S is equal to the sum of S1 and S2, i.e., S = S1 + S2.

Light is the next source for the experiment. The impression appears as bundles of photons fire through the two slits. What is the pattern you think will emerge? Is it similar to that of bullets? Well, light consists of bullet-like particles, so it isn’t farfetched to say the pattern will be the same.

To everyone’s surprise, however, the impression isn’t of two straight lines. The graph pattern that emerges is an interference pattern; there is the brightest impression in the center, and recedes on both sides. An interference pattern is only made when two waves interfere with each other; there is no other possible explanation to it. The pattern shows that the light is moving in waves.

The waves from the two slits are colliding with each other. There is a peculiar formation that develops when two waves collide. A wave has a crest (the part above) and a trough (the part below).

When the crest of one wave collides with the crest of another, it adds and forms constructive interference, seen as a bright spot on the projector. When the crest of one wave and trough of another collide, they cancel each other out and form a destructive pattern, which results in dark spots between the impressions on the projector.

The second slit is closed and the experiment is done again. Now with one slit to move through, the photons form a straight line. Note, here S is not equal to the sum of S1 and S2, and this is also where light’s wave-particle duality comes into focus.

This revelation changed our thinking about light, but the rabbit hole doesn’t end there; things just get weirder when we further iterate the experiment. Now, instead of flashing a bunch of photons together, only single photons are fired through the slits at regular intervals. Given that it is a single photon, and has no other wave to interact with, we can say that the photon will make a single line on the projector, yet the result is counter-intuitive; the formation on the projector is still an interference pattern!

How can this be? How can a single photon know about the photons coming after it and form a pattern resembling that of the group being shot together?

This is where quantum spookiness begins and things get pretty far out. It appears that a single photon is traveling through both the slits and colliding with itself to form the interference pattern. This has bothered physicists a lot, as it does not obey the laws that we see in our Newtonian scale. It turns out that a large assemblage appears to behave in a way that is different from the behavior of its minuscule components.

Now, let’s hit a home run and take this weirdness to another level. This last iteration of the experiment will make you appreciate nature’s absurdness and how totally wacky our world truly is.

Also Read: Wave-Particle Duality: Is An Electron A Particle Or A Wave?

At this point, we have established that a single photon travels from both the slit at the same time and collides with itself to form the interference pattern. As classical physics dictates, it is impossible for the same photon to move through the two slits at the same time. Perhaps it is splitting itself into two parts and interacting with itself. The only way to know is to watch. A detector is placed in one of the slits so when the photon passes through the slit, the detector identifies it.

As the photon passes through the slit, the detector identifies it. The pattern that emerges on the projector is a single line.

Just when you think you’re coming to terms with the quantum scale, things slip over your head. The act of measuring or observing the photon makes it go through only one path, making the impression on the projector of a particle. It doesn’t interact with itself anymore and no interference pattern emerges. When the experiment is carried out with varying degrees of detection, so that the detection is dimmer on every passing photon (say 7-10 photons are being detected and that number keeps decreasing), then the interference pattern starts to slowly emerge again. The photons act as a wave when not being observed and act as particles when they are being observed.

Also Read: What Is The Observer Effect In Quantum Mechanics?

The double-slit experiments is one of the most iterated experiments in scientific history. Electrons, atoms, molecules and even complex fullerenes like Buckyballs have been used as sources for the experiment. The same results are obtained using every source; the pattern is consistent in both light and matter.

Things on the quantum scale don’t follow the deterministic laws of the macro scale. There are many interpretations of this quantum phenomenon. The Copenhagen Interpretation states that the interference pattern is all the probable functions of the photon (a wave function) and the act of observing or measuring it makes the wave select one of the many alternatives (collapsing of the wave function).

Another interpretation is the many-worlds theory, which states that all the possible states of the photon’s wave function exist simultaneously and our detection is just this particular instance of the wave function.

The theories tend to run wild and it’s safe to say that the quantum realm is a little slippery to wrap your head around. However, there’s no need to feel bad, as you’re in good company. As Richard Feynman said:

Also Read: Why Is Quantum Mechanics So Difficult To Understand?

• Copenhagen Interpretation. The University of Oregon
• A Review and Response to the Book "The Grand Design" by ... - TASC. tasc-creationscience.org
• Chapter 14 Interference and Diffraction. web.mit.edu
• Young’s Double Slit Experiment - pressbooks.online.ucf.edu
• Lecture Notes | Quantum Physics III - MIT OpenCourseWare. MIT OpenCourseWare

Vishal is an Architect and a design aficionado. He likes making trippy patterns in his computer. Fascinated by technology’s role in humanity’s evolution, he is constantly thinking about how the future of our species would turn out – sometimes at the peril of what’s currently going on around him.

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Youngs Double Slit Experiment

• Practice Questions

What is Youngs Double Slit Experiment?

Young’s double slit experiment equation.

d: This represents the distance between the two slits in the double slit apparatus. It is a fixed physical measurement of the setup. sinθ: The sine of the angle𝜃, which is the angle of deviation of the light rays from their original path as they head towards a specific point on the detection screen. 𝑚: The order of the fringe observed on the screen. This can be a whole number (0, 1, 2, …), where m=0 corresponds to the central bright fringe, and higher values correspond to successive bright fringes. λ: The wavelength of the light used in the experiment, which is a measure of the distance over which the wave’s shape repeats.

Derivation of Young’s Double Slit Experiment

Young’s double slit experiment is a classic demonstration of the wave nature of light and interference. The key equation derived from this experiment is dsinθ=mλ, where 𝑑 is the distance between the two slits, 𝜃 is the angle of the interference pattern, 𝑚 is the order of the fringe, and 𝜆 is the wavelength of the light used. Here’s a step-by-step derivation:

Step 1 : Understanding the Setup In Young’s double slit experiment, a coherent light source illuminates two closely spaced slits,𝑆1 and 𝑆2. The light emerging from these slits then interferes and creates bright and dark fringes on a screen placed at some distance from the slits.

Step 2 : Path Difference When light from the slits reaches a point 𝑃 on the screen, the path traveled by light from 𝑆1 and 𝑆2 to 𝑃 is generally not the same. The path difference is crucial for determining whether the interference at 𝑃 is constructive or destructive.

Step 3 : Calculating Path Difference Consider a point 𝑃 on the screen that forms an angle 𝜃 with the normal to the screen. If 𝑆1𝑃 is the path from slit 𝑆1 to 𝑃 and 𝑆2𝑃 is the path from 𝑆2 to 𝑃, the path difference (Δ𝑥) can be approximated by the geometry of the setup: Δx=dsinθ Here, 𝑑 is the slit separation, and 𝜃 is the angle made by the line joining the midpoint of the slit to point 𝑃 with the normal.

Step 4 : Condition for Constructive and Destructive Interference Constructive interference occurs when the path difference is an integer multiple of the wavelength, i.e., Δx=mλ where 𝑚 is an integer (0, 1, 2, …). This condition leads to bright fringes. Destructive interference happens when the path difference is an odd multiple of half the wavelength, i.e., Δ(𝑚+0.5)𝜆 Δx=(m+0.5)λ, leading to dark fringes.

Step 5 : The Key Equation Combining the condition for constructive interference with the geometric path difference, we get: d sinθ=mλ This is the fundamental equation of Young’s double slit experiment. It allows us to calculate the positions of the bright fringes on the screen. By measuring these positions and knowing the slit separation 𝑑 and the wavelength 𝜆, one can experimentally verify the wave nature of light.

Examples of Young’s double slit experiment

Young’s Double Slit Experiment is pivotal in demonstrating wave interference and has numerous applications and examples in various fields. Here are some examples that illustrate the impact and application of this experiment:

Demonstrating Light as Waves At its most basic, Young’s Double Slit Experiment is used in educational settings to demonstrate the wave nature of light. This experiment visually and clearly shows that light can interfere with itself, producing a pattern of bright and dark fringes that is characteristic of waves, not particles.

Laser Interferometry In scientific and industrial applications, the principles of Young’s Double Slit Experiment are used in laser interferometry. This technique can measure very small distances with high precision, such as alterations in material dimensions due to temperature changes, or even gravitational waves as in the case of LIGO (Laser Interferometer Gravitational-Wave Observatory).

Optical Coherence Tomography (OCT) In the medical field, Optical Coherence Tomography, which is an imaging method, employs the concepts derived from Young’s experiment. OCT uses light waves to capture two- and three-dimensional images from within optical scattering media (e.g., biological tissue), effectively allowing for non-invasive medical diagnostics.

Diffraction Grating Analysis The experiment is akin to what occurs in diffraction gratings used in spectrometers. This device uses multiple slits (gratings) to disperse light into a spectrum, extensively applied in chemical analysis and the study of atomic and molecular properties.

Quantum Mechanics Illustration Young’s Double Slit Experiment also plays a crucial role in teaching and demonstrating foundational concepts in quantum mechanics, particularly the dual nature of electrons and other subatomic particles. Demonstrations using electrons show that they too produce interference patterns, revealing their wave-like properties in addition to their particle-like nature.

Holography Holography, which involves recording and later reconstructing light wave patterns, fundamentally relies on interference patterns. The principles illustrated by Young’s Double Slit Experiment are central to understanding and creating holograms.

Communications Technology The concepts of wave interference and diffraction are also utilized in the development of various communications technologies, especially in the optimization of signal transmission and reception in environments susceptible to interference.

FAQ’s

What is the young’s slit theory.

Young’s slit theory demonstrates that light exhibits wave-like behavior, causing interference patterns when passing through closely spaced slits, supporting the wave theory of light.

What is the difference between Young’s double-slit and single slit?

Young’s double-slit experiment demonstrates interference between two wave sources, while a single-slit experiment illustrates diffraction patterns from a single wavefront spreading out.

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Chapter 27 Wave Optics

27.3 Young’s Double Slit Experiment

• Explain the phenomena of interference.
• Define constructive interference for a double slit and destructive interference for a double slit.

Although Christiaan Huygens thought that light was a wave, Isaac Newton did not. Newton felt that there were other explanations for color, and for the interference and diffraction effects that were observable at the time. Owing to Newton’s tremendous stature, his view generally prevailed. The fact that Huygens’s principle worked was not considered evidence that was direct enough to prove that light is a wave. The acceptance of the wave character of light came many years later when, in 1801, the English physicist and physician Thomas Young (1773–1829) did his now-classic double slit experiment (see Figure 1 ).

When light passes through narrow slits, it is diffracted into semicircular waves, as shown in Figure 3 (a). Pure constructive interference occurs where the waves are crest to crest or trough to trough. Pure destructive interference occurs where they are crest to trough. The light must fall on a screen and be scattered into our eyes for us to see the pattern. An analogous pattern for water waves is shown in Figure 3 (b). Note that regions of constructive and destructive interference move out from the slits at well-defined angles to the original beam. These angles depend on wavelength and the distance between the slits, as we shall see below.

Take-Home Experiment: Using Fingers as Slits

Look at a light, such as a street lamp or incandescent bulb, through the narrow gap between two fingers held close together. What type of pattern do you see? How does it change when you allow the fingers to move a little farther apart? Is it more distinct for a monochromatic source, such as the yellow light from a sodium vapor lamp, than for an incandescent bulb?

Similarly, to obtain destructive interference for a double slit , the path length difference must be a half-integral multiple of the wavelength, or

The equations for double slit interference imply that a series of bright and dark lines are formed. For vertical slits, the light spreads out horizontally on either side of the incident beam into a pattern called interference fringes, illustrated in Figure 6 . The intensity of the bright fringes falls off on either side, being brightest at the center. The closer the slits are, the more is the spreading of the bright fringes. We can see this by examining the equation

Example 1: Finding a Wavelength from an Interference Pattern

Substituting known values yields

Example 2: Calculating Highest Order Possible

Strategy and Concept

The number of fringes depends on the wavelength and slit separation. The number of fringes will be very large for large slit separations. However, if the slit separation becomes much greater than the wavelength, the intensity of the interference pattern changes so that the screen has two bright lines cast by the slits, as expected when light behaves like a ray. We also note that the fringes get fainter further away from the center. Consequently, not all 15 fringes may be observable.

Section Summary

• Young’s double slit experiment gave definitive proof of the wave character of light.
• An interference pattern is obtained by the superposition of light from two slits.

Conceptual Questions

1: Young’s double slit experiment breaks a single light beam into two sources. Would the same pattern be obtained for two independent sources of light, such as the headlights of a distant car? Explain.

2: Suppose you use the same double slit to perform Young’s double slit experiment in air and then repeat the experiment in water. Do the angles to the same parts of the interference pattern get larger or smaller? Does the color of the light change? Explain.

3: Is it possible to create a situation in which there is only destructive interference? Explain.

4:   Figure 7 shows the central part of the interference pattern for a pure wavelength of red light projected onto a double slit. The pattern is actually a combination of single slit and double slit interference. Note that the bright spots are evenly spaced. Is this a double slit or single slit characteristic? Note that some of the bright spots are dim on either side of the center. Is this a single slit or double slit characteristic? Which is smaller, the slit width or the separation between slits? Explain your responses.

Problems & Exercises

2: Calculate the angle for the third-order maximum of 580-nm wavelength yellow light falling on double slits separated by 0.100 mm.

7: At what angle is the fourth-order maximum for the situation in Problems & Exercises 1 ?

10: What is the smallest separation between two slits that will produce a second-order maximum for 720-nm red light?

11: (a) What is the smallest separation between two slits that will produce a second-order maximum for any visible light? (b) For all visible light?

14: Using the result of the problem above, calculate the distance between fringes for 633-nm light falling on double slits separated by 0.0800 mm, located 3.00 m from a screen as in Figure 8 .

15: Using the result of the problem two problems prior, find the wavelength of light that produces fringes 7.50 mm apart on a screen 2.00 m from double slits separated by 0.120 mm (see Figure 8 ).

9: 1200 nm (not visible)

11: (a) 760 nm

(b) 1520 nm

For two adjacent fringes we have,

Subtracting these equations gives

College Physics Copyright © August 22, 2016 by OpenStax is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

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• Youngs Double Slit Experiment

Young's Double Slit Experiment

What is young’s double slit experiment.

Young’s double slit experiment uses two coherent sources of light placed at a small distance apart. Usually, only a few orders of magnitude greater than the wavelength of light are used. Young’s double slit experiment helped in understanding the wave theory of light , which is explained with the help of a diagram. As shown, a screen or photodetector is placed at a large distance, ‘D’, away from the slits.

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The original Young’s double slit experiment used diffracted light from a single source passed into two more slits to be used as coherent sources. Lasers are commonly used as coherent sources in modern-day experiments.

Table of Contents

• Position of Fringes
• Shape of Fringes
• Intensity of Fringes

Special Cases

• Displacement of Fringes

Each source can be considered a source of coherent light waves . At any point on the screen at a distance ‘y’ from the centre, the waves travel distances  l 1  and  l 2 to create a path difference of Δl at the point. The point approximately subtends an angle of θ at the sources (since the distance D is large, there is only a very small difference between the angles subtended at sources).

Derivation of Young’s Double Slit Experiment

Consider a monochromatic light source ‘S’ kept at a considerable distance from two slits: s 1 and s 2 . S is equidistant from s 1 and s 2 . s 1 and s 2 behave as two coherent sources as both are derived from S.

The light passes through these slits and falls on a screen which is at a distance ‘D’ from the position of slits s 1 and s 2 . ‘d’ is the separation between two slits.

If s 1 is open and s 2 is closed, the screen opposite to s 1 is closed, and only the screen opposite to s 2 is illuminated. The interference patterns appear only when both slits s 1 and s 2 are open.

When the slit separation (d) and the screen distance (D) are kept unchanged, to reach P, the light waves from s 1 and s 2 must travel different distances. It implies that there is a path difference in Young’s double slit experiment between the two light waves from s 1 and s 2 .

Approximations in Young’s double slit experiment 

• Approximation  1: D > > d: Since D > > d, the two light rays are assumed to be parallel.
• Approximation  2:   d/λ >> 1:  Often, d is a fraction of a millimetre, and λ is a fraction of a micrometre for visible light.

Under these conditions, θ is small. Thus, we can use the approximation sin θ = tan θ ≈ θ = λ/d.

∴ path difference, Δz = λ/d

This is the path difference between two waves meeting at a point on the screen. Due to this path difference in Young’s double slit experiment, some points on the screen are bright, and some points are dark.

Now, we will discuss the position of these light and dark fringes and fringe width.

Position of Fringes in Young’s Double Slit Experiment

Position of bright fringes.

For maximum intensity or bright fringe to be formed at P,

Path difference, Δz = nλ (n = 0, ±1, ±2, . . . .)

i.e., xd/D = nλ

The distance of the n th   bright fringe from the centre is

x n = nλD/d

Similarly, the distance of the (n-1) th  bright fringe from the centre is

x (n-1) = (n -1)λD/d

Fringe width,  β =  x n   – x (n-1)  = nλD/d – (n -1)λD/d = λD/d

(n = 0, ±1, ±2, . . . .)

Position of Dark Fringes

For minimum intensity or dark fringe to be formed at P,

Path difference, Δz = (2n + 1) (λ/2) (n = 0, ±1, ±2, . . . .)

i.e., x = (2n +1)λD/2d

The distance of the n th   dark fringe from the centre is

x n = (2n+1)λD/2d

x (n-1) = (2(n-1) +1)λD/2d

Fringe width, β = x n   – x (n-1)  = (2n + 1) λD/2d – (2(n -1) + 1)λD/2d = λD/d

Fringe Width

The distance between two adjacent bright (or dark) fringes is called the fringe width.

If the apparatus of Young’s double slit experiment is immersed in a liquid of refractive index  (μ), then the wavelength of light and fringe width decreases ‘μ’ times.

If white light is used in place of monochromatic light, then coloured fringes are obtained on the screen, with red fringes larger in size than violet.

Angular Width of Fringes

Let the angular position of n th bright fringe is θ n, and because of its small value, tan θ n   ≈ θ n

Similarly, the angular position of (n+1) th bright fringe is θ n+1,  then

∴ The angular width of a fringe in Young’s double slit experiment is given by,

Angular width is independent of ‘n’, i.e., the angular width of all fringes is the same.

Maximum Order of Interference Fringes

But ‘n’ values cannot take infinitely large values as it would violate the 2 nd approximation.

i.e., θ is small (or) y < < D

When the ‘n’ value becomes comparable to d/ λ, path difference can no longer be given by d γ/D.

Hence for maxima, path difference = nλ

The above represents the box function or greatest integer function.

Similarly, the highest order of interference minima

The Shape of Interference Fringes in YDSE

From the given YDSE diagram, the path difference between the two slits is given by

The above equation represents a hyperbola with its two foci as, s 1 and s 2 .

The interference pattern we get on the screen is a section of a hyperbola when we revolve the hyperbola about the axis s 1 s 2 .

If the screen is a yz plane, fringes are hyperbolic with a straight central section.

If the screen is xy plane , the fringes are hyperbolic with a straight central section.

The Intensity of Fringes in Young’s Double Slit Experiment

For two coherent sources, s 1 and s 2 , the resultant intensity at point p is given by

I = I 1 + I 2 + 2 √(I 1 . I 2 ) cos φ

Putting I 1 = I 2 = I 0  (Since, d<<<D)

I = I 0 + I 0 + 2 √(I 0 .I 0 ) cos φ

I = 2I 0 + 2 (I 0 ) cos φ

I = 2I 0 (1 +  cos φ)

For maximum intensity

phase difference   φ = 2nπ

Then, path difference \(\begin{array}{l}\Delta x=\frac{\lambda }{{2}{\pi }}\left( {2}n{\pi } \right)\end{array} \) = nλ

The intensity of bright points is maximum and given by

I max = 4I 0

For minimum intensity

φ = (2n – 1) π

Phase difference φ = (2n – 1)π

Thus, the intensity of minima is given by

If I 1 ≠ I 2 , I min ≠ 0.

Rays Not Parallel to Principal Axis:

From the above diagram,

Using this, we can calculate different positions of maxima and minima.

Source Placed beyond the Central Line:

If the source is placed a little above or below this centre line, the wave interaction with S 1 and S 2 has a path difference at point P on the screen.

Δ x= (distance of ray 2) – (distance of ray 1)

= bd/a + yd/D → (*)

We know Δx = nλ for maximum

Δx = (2n – 1) λ/2 for minimum

By knowing the value of Δx from (*), we can calculate different positions of maxima and minima .

Displacement of Fringes in YDSE

When a thin transparent plate of thickness ‘t’ is introduced in front of one of the slits in Young’s double slit experiment, the fringe pattern shifts toward the side where the plate is present.

The dotted lines denote the path of the light before introducing the transparent plate. The solid lines denote the path of the light after introducing a transparent plate.

Where μt is the optical path.

Then, we get,

Term (1) defines the position of a bright or dark fringe; term (2) defines the shift that occurred in the particular fringe due to the introduction of a transparent plate.

Constructive and Destructive Interference

For constructive interference, the path difference must be an integral multiple of the wavelength.

Thus, for a bright fringe to be at ‘y’,

Or, y = nλD/d

Where n = ±0,1,2,3…..

The 0th fringe represents the central bright fringe.

Similarly, the expression for a dark fringe in Young’s double slit experiment can be found by setting the path difference as

Δl = (2n+1)λ/2

This simplifies to

(2n+1)λ/2 = y d/D

y = (2n+1)λD/2d

Young’s double slit experiment was a watershed moment in scientific history because it firmly established that light behaved like a wave.

The double slit experiment was later conducted using electrons , and to everyone’s surprise, the pattern generated was similar as expected with light. This would forever change our understanding of matter and particles, forcing us to accept that matter, like light, also behaves like a wave.

Wave Optics

Young’s double slit experiment.

Frequently Asked Questions on Young’s Double Slit Experiment

What was the concept explained by young’s double slit experiment.

Young’s double slit experiment helps in understanding the wave theory of light.

What are the formulas derived from Young’s double slit experiment?

For constructive interference, dsinθ = mλ , for m = 0,1,-1,2,-2

For destructive interference, dsinθ = (m+½)λ, for m = 0,1,-1,2,-2 Here, d is the distance between the slits. λ is the wavelength of the light waves.

What is called a fringe width?

The distance between consecutive bright or dark fringe is called the fringe width.

What kind of source is used in Young’s double slit experiment?

A coherent source is used in Young’s double slit experiment.

Put your understanding of this concept to test by answering a few MCQs. Click ‘Start Quiz’ to begin!

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Young’s Double Slit Experiment

Optics is the part of material science that concentrates on the conduct and properties of light, incorporating its connections with issues and the development of instruments that utilise or recognize it. Optics as a rule depicts the conduct of apparent, bright, and infrared light. Since light is an electromagnetic wave, different types of electromagnetic radiation, for example, X-beams, microwaves, and radio waves show comparative properties. Most optical marvels can be represented by utilizing the traditional electromagnetic portrayal of light. 

Complete electromagnetic depictions of light are, in any case, frequently hard to apply practically speaking. Down to earth optics is typically done utilizing worked on models. The most widely recognized of these, mathematical optics, regards light as an assortment of beams that move in straight lines and curve when they go through or reflect from surfaces. Actual optics is a more thorough model of light, which incorporates wave impacts, for example, diffraction and obstruction that can’t be represented in mathematical optics. By and large, the beam based model of light was grown first, trailed by the wave model of light. Progress in the electromagnetic hypothesis in the nineteenth century prompted the disclosure that light waves were indeed electromagnetic radiation.  

Young’s Double Slit Experiment

Young’s double-slit experiment employs two coherent light sources separated by a modest distance, generally a few orders of magnitude larger than the wavelength of light. 

Young’s double-slit experiment aided in the understanding of lightwave theory. The slits are separated by a large distance ‘D’ from a screen or photodetector. Young’s original double-slit experiment employed diffracted light from a single source that was then transmitted through two additional slits to serve as coherent sources. In today’s investigations, lasers are frequently employed as coherent sources.

Each source may be thought of as a coherent lightwave source. The waves travel lengths l1 and l2 to generate a path difference of l at any place on the screen at a distance ‘y’ from the centre. At the sources, the point roughly subtends an angle of (since the distance D is large there is only a very small difference of the angles subtended at sources).

Derivation for Young’s Double Slit Experiment

Consider a monochromatic light source ‘S’ that is kept a long way from two slits s 1 and s 2 . S is in the same plane as s 1 and s 2 . Because both s 1 and s 2 are drawn from S, they act as two consistent sources.

The light travels through these slits and lands on a screen that is positioned at a distance ‘D’ from the apertures s 1 and s 2 . The distance between two slits is denoted by the letter ‘d.’

If s 1 is open and s 2 is closed, the screen opposite s 1 is darkened, leaving just the screen opposite s 2 lit. Only when both slits s 1 and s 2 are open can interference patterns form. 

At the point when the cut partition (d) and the screen distance (D) are kept unaltered, to arrive at P the light waves from s 1 and s 2 should travel various distances. It suggests that there is a way contrast in Young’s twofold cut test between the two light waves from s 1 and s 2 .  

Approximations in Young’s twofold cut analysis-  Guess 1: D > d  Since D > d, the two light beams are thought to be equal.   Guess 2: d/λ >> 1 Often, d is a small amount of a millimeter and λ is a negligible portion of a micrometer for noticeable light.  

Under these conditions θ is little, consequently, we can utilize the estimate,

sin θ = tan θ ≈ θ = λ/d

∴ the path difference, 

Δz = λ/d  

This is the path difference between two waves meeting at a point on the screen. Because of this path difference in Young’s twofold cut investigation, a few focuses on the screen are brilliant and a few focuses are dull.

Position of Fringes In Young’s Double Slit Experiment

• Position of Bright Fringes

For maximum intensity or bright fringe to be formed at P

Path difference, Δz = nλ (n = 0, ±1, ±2, . . . .)

The distance of the nth  bright fringe from the centre is

x n = nλD/d

Similarly, the distance of the (n-1) th bright fringe from the centre is

x (n-1) = (n -1)λD/d

Fringe width,  β = x n  – x (n-1) = nλD/d – (n -1)λD/d = λD/d

(n = 0, ±1, ±2, . . . .)

• Position of Dark Fringes

For minimum intensity or dark fringe to be formed at P,

Path difference, Δz = (2n + 1) (λ/2) (n = 0, ±1, ±2, . . . .)

x = (2n +1)λD/2d

The distance of the nth  dark fringe from the centre is

x n = (2n+1)λD/2d

x (n-1) = (2(n-1) +1)λD/2d

Fringe width, β = x n  – x (n-1) = (2n + 1) λD/2d – (2(n -1) + 1)λD/2d = λD/d

Fringe Width

The fringe width is the distance between two consecutive bright (or dark) fringes. β = λD/d

When Young’s double-slit experiment equipment is submerged in a liquid with a refractive index of (μ), the wavelength of light and the fringe width both fall by ” times.

When white light is utilised instead of monochromatic light, coloured fringes appear on the screen, with red fringes being bigger than violet fringes.

Maximum Order of Interference Fringes

On the screen, the position of n th order maximum is,

where n=0, ±1, ±2, …

However, because the 2 nd approximation would be violated, ‘n’ values cannot take infinitely high values. i.e. θ is small (or) y << D.

⇒ γ/D = nλ/d <<1

As a result, the above formula for interference maxima can be used n<< d/λ. When the value of ‘n’ equals that of d/λ, the path difference can no longer be calculated as dγ/D.

Hence for maxima, path difference = nλ

⇒ dsinθ = nλ

​n = dsinθ/λ 

n max = d/λ

The above represents the box function or greatest integer function. Similarly, the highest order of interference minima is given by,

​n min =[d/λ+1/2]

Shape of Interference Fringes in YDSE

The route difference between the two slits is represented by the YDSE diagram.

s 2 p−s 1 p≈dsinθ (constant)

The preceding equation depicts a hyperbola with two foci denoted by the letters s 1 and s 2 .

When we rotate a hyperbola on the axis s 1 s 2 , we obtain an interference pattern on the screen that is a segment of a hyperbola. Fringes are hyperbolic with a straight middle portion of the screen is in the yz plane.

Intensity of Fringes in YDSE

The resulting intensity at location p for two coherent sources s1 and s2 is given by

I = I 1 + I 2 + 2 √(I 1 . I 2 ) cos φ

Putting, I 1 = I 2 = I 0 (Since, d<<<D).

I = I 0 + I 0 + 2 √(I 0 .I 0 ) cos φ

  = 2I 0 + 2 (I 0 ) cos φ

  = 2I 0 (1 +  cos φ)

  = 4I 0 cos 2 (ϕ/2)

Constructive and Destructive Interference

The path difference must be an integral multiple of the wavelength for constructive interference to occur. As a result, if a brilliant fringe is at ‘y,’

where n = ±0,1,2,3…..

The centre brilliant fringe is represented by the 0th fringe. Similarly, in Young’s double-slit experiment, the expression for a black fringe may be obtained by setting the path difference to:

Δl = (2n+1)λ/2

This simplifies to,

(2n+1)λ/2 = y d/D

y = (2n+1)λD/2d

Young’s double-slit experiment was a breakthrough point in science because it proved beyond a shadow of a doubt that light behaved like a wave. Later, the Double Slit Experiment was repeated using electrons, and to everyone’s amazement, the pattern produced was nearly identical to that seen with light. This would forever alter our perceptions of matter and particles, requiring us to believe that matter, like light, acts like a wave.

Sample Questions

Question 1: In Young’s double-slit experiment, the ratio of brightness at minima to peaks is 9:25. Calculate the ratio of the two-slit widths.

I max /I min = (a 1 +a 2 ) 2 /(a 1 -a 2 ) 2                               = 9/25 Solving, a 1 /a 2 = 4/1  Therefore, Ratio of slit width , w 1 /w 2 = a 1 2 /a 2 2 = 16.

Question 2: The distance between the slits in a double-slit experiment is 3 mm, and the slits are 2 m apart from the screen. On the screen, two interference patterns can be observed, one caused by light with a wavelength of 480 nm and the other by light with a wavelength of 600 nm. What is the distance between the fifth-order brilliant fringes of the two interference patterns on the screen?

Separation is given by, y= nλD/d ​where, d = 3 mm = 3 × 10 −3 m D = 2 m λ 1 = 480 nm = 480×10 −9 m λ 2 = 600 nm = 600×10 −9 m n 1 ​=n 2 =5 So, y 1​ =  nλ 1 D/d y 1 = 5×480×10 −9 ×2 / 3×10 −3 ​y 1 =1.6×10 −3 m Also,   y 2 = nλ 2 D /d ​y 2 =  5×600×10 −9 ×2 / 3×10 −3 ​y 2 =2×10 −3 m As , y 2 > y 1 ​y 2 − y 1 ​= 2×10 −3 −1.6×10 −3             = 4×10 −4 m Therefore the separation on the screen between the fifth order bright fringes of the two interference patterns is 4×10 −4 m.

Question 3: The widths of two slits in Young’s experiment are 1: 25. The intensity ratio at the interference pattern’s peaks and minima, I max /I min is

Intensity is proportional to width of the slit. thus, I 1 /I 2 = 1/25 or a 1 /a 2 =  1/5 Imax/Imin = (a 1 +a 2 ) 2 /(a 1 -a 2 ) 2                  = (a 1 +5a 1 ) 2 /(a 1 -5a 1 ) 2                  = 36/16                  = 9/4

Question 4: Two lucid point sources S 1 and S 2 vibrating in stage radiate light of frequency λ. The division between the sources is 2λ. Consider a line going through S 2 and opposite to the line S 1 S 2 . What is the littlest separation from S 2 where at least power happens?

For minimum  intensity of light, path difference must be equal to path difference for dark e.g Δx=λ/2,3λ/2,5λ/2 Consider Δx=(2λ−λ/2)=3λ/2 Now, path difference=S 1 P−S 2 P Δx=  √(4λ 2 +x 2 )−x 3λ/2+x=  √4λ 2 +x 2  Taking square on both sides, 9λ 2 /4+x 2 +3λx=4λ 2 +x 2  3λx=4λ 2 −9λ 2 /4 x=7λ/12 The smallest distance from S 2 where a minimum of intensity occurs is 7λ/12

Question 5: A glass lens is coated with a thin layer having a refractive index of 1.50. The glass has a refractive index of 1.60. What is the thinnest film coating that will reflect 546 nm light extremely strongly (constructive thin film interference)?

Light is entering in a medium of higher refractive index (n 2 =1.60) from a medium of lower index (n 1 =1.50), therefore net path difference in the reflected rays from the two interfaces will be equal to 2t (where t is thickness of thin film) , because when light goes from air to thin film path shift in reflected ray =λ’/2, when light goes from  thin film to glass path shift in reflected ray =λ’/2+2t for constructive interference,     2t=mλ’ or 2t=mλ/n 1 where λ’= wavelength in thin film  , λ=546nm(given) wavelength in vacuum , for thinnest coating , m=0(minimum) , therefore, t min = λ/2n 1                      ​= 546/(2×1.50) = 182nm

Question 6: The initial minimum of the interference pattern of monochromatic light of wavelength e occurs at an angle of λ/a for a single slit of width “a.” We find a maximum for two thin slits separated by a distance “a” at the same angle of λ/a. Explain.

Width of the slit is a. The path difference between two secondary wavelets is given by, Nλ=asinθ Since, θ is very small, sinθ=θ So, for the first order diffraction n=1, the angle is  λ/a  Now, we know that θ must be very small θ=0 (nearly) because of which the diffraction pattern is minimum. Now for interference case, for two interfering waves of intensity l 1 and l 2 ​we must have two slits separated by a distance. We have the resultant intensity, l=l 1 +l−2+ 2 √l 1 l 2 cosθ ​Since, θ=0 (nearly) corresponding to angle λ/a, so cosθ=1 (nearly) So, l=l 1 +l 2  +2 √ l 1 l 2 cosθ ​l=l 1 +l 2 +2 √ l 1 l 2 cos0 ​l=l 1 +l 2 +2 √ l 1 l 2 ​We see the resultant intensity is sum of the two intensities, so there is a maxima corresponding to the angle  λ/a ​This is why at the same angle λ/a we get a maximum for two narrow slits separated by a distance a.

Question 7: The highest and minimum intensities in an interference pattern created by two coherent sources of light have a 9:1 ratio. what is the brightness of the light used?

Imax /Imin = (a 1 +a 2 ) 2 / (a 1 -a 2 ) 2 9/1 = (a 1 +a 2 ) 2 / (a 1 -a 2 ) 2 a 1 /a 2 = 2/1  a 1 2 / a 2 2 = l 1 / l 2                = 4/1 

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• Published: 03 September 2024

Quantum double slit experiment with reversible detection of photons

• Vipin Devrari 1 &
• Mandip Singh 1  

Scientific Reports volume  14 , Article number:  20438 ( 2024 ) Cite this article

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• Quantum mechanics
• Single photons and quantum effects

Principle of quantum superposition permits a photon to interfere with itself. As per the principle of causality, a photon must pass through the double-slit prior to its detection on the screen to exhibit interference. In this paper, a double-slit quantum interference experiment with reversible detection of Einstein–Podolsky–Rosen quantum entangled photons is presented. Where a photon is first detected on a screen without passing through a double-slit, while the second photon is propagating towards the double-slit. A detection event on the screen cannot affect the second photon with any signal propagating at the speed of light, even after its passage through the double-slit. After the detection of the first photon on the screen, the second photon is either passed through the double-slit or diverted towards a stationary photon detector. Therefore, the question of whether the first photon carries the which-path information of the second photon in the double-slit is eliminated. No single photon interference is exhibited by the second photon, even if another screen is placed after the double-slit.

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Introduction.

In 1801, Young’s double-slit interference experiment proved that light behaves as a wave 1 , 2 . A first experimental observation of interference with very low intensity of light was reported by Taylor 3 . However, quantum mechanically, light consists of discrete energy packets known as photons, which can exhibit particle- or wave-like behaviour. According to the principle of quantum superposition, a single particle can exist at different locations simultaneously 4 , 5 . This counter-intuitive law of nature gives wave nature to a particle, and by its consequence, a particle can interfere with itself, i.e. all quantum superimposed states of a particle interfere with each other. In a single particle quantum double-slit experiment, a single particle is passed through a double-slit, and an interference pattern gradually emerges on the screen by accumulating particle detections by repeating the experiment. Each detection of a particle on the screen determines its position on the screen, whereas this measurement cannot determine the path of a particle in the double-slit. However, the interference pattern cannot be formed, when the which-path information of a particle is measured or stored by modifying the experiment. The casual temporal order of this experiment signifies a detection on the screen after the passage of a particle through the double-slit. This casual self interference was demonstrated experimentally with electrons 6 , 7 , 8 , 9 , neutrons 10 , 11 , photons 12 , 13 and positrons 14 . Quantum mechanics exerts no restriction on the self interference of macromolecules, which is experimentally demonstrated 15 , 16 , 17 , 18 , 19 , 20 . An experiment demonstrating self interference of two-photon amplitudes in a double-double-slit is performed with momentum entangled photons 21 , 22 . Another version of a double-slit experiment is realised by placing a double-slit in the path of one photon, where the interference pattern is formed only when both photons are measured 23 , 24 , 25 , 26 , 27 , 28 , 29 . However, in these experiments, both photons are measured after one of them is passed through the double-slit.

In this paper, a quantum double-slit experiment with reversible detection of photons is presented, which is carried out with continuous variable Einstein–Podolsy–Rosen (EPR) 30 quantum entangled photon pairs. A reversible detection implies that a photon of a quantum entangled pair is first detected on a screen while the other photon is propagating towards a double-slit, and later it can pass either through the double-slit or it can be diverted towards a stationary single photon detector. The experiment is configured such that the detection of a first photon on the screen cannot affect the second photon through any local communication, even after its interaction with the double-slit. This is because the second photon is separated from the detection event by a lightlike interval. Since the second photon passes through the double-slit after the detection of the first photon therefore, the first photon carried no which-path information of the second photon in the double-slit. The second photon is detected by stationary single photon detectors, which are placed at fixed locations throughout the interference experiment. The interference pattern is produced on the screen by repeating the experiment each time with a new EPR entangled pair, provided those photon detections on the screen are considered when the second photon is detected by a stationary detector positioned after the double-slit. However, position measurements of individual photons do not produce any interference pattern, even if the detector placed after the double-slit is displaced gradually to count photons at different locations. The experiment is performed with continuous variable EPR entangled photon pairs produced simultaneously in a Beta Barium Borate (BBO) nonlinear crystal by Type-I spontaneous parametric down conversion (SPDC) in a noncollinear configuration 31 , 32 , 33 , 34 , 35 , 36 , 37 . A real double-slit is used in this experiment, whereas the quantum entangled pair production rate is intentionally reduced to keep one entangled photon pair in the experiment until its detection. The second EPR entangled pair of photons is produced considerably later than the detection of the first entangled pair of photons. In addition, this paper presents a theoretical analysis of the experiment.

Concept and analysis

The EPR state is a continuous variable entangled quantum state of two particles, where both particles are equally likely to exist at all position and momentum locations. A one-dimensional EPR state in position basis is written as \(|\alpha \rangle =\int ^{\infty }_{-\infty }|x\rangle _{1}|x+{\textbf {x}}_{o}\rangle _{2} \textrm{d}x\) , where subscripts 1 and 2 represent particle-1 and particle-2, respectively. A constant \({\textbf {x}}_{o}\) corresponds to the position difference of particles. The same EPR state is expressed in momentum basis as \(|\alpha \rangle =\int ^{\infty }_{-\infty }e^{i \frac{p x_{o}}{\hslash }}|p\rangle _{1}|-p\rangle _{2}\textrm{d}p\) , where particles have opposite momenta, and \(\hslash =h/2\pi\) is the reduced Planck’s constant. Therefore, both position and momentum of each particle are completely unknown. If the position of any one particle is measured, then the EPR state is randomly collapsed onto \(|x'\rangle _{1}|x'+{\textbf {x}}_{o}\rangle _{2}\) where a prime on x indicates a single measured position value from the integral range. Therefore, the measured positions of particles are correlated, i.e. they are separated by \({\textbf {x}}_{o}\) irrespective of \(x'\) . Instead of position, if momentum, which is a complementary observable to the position, of a particle is measured, then the EPR state is randomly collapsed onto \(| p'\rangle _{1}|-p'\rangle _{2}\) , where both the particles exhibit opposite momenta irrespective of \(p'\) thus, their measured momenta are correlated.

A schematic diagram of the experiment, where a screen corresponds to a single photon detector capable of detecting locations of photon detection events. A screen is placed considerably closer to the source than a beam splitter and a double-slit.

In this paper, the EPR state of two photons in three-dimensions, propagated away from a finite size of source, is evaluated as follows: Consider a schematic of the experiment shown in Fig.  1 , where EPR entangled photons are produced by a finite source size. Photon-1 is detected on a screen, which can record the position of a detected photon as a point on the screen. This measurement corresponds to a position measurement of photon-1 while photon-2 is propagating towards a double-slit, and later it passes through a 50:50 beam splitter. The reflected probability amplitude of photon-2 is incident on a single photon detector-3, which is placed at the focal point of a convex lens. Whereas the transmitted probability amplitude is passed through a double-slit and incident on a single photon detector-2. The detector-2 is stationary, and it measures the position of photon-2 behind the double-slit. Each single photon detector is equipped with a very narrow aperture in order to measure the position of a photon around a location.

To evaluate the EPR state of two photons emanating from a three-dimensional source of finite extension, consider a source placed around the origin of a right-handed Cartesian coordinate system, as shown in Fig.  1 . Two photons are produced simultaneously from each point in the source as a consequence of the EPR constraint. Corresponding to an arbitrary point \(\mathbf {r'}\) within the source, a two-photon probability amplitude to find photon-1 at a point \(o_{a}\) in region- a left to the source and photon-2 at a point \(o_{b}\) in region- b right to the source is written as \(\frac{e^{ip_{1}|\textbf{r}_{a}-\textbf{r}'|/\hslash }}{|\textbf{r}_{a}-\textbf{r}'|}\frac{e^{ip_{2}|\textbf{r}_{b}-\textbf{r}'|/\hslash }}{|\textbf{r}_{b}-\textbf{r}'|}\) 38 , 39 , where \(p_{1}\) and \(p_{2}\) are magnitudes of momentum of photon-1 and of photon-2, respectively, and \(\textbf{r}_{a}\) and \(\textbf{r}_{b}\) are the position vectors of points \(o_{a}\) and \(o_{b}\) from the origin. Since the source size is finite, the total finite amplitude to find a photon at \(o_{a}\) and a photon at \(o_{b}\) is a linear quantum superposition of amplitudes originating from all points located in the source, which is written as

where both photons have the same linear polarisation state. A case for different polarisation states of photons leads to a hyper-entangled state, which is reported in Refs. 40 , 41 . However, for this experiment, an EPR entanglement is sufficient. Therefore, both photons are assumed to have the same linear polarisation state along the y -axis, which is omitted in this analysis. In Eq. ( 1 ), \(A_{o}\) is a constant, and \(\psi (x',y',z')\) is the probability amplitude of a pair production at a position \(r'(x',y',z')\) in the source. This amplitude is constant for an infinitely extended EPR state at any arbitrary position vector \(\textbf{r}'\) in the source. This integral represents the amplitude of two photons emanating from a three-dimensional photon pair source of finite size. It leads to a two-photon amplitude, which corresponds to the probability amplitude to find two photons together at different locations. Further, the magnitudes of momenta of photons are considered to be equal \(p_{1}=p_{2}=p\) , for the degenerate photon pair production. The amplitude of pair production \(\psi (x',y',z')\) is considered to be a three-dimensional Gaussian function such that, \(\psi (x',y',z')= a e^{-(x'^2+y'^2)/\sigma ^2}e^{-z'^2/w^2}\) , where a is a constant, \(\sigma\) and w are the widths of the Gaussian.

To evaluate the integral, consider two planes oriented perpendicular to the z -axis such that a plane-1 is located at a distance \(s_{1}\) and a plane-2 is located at a distance \(s_{2}\) from the origin. These planes are not shown in Fig.  1 however, a screen can be placed in a plane-1 and a double-slit can be placed in a plane-2. The amplitude to find photon-1 on plane-1 and photon-2 on plane-2 is evaluated as follows: Consider the distances of planes from the origin are such that, \(\sigma ^{2}p/h s_{1}\ge 1\) and \(\sigma ^{2}p/h s_{2} \ge 1\) , where the magnitudes of \(s_{1}\) and \(s_{2}\) are considerably larger than \(\sigma\) and w . This approximation is valid for the experimental considerations of this paper. Since the double-slit and the detectors are placed close to the z -axis therefore, Eq. ( 1 ) can be written as

where \(\Phi (x_{1},y_{1}; x_{2}, y_{2})\) is a two-photon position amplitude with variables of its argument separated by a semicolon denoting a position of photon-1 on plane-1 and of photon-2 on plane-2. After solving the integral, \(\Phi (x_{1},y_{1}; x_{2}, y_{2})\) is written as

where \(c_{n}\) is a constant and tan( \(\Phi\) )=–p(s 1 +s 2 )σ 2 /2 ℏ s 1 s 2 . It is evident from Eq. ( 3 ) that both photons can be found at arbitrary positions. Once a photon is detected at a well-defined location ( \(x'_{i}, y'_{i}\) ), where a label \(i\in \{1,2\}\) corresponds to any single measured photon, then its position is determined. This measurement collapses the total wavefunction of both photons. Note that when a photon is detected at a well-defined position, even then the amplitude to find the other photon in the position space is delocalised, i.e. the projected position wavefunction has a nonzero spread. This wavefunction projection happens immediately once a photon is detected.

The second order quantum interference is exhibited if photon-1 detections are retained on the screen with the condition that photon-2 is detected after the double-slit by a stationary detector-2 as shown in Fig.  1 . However, this stationary detector will not always detect photon-2 since, photon has a nonzero amplitude to exist at different positions even after passing through the double-slit. The conditional detection corresponds to a joint measurement of photons. If all photon-1 detections on the screen are considered, then the interference pattern does not appear. Single photon interference is suppressed on the screen as well as after the double-slit, since photons are EPR entangled. To evaluate the second order interference pattern, consider a screen placed at \(z=-s_{1}\) and a double-slit placed at \(z=s_{2}\) with their planes oriented perpendicular to the z -axis. If the transmission function of the double-slit is \(A_{T}(x_{2},y_{2})\) then the joint amplitude to detect photon-1 on the screen at a position \((x_{1}, y_{1})\) and photon-2 by a stationary detector-2 is written as

where an integration represents a projection onto a quantum superposition of position states of the photon-2 in the plane of the double-slit. A phase multiplier \(B(x_{2}, y_{2})=e^{ipr_{d}/\hslash }\) represents a phase acquired by a photon to reach detector-2 from the double-slit plane. The distance between detector-2 location ( \(x_{o}, y_{o}, z_{o}\) ) and an arbitrary point location ( \(x_{2}, y_{2}, s_{2}\) ) in the double-slit plane is \(r_{d}=(D^{2}+(x_{2}-x_{o})^{2}+ (y_{2}-y_{o})^{2})^{1/2}\) , where \(D=z_{o}-s_{2}\) is the distance of detector-2 from the double-slit. Note that \(x_{o}\) is different than the symbol \({\textbf {x}}_{o}\) which is denoting separation of particles in the one-dimensional EPR state. Thus, the second order interference pattern depends on the position of detector-2. For a double-slit with slit separation d along the x -axis and infinite extension along the y -axis, the transmission function is given by \(A_{T}(x_{2},y_{2})= [\delta (x_{2}-d/2)+\delta (x_{2}+d/2)]/\sqrt{2}\) . In the following experiment, each slit of the double-slit is largely extended along the y -axis as compared to its width. The effect of slit width and position resolution of single photon detectors is considered in the analysis of the following experiment. It is also evident that the two-photon interference pattern exhibits a shift when the position of the stationary detector-2 is shifted.

Experimental results

An experiment is performed with continuous variable EPR entangled photons of equal wavelength 810 nm, which are produced by the Type-I SPDC in a negative-uniaxial BBO nonlinear crystal. An experimental diagram of the setup is shown in Fig.  2 , where the x -axis is perpendicular to the optical table passing through the crystal. This experimental setup is a folded version of a diagram shown in Fig.  1 , where folding is along the x -axis such that photons propagate close to the angle of the conical emission pattern in a horizontal plane parallel to the optical table. Furthermore, photons propagating at a small inclination w.r.t. a horizontal plane pass through the double-slit. A vertical linearly polarised laser beam, along the x -axis, of wavelength 405 nm is expanded ten times to obtain a beam diameter of 8 mm at the full-width-half-maximum. The expanded laser beam is passed through the BBO crystal, whose optic-axis can be precisely tilted in a vertical plane passing through the crystal. This configuration results in noncollinear spontaneous down-converted photon pair emission in a broad conical pattern, where both the photons of each pair have the same linear polarisation state perpendicular to the polarisation state of the pump photons. The down-converted photons are EPR entangled in a plane perpendicular to the symmetry axis of the cone. The pump laser beam, after passing through the nonlinear crystal, is absorbed by a beam dumper to minimise unwanted background light.

An experimental diagram, where EPR entangled pairs of photons are emanated in a conical emission pattern. The paths of entangled photons are represented by red lines. The pump laser beam, after passing through the crystal, is represented by a narrow white line for clarity. The x -axis is perpendicular to the optical table and passing though the nonlinear crystal.

A screen is represented by a movable single photon detector-1 ( \(D_{1}\) ), which is placed close to the crystal at a distance of 26.4 cm to detect photon-1 at about 5.68 ns prior to the detection of photon-2. The aperture of a single photon detector \(D_{1}\) is an elongated single-slit of width 0.1 mm along the x -axis, which represents an effective detector width. It also corresponds to the resolution of the position measurements along the x -axis. This detector can be displaced parallel to the x -axis in steps of 0.1 mm to detect photons at different positions. Photon-1 is passed through a band-pass filter of band-width 10 nm at the centre wavelength 810 nm prior to its detection. Photon-2 is incident on a 50:50 polarisation independent beam splitter, which is placed at a distance of 93.8 cm from the crystal. A double-slit with an orientation of single slits perpendicular to the x -axis is placed after the beam splitter at a distance of 3 cm. Another elongated single-slit aperture of width 0.1 mm along the x -axis is placed after the double-slit at a distance of 23 cm from the double-slit in front of an optical fibre coupler. After passing through the double-slit, photon-2 is filtered by a band-pass filter of band-width 10 nm at the centre wavelength 810 nm. It is then passed through the aperture and directed towards a single photon detector-2 ( \(D_{2}\) ) with a multimode optical fibre of length 0.5 m. This single-slit aperture can be displaced along the x -axis with a resolution of 0.1 mm. However, it is positioned at a predetermined location during one complete interference pattern data collection. In this experimental configuration, photon-1 is detected much earlier while photon-2 is propagating towards the beam splitter. Detection of photon-1 cannot affect photon-2 through any signalling limited by the speed of light until it reaches at an optical fibre coupler placed after the double-slit. Photon-2 arrives at the beam splitter 2.26 ns after the detection of photon-1, and from the beam splitter, its transmitted amplitude takes about 0.1 ns to arrive at the double-slit. The reflected amplitude of photon-2 is detected after passing through a band-pass filter by another optical fibre coupled single photon detector-3 ( \(D_{3}\) ) without any aperture. Photons are focused on an optical fibre input with a convex lens, which projects the incident quantum state of photon-2 onto an eigen-state of the transverse momentum, provided photon-2 is detected by a single photon detector \(D_{3}\) . Distance of the lens from the beam splitter is 25 cm, where this lens and the single photon detector \(D_{3}\) are positioned at predetermined fixed locations throughout the experiment.

( a ) Quantum interference pattern obtained by measuring the coincidence detection of photons by a variable position single photon detector \(D_{1}\) and a stationary single photon detector \(D_{2}\) , where a solid line represents the theoretically evaluated interference pattern. ( b ) Coincidence detection of photons results in no interference, when photon-2 is detected by a stationary single photon detector \(D_{3}\) and photon-1 is detected by \(D_{1}\) . Each data point is an average of ten repetitions of the experiment with 60 s time of exposure.

The shift in the two-photon quantum interference pattern when, ( a ) single photon detector \(D_{2}\) position is \(x_{o} = +0.11\) mm, ( b ) \(D_{2}\) position is \(x_{o} = -0.11\) mm. Single photons do not interfere in this experiment. Each data point is an average of ten repetitions of the experiment with 60 s time of exposure.

The experiment is performed with 19 mW power of the pump laser beam, which is incident on the crystal. Each single photon detector output is connected to an electronic time correlated single photon counter (TCSPC), which measures the single and coincidence photon counts with 81 ps temporal resolution. A selected width of time window for the coincidence detection of photons is 81 ns. Single photon counts of each detector and coincidence photon counts of \(D_{1}\) and \(D_{2}\) , \(D_{1}\) and \(D_{3}\) are measured for 60 s. These measurements are repeated ten times to obtain an average of photon counts. A two-photon quantum interference pattern with a reversible detection of photons is shown in Fig.  3 a, where open circles represent the measured coincidence photon counts of single photon detectors \(D_{1}\) and \(D_{2}\) and the single photon counts of \(D_{1}\) . Whereas, a solid line corresponds to the theoretical calculation of two-photon quantum interference using Eq. ( 4 ) by considering the finite width of each slit of the double-slit and position resolution of \(D_{2}\) . A position of \(D_{2}\) relative to the double slit is \((x_{o}, D)\) in a vertical plane with \(D=23\) cm. The two-photon quantum interference pattern exhibits a shift as the position \(x_{o}\) of \(D_{2}\) is displaced, which is due to the phase-shift multiplier term \(B(x_{2}, y_{2})=e^{ipr_{d}/\hslash }\) in Eq. ( 4 ). The slit separation of the double-slit is 0.75 mm and the width of each slit is 0.15 mm. A fixed position of a single photon detector \(D_{2}\) is taken to be the reference point with \(x_{o}=0\) . There is no single photon interference pattern produced in this experiment by scanning the detector \(D_{1}\) or \(D_{2}\) . When photon-1 is detected, photon-2 is still propagating towards the beam splitter, and later its transmitted amplitude is detected by a fixed position single photon detector \(D_{2}\) at a time lapse of 5.68 ns after the detection of a photon-1. On the other hand, if the reflected amplitude of photon-2 is detected by a single photon detector \(D_{3}\) then \(D_{2}\) will not measure any photon. In this case, photon-2 is not passed through the double-slit, and therefore, no two-photon quantum interference results as shown in Fig.  3 b, which shows coincidence counts of single photon detectors \(D_{1}\) and \(D_{3}\) and the single counts of \(D_{1}\) . A choice of whether to detect a photon after the double-slit or not is naturally and randomly occurring due to the presence of a beam splitter in the path of photon-2 after its detection. A path superposition quantum state of photon-2 after the beam splitter is projected either onto the transmitted or the reflected path due to a single photon detection by a detector \(D_{2}\) or \(D_{3}\) , respectively. The main characteristic of two-photon quantum interference is that it exhibits a shift of the entire pattern as the single photon detector \(D_{2}\) is displaced to another fixed position. This shift in the pattern is shown in Fig.  4 when, (a) \(D_{2}\) is placed at a position \(x_{o}= 0.11\) mm, (b) \(D_{2}\) is placed at a position \(x_{o}=-0.11\) mm with same D . This shift is also observed experimentally in the quantum ghost interference experiment by Strekalov et al. 23 . As a consequence of the EPR entanglement, there is no single photon interference. Therefore, the experiment in this paper presents a quantum two-photon interference with a reversible detection of photons, which has no classical counterpart.

This paper presents a two-photon double-slit experiment with the reversible detection of photons. Continuous variable EPR entangled photons are produced by the Type-I SPDC process, where photon-1 is detected on a screen while photon-2 is propagating towards a beam splitter. At a later time, photon-2 is produced in a quantum superposition of reflected and transmitted path amplitudes at the beam splitter. The transmitted amplitude is passed through the double-slit, and if this amplitude is detected by a detector-2 then the path quantum superposition state of photon-2 is collapsed onto the transmitted path. Then detector-3 does not detect this photon. Since photon-2 interacted with the double-slit considerably later than the detection of photon-1 therefore, it is ruled out that photon-1 has carried the path information of photon-2 in the double-slit to suppress the single photon interference. In addition, a position measurement of photon-1 cannot affect photon-2 through any signal propagating with speed, which is limited by the speed of light. If photon-2 is detected by a detector-3 then the quantum superposition state is collapsed onto the reflected path. Therefore, detector-2 does not detect photon-2, which results in no interference in single photon and two-photon measurements.

It is very important to expand the beam diameter of the pump laser beam to produce a continuous variable EPR quantum entangled state. It also leads to a broader envelope of the interference pattern. To achieve low background counts limited by the dark counts of the single photon detectors, the pump laser beam should have minimal scattering from optical components, and it should be properly dumped after passing through the crystal. A source of EPR entangled photons consists of a thin crystal in Type-1 SPDC configuration, where down-converted photons have the same linear polarisation. The nonlinear crystal is anti-reflection coated for wavelengths of pump and down-converted photons to reduce scattering and back reflection. The nonlinear crystal is kept at room temperature without any temperature control. Its optical-axis is precisely aligned w.r.t. the polarisation vector of the pump laser beam to obtain a broad conical emission pattern of down-converted photons with a full cone angle of  9.5°. The optical power of the pump laser beam is 19 mW, which is x -polarised. Single-slit apertures, which are placed in front of \(D_{1}\) and an input coupler of an optical fibre of \(D_{2}\) , are attached to translational stages to displace them precisely to collect photons corresponding to different positions of apertures. To increase the number of photons passing through the double slit, a double slit consists of two elongated single slits separated by a distance of 0.75 mm along the x -axis, where the width of each slit is 0.15 mm. In the experimental configuration, photons are EPR entangled in a plane perpendicular to the direction of propagation of the pump laser beam. The efficiency of each single photon detector is about 65 %. The single photon detector \(D_{1}\) equipped with a convex lens is directly collecting photons and it is placed close to the crystal. Whereas, the single photon detectors \(D_{2}\) and \(D_{3}\) are coupled to multimode optical fibres of length 0.5 m. The input of each optical fibre is attached to respective optical fibre couplers, each consisting of a convex lens of diameter  1 cm. Photons are collected by the lenses after passing through the single-slit apertures to measure the position of photons by \(D_{1}\) and \(D_{2}\) . However, a coupler of a single photon detector \(D_{3}\) is not equipped with any aperture. A band-pass optical filter of band-width 10 nm at centre wavelength  810 nm is placed at the input of each single photon detector to filter the unwanted scattered photons of the pump laser and background light.

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Acknowledgements

Mandip Singh acknowledges research funding by the Department of Science and Technology, Quantum Enabled Science and Technology grant for project No. Q.101 of theme title “Quantum Information Technologies with Photonic Devices”, DST/ICPS/QuST/Theme-1/2019 (General).

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Advanced agricultural supply chain management: integrating blockchain and young’s double-slit experiment for enhanced security

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• Esakki Muthu Santhanam 1 &
• Kartheeban kamatchi 1  

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In the agricultural supply and food, chain Ensuring product safety is important which includes monitoring the effective logistics management and advancements of agricultural products. An effective model that guarantees sufficient safety of the product is required because many issues have been raised regarding contamination risks and food safety. Thus, an efficacious model is introduced in this article referred to as Blockchain Based-Crossover Young’s double-slit (BC-CYD) algorithm, which enables securing agriculture-based data in supply chain management. The developed approach successfully executes the transactions in the traceability and tracking of products with high-level security for the agricultural supply chain. The developed method utilizes an authentication process in provenance tracking and product information storage. The developed BC-CYD method improves safety and efficiency by obtaining higher security, reliability, and integrity. Here, product transactions are stored in the blockchain ledger, thereby, the developed model offers high-level traceability and transparency in a capable manner in the supply chain management. The effectiveness of the proposed BC-CYD method is assayed, where evaluation parameters quantify the efficiency of the developed BC-CYD method. Based on the performance rates of Precision, ROC, accuracy, and Processing time, the developed BC-CYD method’s effectiveness is ascertained as higher. The suggested BC-CYD method yields a greater precision of 97.4% and its accuracy is 98.8% with lower processing time and training time.

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Santhanam, E.M., kamatchi, K. Advanced agricultural supply chain management: integrating blockchain and young’s double-slit experiment for enhanced security. Int. j. inf. tecnol. (2024). https://doi.org/10.1007/s41870-024-02180-7

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