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. (a) `sin^-1((nlambda)/(d))`
B. (b) `tan^-1((nlambda)/(d))`
C. (c) `sin^-1((nlambda)/(2d))`
D. (d) `cos^-1((nlambda)/(2d))`

Answer

C

Explanation

Path difference `=2dsintheta`

`:'` For consecutive interference
`2dsintheta=nlambda`
`impliesthetasin^-1((nlambda)/(2d))`