Question

There is a prism with refractive index equal to $\sqrt{2}$ and the refracting angle to ${30}^o$. One of the refracting surface of the prism is polished. A beam of monochromatic light will retrace its path if its angle of incidence over the first refracting surface of the prism is:-

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

Answer 1

The correct option is C ${45}^O$

$\begin{array}{c}\text{Light is retraced if it gets}\\ \text{reflected back normally.}\end{array}$

$\begin{array}{c}\text{we know,}\\ \begin{array}{cc}\angle A& =\angle r_1+\angle r_2\\ A& ={30}^{\circ },r_2=0^{\circ }\end{array}\\ \Rightarrow {30}^{\circ }=r_1+0^{\circ }\\ \Rightarrow r_1={30}^{\circ }\end{array}$

$\begin{array}{c}\text{at point}D\\ n_i\sin i=n_1\sin r_1\\ 1\times \sin i=\sqrt{2}\sin {30}^{\circ }\\ \sin i=\frac{1}{\sqrt{2}}\\ \Rightarrow i={45}^{\circ }\end{array}$