question_answer

If one face of prism is silvered having prism angle\[30{}^\circ \]and\[\mu =\sqrt{2}.\]What will be the angle of incidence, so that the incident ray retraces its path?

A)  \[30{}^\circ \]            

B)  \[60{}^\circ \]

C)  \[90{}^\circ \]             

D)  \[45{}^\circ \]

Correct Answer: D

Solution :

 The ray retraces its path after reflection from the silvered face AC. Therefore,\[\angle ARQ=90{}^\circ \]. As is clear from the figure, the angle of reflection RQN at face AB is\[30{}^\circ \]. Therefore, by Snells law, we have \[n=\frac{\sin i}{\sin r}\] Given,      \[n=\sqrt{2},r=30{}^\circ \] \[\therefore \] \[\sin i=\frac{\sqrt{2}}{2}=\frac{1}{\sqrt{2}}\] \[\Rightarrow \] \[i=45{}^\circ \]