question_answer

The angle of a prism is 'A'. One of its refracting surfaces is silvered. Light rays falling at an angle of incidence 2A on the first surface returns back through the same path after suffering reflection at the silvered surface. The refractive index u, of the prism is:

A) 2 sin A             

B) 2 cos A

C) \[\frac{\cos  A}{2}\]                  

D) tan A

Correct Answer: B

Solution :

Apply snells law at PQ \[{{\mu }_{1}}\,\,\sin 2\operatorname{A}\,\,cosA={{\mu }_{2}}\sin \operatorname{A}\] \[{{\mu }_{1}}2\,\,\sin \operatorname{A}\,\,cosA={{\mu }_{2}}\sin \operatorname{A}\] \[1\times 2\,\,\cos A={{\mu }_{2}}\] \[{{\mu }_{2}}=2\cos \operatorname{A}\]