question_answer

Angle of a prism is 30° and its refractive index is \[\sqrt{2}\] and one of the surface is silvered. At what angle of incidence, a ray should be incident on one surface so that after reflection from the silvered surface, it retraces its path [MP PMT 1991; UPSEAT 2001; CBSE PMT 2004]

A)            30°

B)            60°

C)            45°

D)            \[{{\sin }^{-1}}\sqrt{1.5}\]

Correct Answer: C

Solution :

                   \[A=r+0\]\[\Rightarrow r={{30}^{o}}\] From Snell?s law at surface AB \[\mu =\frac{\sin i}{\sin r}\]                                                          \[\Rightarrow \sqrt{2}=\frac{\sin i}{\sin {{30}^{o}}}\Rightarrow i={{45}^{o}}\]