Optics Question 174
Question: The ratio of the intensity at the centre of a bright fringe to the intensity at a point one-quarter of the distance between two fringe from the centre is
Options:
A) 2
B) 1/2
C) 4
D) 16
Show Answer
Answer:
Correct Answer: A
Solution:
$ I=4I _{0}{{\cos }^{2}}\frac{\varphi }{2} $ At central position $ I _{1}=4I _{0} $ –(i)
Since the phase difference between two successive fringes is $ 2x, $
the phase difference between two points separated by a distance equal to one quarter of the distance between the two, successive fringes is equal to $ \delta =(2\pi )( \frac{1}{4} )=\frac{\pi }{2} $ radian
$ \Rightarrow I _{2}=4I _{0}{{\cos }^{2}}( \frac{\frac{\pi }{2}}{2} )=2I _{0} $ –(ii)
Using (i) and (ii), $ \frac{I _{1}}{I _{2}}=\frac{4I _{0}}{2I _{0}}=2 $
