# Double-slit experiment

The Double slit experiment describes the interference patterns observed when a light-source diffracts through two slits producing fringes on a screen. These fringes have light and dark regions corresponding to where the light has constructively and destructively interfered.

The experiment was devised by Thomas Young in the 18th century.

Explanation of experiment

The light from the source splits as it encounters the two slits. As they exit each slit the waves then diffract and interfere with each other

Conditions for interference

The waves interfering must be coherent, ie the light has the same frequency and is in the same phase. This is why a single light source is used and is split by the two fringes. It would be impossible for two light sources to be used because they would not be coherent. Also the amplitudes of the sources must be similar to get a nice pattern; otherwise the bands are not fully dark/bright.

The source must be polarised or have significantly resolved parts in the same plane.

The slits must be close (about 1000 times the wavelength of the source), otherwise the interference pattern would be too close to be seen.

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

Results observed

On the area of the screen directly facing the spot inbetween the two slits, a band of light is observed. Either side of the band their is a dark region. This is followed by another band of light on both sides. After the appropriate dark regions their is a further band on either side.

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. If two light rays have travelled the same distance or their distances are both multiples of the wavelength, this is the cause of constructive interference. If, however, their distances are not multiples of the wavelength then dark regions are observed - destructive interference.

A formula linking the slit separation s, wavelength of light λ, distance from the slits to the screen D, and fringe width (the distance between the centres of the observed bands of light - x) exists:

λ / s = x / D

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.

Quantum theory and the double-slit experiment

It has been said that all the important principles of quantum theory can be demonstrated in the double-slit experiment. Due to Wave-Particle duality, even if single photons were shot through the gap they would interfere with themselves and produce an interference pattern. The experiment can also be performed with electrons, and shows similar results, illustrating the wave-like nature of matter.