Optics Question 161
Question: 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,??)
Options:
A) $ {{\sin }^{-1}}( \frac{n\lambda }{d} ) $
B) $ {{\tan }^{-1}}( \frac{n\lambda }{d} ) $
C) $ {{\sin }^{-1}}( \frac{n\lambda }{2d} ) $
D) $ {{\cos }^{-1}}( \frac{n\lambda }{2d} ) $
Show Answer
Answer:
Correct Answer: C
Solution:
Path difference $ =2d\sin \theta $
$ \therefore $ For constructive interference $ 2d\sin \theta =n\lambda $
$ \Rightarrow \theta ={{\sin }^{-1}}( \frac{n\lambda }{2d} ) $
