question_answer

One of the refracting surfaces of a prism of angle \[{{30}^{o}}\] is silvered. A ray of light incident at an angle of \[{{60}^{o}}\]retraces its path. The refractive index of the material of prism is :-

A)  \[\sqrt{3}\]                                       

B)  \[\frac{3}{2}\]

C)  \[2\]                            

D)  \[\sqrt{3}\]

Correct Answer: D

Solution :

As is clear from fig., \[A={{30}^{o}},\,\,{{i}_{1}}={{60}^{o}},\] As the ray retraces its path on reflection at the silvered face, therefore,             \[{{i}_{2}}=0,\,\,{{r}_{2}}=0\] As    \[{{r}_{1}}+{{r}_{2}}=A\] \[\therefore \]      \[{{r}_{1}}+0={{30}^{o}}\] or \[{{r}_{1}}={{30}^{o}}\] \[\mu =\frac{\sin {{i}_{1}}}{\sin {{r}_{1}}}=\frac{\sin {{60}^{o}}}{\sin {{30}^{o}}}=\frac{\sqrt{3}/2}{1/2}=\sqrt{3}\]