question_answer

A ray of light travelling in air is incident on a medium of refractive index\[\mu .\] If the angle of refraction is twice the incident angle, the incident angle is

A) \[\sin {{\,}^{-1}}\left( \frac{1}{2\mu } \right)\]                   

B) \[\sin {{\,}^{-1}}(2\mu )\]

C) \[\cos {{\,}^{-1}}(2\mu )\]           

D)        \[\cos {{\,}^{-1}}\left( \frac{1}{2\mu } \right)\]

Correct Answer: D

Solution :

By Snells law,                 \[\mu =\frac{\sin i}{\sin r}\] Here,     \[\sin i=\mu \sin 2i\]                 \[\sin i=2\mu \sin i\cos i\]                 \[i={{\cos }^{-1}}\left( \frac{1}{2\mu } \right)\]