question_answer

A prism ABC of angle \[30{}^\circ \] has its face AC silvered. A ray of light incident at an angle of \[{{45}^{o}}\] at the face AB retraces its path after refraction at face AB and reflection at face AC. The refractive index of the material of the prism is :-

A)  \[1.5\]

B)  \[\frac{3}{\sqrt{2}}\]

C)  \[\sqrt{2}\]

D)  \[\frac{4}{3}\]

Correct Answer: B

Solution :

\[A=r+0\Rightarrow r={{30}^{o}}\] \[\therefore \] \[\mu =\frac{\sin i}{\sin r}=\frac{\sin {{45}^{o}}}{\sin {{30}^{o}}}=\sqrt{2}\]