Question

Interference fringes are produced by two pencils of light one proceeding directly from the source S₁ and the other being reflected from a mirror MM′ (Fig. 12.7). Find the conditions for maximum and minimum brightness of fringes on the screen AB. (This arrangement for obtaining a double-slit interference pattern from a single slit is called Lloyd’s mirror.)

Answer 1

Here, the source S₁ and its virtual image S₂ act as two coherent sources

Suppose d is the separation between the two sources. The ray reflected by the mirror has gone a phase change of π which results in a path difference of λ/2. Thus, the conditions for maximum and minimum brightness are minima d sin θ = mλ, m = 0, 1, 2, ....

The fringe width on the screen is given by

The interference between the two wave trains occurs in the region of overlapping AB.