A beam with wavelength `lambda` falls on a stack of partially reflecting planes with separation `d`. The angle `theta` that the beam should make with planes so that the beams reflected from successive planes may interfere constructively is (where n=1, 2, ...)

Options

A. `sin^(-1)((n lambda)/(d))`
B. `tan^(-1)((n lambda)/(d))`
C. `sin^(-1)((n lambda)/(2d))`
D. `cos^(-1)((n lambda)/(2d))`

Answer

C

Explanation

Path diff. between the beams reflected from successive planes `= AM + AN = 2 d sin theta`.

for constructive interference, `2 d sin theta = n lambda`
`sin theta = (n lambda)/(2 d) , theta = sin^(-1)((n lambda)/(2 d))`