15.5 Young's Double Slit Experiment

15.5 Young's Double Slit Experiment

We will take a close look at a famous experiment which Thomas Young performed in 1801. He used this experiment to show the wave nature of light. A beam of light is shown 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 bright and dark bands called 'fringes' is formed on the screen.

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 (Fig. 15.8). Now we have two overlapping sets of waves, and the pattern of fringes on the screen shows us the result of their interference. How does this pattern arise? We will consider three points on the screen (Fig. 15.9-a,b,c), and work out what we would expect to observe at each point.

(Fig. 15.9: Double Slit Arrangement)

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 $\mathrm{AB} = \mathrm{BC}$. 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 (Fig. 15.21) can be explained in this way.

(Fig. 15.9: (a) for $\theta = 0$ Central Bright region. Fig. 15.9 (b) For first order bright region (c) For first dark region)

To simplify the analysis of Young's experiment, we assume that the distance $L$ from the slits to the screen is so large in comparison to the distance $d$ between the slits that the lines from $S_{1}$ and $S_{2}$ to $P$ are very nearly parallel, as in Fig. 15.9.c. This is usually the case for experiments with light; the slit separation is typically a few millimeters, while the screen may be a meter or more away. The difference in path length is then given by

Where $\theta$ is the angle between a line from slits to screen and the normal to the plane of the slits (shown as a thin black line).