question_answer

A prims having refractive index 1.414 and refracting angle \[30{}^\circ \]has one of the refracting surfaces silvered A beam of light incident on the other refracting surface will retrace its path, if the angle of incidence is:

A) \[0{}^\circ \]                            

B) \[\frac{\pi }{6}\]

C) \[\frac{\pi }{3}\]                        

D) \[\frac{\pi }{4}\]

Correct Answer: D

Solution :

[d] Apply snell?s law at AB surface \[{{\mu }_{1}}Sini={{\mu }_{2}}Sinr\] \[1\,\sin i=1.41\,\sin \,30\] \[Sini\,=\sqrt{2}\frac{1}{2}\] \[Sini\,=\frac{1}{\sqrt{2}}\] \[i=45{}^\circ \,or\,\frac{\pi }{4}\] Note: Question asked in prism required basic knowledge of Geometry