10.5 Interference of Light Waves and Young’s Experiment

We will now discuss interference using light waves. If we use two sodium lamps illuminating two pinholes (Fig. 10.11) we will not observe any interference fringes. This is because of the fact that the light wave emitted from an ordinary source (like a sodium lamp) undergoes abrupt phase changes in times of the order of $10^{-10}$ seconds. Thus the light waves coming out from two independent sources of light will not have any fixed phase relationship and would be incoherent, when this happens, as discussed in the previous section, the intensities on the screen will add up.

The British physicist Thomas Young used an ingenious technique to “lock” the phases of the waves emanating from $S_1$ and $S_2$. He made two pinholes $S_1$ and $\mathrm{S}_2$ (very close to each other) on an opaque screen [Fig. 10.12(a)]. These were illuminated by another pinholes that was in turn, lit by a bright source. Light waves spread out from $S$ and fall on both $S_1$ and $S_2$. $S_1$ and $S_2$ then behave like two coherent sources because light waves coming out from $S_1$ and $S_2$ are derived from the same original source and any abrupt phase change in S will manifest in exactly similar phase changes in the light coming out from $\mathrm{S}_1$ and $\mathrm{S}_2$. Thus, the two sources $\mathrm{S}_1$ and $S_2$ will be locked in phase; i.e., they will be coherent like the two vibrating needle in our water wave example [Fig. 10.8(a)].

The spherical waves emanating from $S_1$ and $S_2$ will produce interference fringes on the screen $\mathrm{GG}^{\prime}$, as shown in Fig. 10.12(b). The positions of maximum and minimum intensities can be calculated by using the analysis given in Section 10.4.

We will have constructive interference resulting in a bright region when $\frac{x d}{D}=n \lambda$. That is,
$x=x_n=\frac{n \lambda D}{d} ; \mathrm{n}=0, \pm 1, \pm 2, \ldots(10.13)$
On the other hand, we will have destructive interference resulting in a dark region when $\frac{x d}{D}=\left(n+\frac{1}{2}\right) \lambda$ that is
$x=x_{\mathrm{n}}=\left(n+\frac{1}{2}\right) \frac{\lambda D}{d} ; n=0, \pm 1, \pm 2 \dots(10.14)$
Thus dark and bright bands appear on the screen, as shown in Fig. 10.13. Such bands are called fringes. Equations (10.13) and (10.14) show that dark and bright fringes are equally spaced.