# Doubleslit experiment

The double-slit experiment consists of letting light diffract through two slits producing fringes on a screen. These fringes or interference patterns have light and dark regions corresponding to where the light waves have constructively and destructively interfered. The experiment can also be performed with a beam of electrons or atoms, showing similar interference patterns; this is taken as evidence of the "wave-particle duality" predicted by quantum physics. Note, however, that a double-slit experiment can also be performed with water waves in a ripple tank; the explanation of the observed wave phenomena does not require quantum mechanics in any way. The phenomenon is quantum mechanical only when quantum particles, such as atoms or electrons, manifest as waves.

## Importance to physics

Although the double-slit experiment is now often referred to in the context of quantum mechanics, it was originally performed by the English scientist Thomas Young some time around 1805 in an attempt to resolve the question of whether light was composed of particles (the "corpuscular" theory), or rather consisted of waves travelling through some aether, just as sound waves travel in air.

The interference patterns observed in the experiment seemed to discredit the corpuscular theory, and the wave theory of light remained well accepted until the early 20th century, when evidence began to accumulate which seemed instead to confirm the particle theory of light.

The double-slit experiment, and its variations, then became a classic Gedankenexperiment (thought experiment) for its clarity in expressing the central puzzles of quantum mechanics; although in this form the experiment was not actually performed until 1961 (Claus Jönsson University of Tübingen, Zeitschrift für Physik 161, 454; C. Jönsson 1974 Electron diffraction at multiple slits American Journal of Physics 42 4-11), and not until 1974 in the form of "one electron at a time", in a laboratory at the University of Milan, by researchers led by Pier Giorgio Merli, of LAMEL-CNR Bologna.

The results of the 1974 experiment were published and even made into a short film, but did not receive wide attention. The experiment was repeated in 1989 by Tonomura et al at Hitachi in Japan. Their equipment was better, reflecting 15 years of advances in electronics and a dedicated development effort by the Hitachi team. Their methodology was more precise and elegant, but the results are unmistakably the same. Tonomura wrote that the Italian experiment had not detected electrons one at a time, a key to demonstrating the wave-particle paradox, but single electron detection is clearly visible in the photos and film taken by Merli and his group.

In September 2002, the double-slit experiment of Claus Jönsson was voted "the most beautiful experiment" by readers of Physics World.

## Explanation of experiment

In Young's original experiment, sunlight passes first through a single slit, and then through two thin vertical slits in otherwise solid barriers, and is then viewed on a rear screen.

When either slit is covered, a single peak is observed on the screen from the light passing through the other slit.

But when both slits are open, instead of the sum of these two singular peaks that would be expected if light were made of particles, a pattern of light and dark fringes is observed.

This pattern of fringes was best explained as the interference of the light waves as they recombined after passing through the slits, much as waves in water recombine to create peaks and swells. In the brighter spots, there is "constructive interference", where two "peaks" in the light wave coincide as they reach the screen. In the darker spots, "destructive interference" occurs where a peak and a trough occur together.

## Replicating Young's experiment

This experiment can easily be demonstrated in just the way that Young demonstrated it to the Royal Society of London. An assistant outside used mirrors to direct sunlight at a pinhole opening. The beam from the opening was then bisected by "a slip of card". To make things easier, a modern experimenter can replace the sunlight and mirrors with a laser pointer covered, except for a pinhole, by black paper. Splitting the beam with a small strip of notecard will produce a visible interference pattern when the beam is projected across the room. [1]

## The thought experiment

By the 1920s, various other experiments (such as the photoelectric effect) had demonstrated that light interacts with matter only in discrete, "quantum"-sized packets called photons.

If sunlight is replaced with a light source that is capable of producing just one photon at a time, and the screen is sensitive enough to detect a single photon, Young's experiment can, in theory, be performed one photon at a time -- with identical results.

If either slit is covered, the individual photons hitting the screen, over time, create a pattern with a single peak -- much as if gunshot were being poorly aimed at a target.

But if boths slits are left open, the pattern of photons hitting the screen, over time, again becomes a series of light and dark fringes.

This result seems to both confirm and contradict the wave theory. On the one hand, the interference pattern confirms that light still behaves much like a wave, even though we send it one particle at a time.

On the other hand, each time a photon with a certain energy is emitted, the screen detects a photon with the same energy. Since the photons are emitted one at a time, the photons are not interfering with each other -- so exactly what is the nature of the "interference"?

Modern quantum theory resolves these questions by postulating probability waves which describe the likelihood of finding the particle at a given location -- these waves interfere with each other just like ordinary waves do.

A refinement of this experiment consists in putting a detector at each of the two slits, to determine which slit the photon passes through on its way to the screen. But when the experiment is arranged in this way, the fringes disappear -- for reasons related to the collapse of the wavefunction.

## Conditions for interference

The two slits must be close to each other (about 1000 times the wavelength of the source), otherwise the spacing of the interference fringes would be too narrow to discern the interference pattern.

A necessary condition for obtaining an interference pattern in a double-slit experiment concerns the difference in pathlength between two paths that light can take to reach a zone of constructive interference on the viewing screen. This difference must be the wavelength of the light that is used, or a multiple of this wavelength. If a beam of sunlight is let in, and that beam is allowed to fall immediately on the double slit, then the fact that the Sun is not a point source degrades the interference pattern. The light from a source that is not a point source behaves like the light of many point sources side by side. Each can create an interference pattern, but the interference patterns of each of the many-side-by-side sources does not coincide on the screen, so they average each other out, and no interference pattern is seen.

The presence of the first slit is necessary to ensure that the light reaching the double slit is light from a single point source. The path length from the single slit to the double slit is equally important for obtaining the interference pattern as the path from the double slit to the screen.

Newton's rings show that light does not have to be coherent in order to produce an interference pattern. Newton's rings can be readily obtained with plain sunlight.Template:Fn More rings are discernable if for example light from a Sodium lamp is used, since Sodium lamp light is only a narrow band of the spectrum. Light from a Sodium lamp is incoherent. Other examples of interference patterns from incoherent light are the colours of soap bubbles and of oil films on water.

The width of the slits is usually slightly smaller than the wavelength (λ) of the light, allowing the slits to be treated as point-sources of spherical waves, and reducing the effects of single slit diffraction on the results.

In general, interference patterns are clearer when monochromatic or near-monochromatic light is used. Laserlight is as monochromatic as light can be made, therefore laserlight is used to obtain an interference pattern.

If the two slits are illuminated by coherent waves, but with polarizations perpendicular with respect to each other, the interference pattern disappears.

## Results observed

The bright bands observed on the screen happen when the light has interfered constructively -- where a crest of a wave meets a crest. The dark regions show destructive interference -- a crest meets a trough.

${\displaystyle {\frac {\lambda }{s}}={\frac {x}{D}}\,}$
where
λ is the wavelength of the light
s is the separation of the slits
x is the distance between the bands of light
D is the distance from the slits to the screen

This is only an approximation and depends on certain conditions.

It is possible to work out the wavelength of light using this equation and the above apparatus. If s and D are known and x is observed, then λ can be easily calculated.