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, $m=01,2, \ldots . .$
Phase difference $=\left(m+\frac{1}{2}\right) 2 \pi$