Question

A monochromatic light ray is incident at an angle ${60}^{\circ }$ to a face of a transparent trihedral prism having a refractive index of $\sqrt{3}.$ Having undergone double refraction, the ray emerges in a direction normal to its face. Angle of prism is -

• A. ${37}^{\circ }$
• B. ${30}^{\circ }$
• C. ${45}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

Answer: (D)

${60}^{\circ }$

$\begin{array}{c}i={60}^{\circ }\\ \mu =\sqrt{3}\\ A=?\\ \text{snell's law}\\ \mu =\frac{\sin i}{\sin r}\\ \sqrt{3}=\frac{\sin 60}{\sin r}\end{array}$ .

$\begin{array}{cc}\sin r_1& =\frac{\sqrt{3}}{2}\times \sqrt{3}\\ r_1& ={30}^{\circ }\end{array}$

$\begin{array}{c}{r}_2=90\text{vertically given opposite angle}\end{array}$

$\begin{array}{cc}\angle D& =180-90-30\\ & ={60}^{\circ }\\ \therefore \angle A& =\angle D={60}^{\circ }\end{array}$