Optics Question 162
Question: Two coherent sources separated by distance $ d $ are radiating in phase having wavelengthl. A detector moves in a big circle around the two sources in the plane of the two sources. The angular position of n = 4 interference maxima is given as
Options:
A) $ {{\sin }^{-1}}\frac{n\lambda }{d} $
B) $ {{\cos }^{-1}}\frac{4\lambda }{d} $
C) $ {{\tan }^{-1}}\frac{d}{4\lambda } $
D) $ {{\cos }^{-1}}\frac{\lambda }{4d} $
Show Answer
Answer:
Correct Answer: B
Solution:
Here path difference at a point $ P $ on the circle is given by $ \Delta x=d\cos \theta $ … (i)
For maxima at $ P $
$ \Delta x=n\lambda $ … (ii)
From equation (i) and (ii) $ n\lambda =d\cos \theta \Rightarrow \theta {{\cos }^{-1}}( \frac{n\lambda }{d} )={{\cos }^{-1}}( \frac{4\lambda }{d} ) $
