Now we will take a close look at a famous experiment that Thomas Young performed in 1801. He used this experiment to show the wave-nature of light. A beam of light is shone on a pair of parallel slits placed at right angles to the beam. Light diffracts and spreads outwards from each slit into the space beyond.
The light from the two slits overlaps on a screen. An interference pattern of light and dark bands called ‘fringes’ is formed on the screen.

Explaining the experiment

In order to observe interference, we need two sets of waves. The sources of the waves must be coherent–the phase difference between the waves emitted at the sources must remain constant. This also means that the waves must have the same wavelength. Today, this is readily achieved by passing a single beam of laser light through the two slits. A laser produces intense coherent light. As the light passes through the slits, it is diffracted so that it spreads out into the space beyond (Figure 13.20). Now we have two overlapping sets of waves, and the pattern of fringes on the screen shows us the result of their interference (Figure 13.21).

Point A

This point is directly opposite the midpoint of the slits. Two rays of light arrive at A, one from slit 1 and the other from slit 2. Point A is equidistant from the two slits, and so the two rays of light have travelled the same distance. The path difference between the two rays of light is zero. If we assume that they were in phase (in step) with each other when they left the slits, then they will be in phase when they arrive at A. Hence they will interfere constructively, and we will observe a bright fringe at A.

Point B

This point is slightly to the side of point A, and is the midpoint of the first dark fringe. Again, two rays of light arrive at B, one from each slit. The light from slit 1 has to travel slightly further than the light from slit 2, and so the two rays are no longer in step. Since point B is at the midpoint of the dark fringe, the two rays must be in antiphase (phase difference of ${180^ \circ }$). The path difference between the two rays of light must be half a wavelength, and so the two rays interfere destructively.

Point C

This point is the midpoint of the next bright fringe, with $AB = BC$. Again, ray 1 has travelled further than ray 2; this time, it has travelled an extra distance equal to a whole wavelength $\lambda $. The path difference between the rays of light is now a whole wavelength. The two rays are in phase at the screen. They interfere constructively, and we see a bright fringe.
The complete interference pattern (Figure 13.21) can be explained in this way.

Determining wavelength $\lambda $

The double-slit experiment can be used to determine the wavelength λ of monochromatic light. The following three quantities have to be measured:
- Slit separation a – This is the distance between the centres of the slits, which is the distance between slits 1 and 2 in Figure 13.22.
- Fringe separation x – This is the distance between the centres of adjacent bright (or dark) fringes, which is the distance AC in Figure 13.22.
- Slit-to-screen distance D – This is the distance from the midpoint of the slits to the central fringe on the screen.
Once these three quantities have been determined, the wavelength $\lambda $ of the light can be found using the relationship:

$\lambda  = \frac{{ax}}{D}$

where $\lambda $ is the wavelength of the monochromatic light incident normally at the double-slit. a is the separation between the centres of the slits, x is the separation between the centres of adjacent bright (or dark) fringes and D is distance between the slits and the screen.