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

Answer

C

Explanation

Path difference = `2d sintheta` For constructive interference `2d sintheta= nlambda`
`theta= sin^(-1)((nlambda)/(2d))`