Question

The refractive index of the material of a prism is $\sqrt{2}$ and the angle of the prism is ${30}^0$. One of the two refracting surfaces of the prism is made a mirror facing inwards by silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface), if its angle of incidence on the prism is

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

Answer 1

The correct option is B ${45}^0$


$r_2=0°r_1=A=30°\sin i=\mu \sin r\sin i=\sqrt{2}\sin 30°=\sqrt{2}\times \frac{1}{2}=\frac{1}{\sqrt{2}}\sin i=\frac{1}{\sqrt{2}}\angle i=45°$