question_answer

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

A)            \[{{\sin }^{-1}}\left( \frac{n\lambda }{d} \right)\]

B)            \[{{\tan }^{-1}}\left( \frac{n\lambda }{d} \right)\]

C)            \[{{\sin }^{-1}}\left( \frac{n\lambda }{2d} \right)\]

D)            \[{{\cos }^{-1}}\left( \frac{n\lambda }{2d} \right)\]

Correct Answer: C

Solution :

           Path difference \[=2d\sin \theta \] \[\therefore \] For constructive interference \[2d\sin \theta =n\lambda \] \[\Rightarrow \theta ={{\sin }^{-1}}\left( \frac{n\lambda }{2\,d} \right)\]