question_answer

The refractive index of the material of a prism is \[\sqrt{2}\] and the angle of the prism is\[\text{30 }\!\!{}^\circ\!\!\text{ }\]. One of the two refracting surfaces of the prism is made a mirror inwards, by silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface) if its angle of incidence on the prism is                                                                                                   [NEET - 2018]

A)  \[\text{30 }\!\!{}^\circ\!\!\text{ }\]                     

B)       \[45{}^\circ \]

C)  \[60{}^\circ \]             

D)       Zero

Correct Answer: B

Solution :

[b] For retracing its path, light ray should be normally incident on silvered face.

Applying Snell's law at M,

[\frac{\sin i}{\sin 30{}^\circ }=\frac{\sqrt{2}}{1}\]

\[\Rightarrow \sin i=\sqrt{2}\times \frac{1}{2}\]

\[\sin i=\frac{1}{\sqrt{2}}i.e.i=45{}^\circ \]