question_answer

A ray PQ incident on the refracting face BA is refracted in the prism BAC as shown in the figure and emerges from the other refracting face AC as RS such that \[AQ=AR\]. If the angle of prism \[A=60{}^\circ \] and the refractive index of the material of prism is \[\sqrt{3},\] then the angle of deviation of the ray is

A) \[60{}^\circ \]                    

B) \[45{}^\circ \]

C) \[30{}^\circ \]                    

D) None of these

Correct Answer: A

Solution :

            

Given \[AQ=AR\]and \[\angle A=60{}^\circ \]

\[\therefore \,\,\angle AQR=\angle ARQ=60{}^\circ \]

\[\therefore \,\,\,{{r}_{1}}={{r}_{2}}=30{}^\circ \]

Applying Snell's law on face AB.

1. \[\sin \,{{i}_{1}}=\mu \,\sin \,{{r}_{1}}\]

\[\Rightarrow \,\,\sin {{i}_{1}}=\sqrt[{}]{3}\sin 30{}^\circ =\sqrt{3}\times \frac{1}{2}=\frac{\sqrt{3}}{2}\]

\[\therefore \,\,{{i}_{1}}=60{}^\circ \]

Similarly, \[{{i}_{2}}=60{}^\circ \]

In a prism, deviation \[\delta ={{i}_{1}}+{{i}_{2}}-A=60{}^\circ +60{}^\circ -60{}^\circ =60{}^\circ \]