Question

Coherent light is incident on two fine parallel slits $S_1$ and $S_2$ as shown in Fig.



If a dark fringe occurs at $P$, which of the following gives possible phase difference for the light waves arriving at $P$ from $S_1$ and $S_2?$

• A. $2\pi ,4\pi ,6\pi$
• B. $1/2\pi ,5/2\pi ,9/2\pi$
• C. $\pi ,3\pi ,5\pi$
• D. $1/2\pi ,3/2\pi ,5/2\pi$

Answer 1

Answer: (C)

By principle of superposition at $P$, the optical difference for two coherent light waves from $S_1$ and $S_2$ must be $\left(m+\frac{1}{2}\right)\lambda$ if dark fringes occurs at $P,\lambda =$
wavelength of the monochromatic light wave. Where
$m=$ positive integers, $m=01,2,\dots ..$
Phase difference $=\left(m+\frac{1}{2}\right)2\pi$