### NEET Solved Paper 2014 Question 38

##### Question: The angle of a prism is A. One of its refracting surfaces is silvered. Light rays falling at an angle of incidence 2 A on the first surface returns back through the same path after suffering reflection at the silvered surface. The refractive index $ \mu $ , of the prism is [AIPMT 2014]

#### Options:

A) $ 2\sin A $

B) $ 2\cos A $

C) $ \frac{1}{2}\cos A $

D) $ \tan A $

## Show Answer

#### Answer:

Correct Answer: B

#### Solution:

For the given condition above ray diagram will sift.

$ \angle MON=90-\overset{{}^\circ}{\mathop{A}}, $ So $ \angle r=90-(90-A) $

$ \Rightarrow $ $ \angle r=\overset{{}^\circ }{\mathop{A}}, $ By Snell?s law $ \frac{\sin i}{\sin r}=\mu $ $ \frac{\sin (2A)}{\sin (A)}=\mu $ $ \frac{2\sin A\cos A}{\sin A}=\mu $

$ \Rightarrow $ $ \mu =2\cos A $