question_answer

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]

A)  \[2\sin A\]

B)  \[2\cos A\]

C)  \[\frac{1}{2}\cos A\]

D)  \[\tan A\] 

Correct Answer: B

Solution :

For the given condition above ray diagram will sift. \[\angle MON=90-\overset{\text{ }\!\!{}^\circ\!\!\text{ }}{\mathop{\text{A}}}\,\] So        \[\angle r=90-(90-A)\] \[\Rightarrow \]\[\angle r=\overset{{}^\circ }{\mathop{\text{A}}}\,\] By Snell?s law   \[\frac{\sin i}{\sin r}=\mu \] \[\frac{\sin (2A)}{\sin (A)}=\mu \] \[\frac{2\sin A\cos A}{\sin A}=\mu \] \[\Rightarrow \] \[\mu =2\cos A\]