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 :

For retracing its path, light ray should be normally incident on silvered face. Applying Snell's law at M, \[\frac{\sin i}{\sin 30{}^\circ }=\frac{\sqrt{2}}{1}\] \[\Rightarrow \sin i=\sqrt{2}\times \frac{1}{2}\] \[\sin i=\frac{1}{\sqrt{2}}i.e.i=45{}^\circ \]