Question

A ray of light is incident at an angle ${60}^o$ on one face of a prism of angle ${80}^o$. The segment ray of light makes an angle of ${30}^o$ with incident ray. The angle made by the emergent ray with second face of prism will be

• A. $0^o$
• B. ${90}^o$
• C. ${45}^o$
• D. ${30}^o$

Answer 1

Answer: (A)

$0^o$

$\begin{array}{c}i={60}^{\circ }\\ A={80}^{\circ }\\ r_1={30}^{\circ }\end{array}$

$\begin{array}{c}\text{We know, in a prism}\\ \begin{array}{c}{r}_1+r_2=A\\ {30}^0+r_2={80}^{\circ }\\ r_2={50}^{\circ }\end{array}\end{array}$

$\begin{array}{c}\text{now, let refractive index of}\\ \text{prism is a}\mu \\ \text{then}\\ 1\times \sin i=\mu \sin r_1\\ \begin{array}{cc}\sin {60}^{\circ }& =\mu \times \sin {30}^{\circ }\\ \mu & =\sqrt{3}\end{array}\end{array}$

$\begin{array}{c}{a}^{\prime \prime 0}\\ \mu \times \sin r_2=1\times \sin e\\ e\to \text{emergent angle}\end{array}$

$\begin{array}{c}\Rightarrow \sqrt{3}\sin {50}^{\circ }=\sin e\\ 1.32,\text{which is not possible}\\ \text{because greater than}1\\ \therefore T:I\cdot R\text{will take place}\\ \text{ray will not emerge}\end{array}$

Hence, option $A$ is the correct answer.