question_answer

A prism ABC of angle 30° has its face AC silvered. A ray of light incident at an angle of 45° 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 [MP PMT 1992; EAMCET 2001]

A)            1.5

B)            \[\frac{3}{\sqrt{2}}\]

C)            \[\sqrt{2}\]

D)            \[\frac{4}{3}\]

Correct Answer: C

Solution :

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