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,                 \[\angle FQR=\frac{{{60}^{o}}}{2}={{30}^{o}}=\angle FRQ\] Hence, angle of deviation of the ray is\[{{60}^{o}}\].