Optics Question 843
Question: Young’s double slit experiment is made in a liquid. The $ 10^{th} $ bright fringe lies in liquid where $ 6^{th} $ dark fringe lies in vacuum. The refractive index of the liquid is approximately
Options:
A) 1.8
B) 1.5
C) 1.3
D) 1.6
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Fringe width $ \omega =\frac{\lambda D}{d} $
When the apparatus is immersed in a liquid, then $ \lambda $ will decrease $ \mu $ times and hence $ \omega $ is reduced $ \mu $ (refractive index) times.
$ 10\omega ‘=(5.5)\omega $
or $ 10\lambda ‘( \frac{D}{d} )=(5.5)\frac{\lambda D}{d} $ or $ \frac{\lambda }{\lambda ‘}=\frac{10}{5.5}=\mu $
or $ \mu =1.8 $
