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 \[A={{60}^{o}}\]and the refractive index of the material of prism is \[\sqrt{3},\]then the angle of deviation of the ray is

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

B)  \[{{45}^{o}}\]

C)  \[{{30}^{o}}\]

D)  None of these

Correct Answer: A

Solution :

 For a given prism, the angle of deviation depends upon the angle of incidence of the light rays falling on the prism. Taking triangle FQR, we have \[S=\angle FQR+\angle FRQ\] Since,\[\Delta AQR\] is an equilateral triangle, therefore, \[\angle FQR=\frac{{{60}^{o}}}{2}={{30}^{o}}=\angle FRQ\] \[\therefore \] \[\delta ={{30}^{o}}+{{30}^{o}}={{60}^{o}}\] Hence, angle of deviation of the ray is \[{{60}^{o}}.\]