Coherent light is incident on two fine parallel slits `S_(1)` and `S_(2)` as show 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)` ?

Options

A. (a) `2pi, 4pi, 6pi`
B. (b) `1//2pi, 5//2pi, 9//2pi`
C. (c) `pi, 3pi, 5pi…`
D. (d) `1//2pi, 3//2pi, 5//2pi`

Answer

C

Explanation

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