question_answer

A ray of monochromatic light is incident on one refracting face of a prism of angle 75°. It passes through the prism and is incident on the other face at the critical angle. If the refractive index of the material of the prism is \[\sqrt{2}\], the angle of incidence on the first face of the prism is [EAMCET 1983]

A)            30°

B)            45°

C)            60°

D)            0°

Correct Answer: B

Solution :

                   From figure \[A={{r}_{1}}+c={{r}_{1}}+{{\sin }^{-1}}\left( \frac{1}{\mu } \right)\]                    \[\Rightarrow {{r}_{1}}=75-{{\sin }^{-1}}\left( \frac{1}{\mu } \right)\]                    \[\Rightarrow 75-45={{30}^{o}}\]                    From Snell?s law At B            \[\mu =\frac{\sin i}{\sin {{r}_{1}}}\]\[\Rightarrow \sqrt{2}=\frac{\sin i}{\sin {{30}^{o}}}\]\[\Rightarrow i={{45}^{o}}\]