Question

A ray of monochromatic light is incident on one refracting face of a prism of angle ${75}^o$. 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 :

• A. ${30}^o$
• B. ${45}^o$
• C. ${60}^o$
• D. $0^o$

Answer 1

The correct option is B ${45}^o$

$\begin{array}{c}Criticalangle,C={\sin }^{-1}\left(\frac{1}{\mu }\right)\\ \therefore C={\sin }^{-1}\left(\frac{1}{\sqrt{2}}\right)\\ \therefore C={45}^0\\ A=r_1+r_2\\ {75}^0=r_1+45\\ \therefore r_1={30}^0\\ Now,\\ \frac{\sin i}{\sin r}=\mu \\ \therefore \frac{\sin i}{\frac{1}{2}}=\sqrt{2}\\ \therefore \sin i=\sqrt{2}\times \frac{1}{\sqrt{2}}=\sqrt{2}\\ \therefore i={45}^0\end{array}$