Question

What is the refractive index of a prism whose angle $A={60}^o$ and angle of minimum deviation $d_m={30}^o$?

• A. $\sqrt{2}$
• B. $\frac{1}{\sqrt{2}}$
• C. $1$
• D. $\frac{1}{\sqrt{3}}$

Answer 1

Answer: (A)

$\sqrt{2}$

Given : $d_m={30}^o$ $A={60}^o$

Refractive index $\mu =\frac{\sin \left(\frac{A+d_m}{2}\right)}{\sin \frac{d_m}{2}}$

$\therefore$ $\mu =\frac{\sin \left(\frac{60+30}{2}\right)}{\sin \frac{60}{2}}$

$⟹$ $\mu =\frac{\sin {45}^o}{\sin {\frac{3}{0}}^o}=\frac{1/\sqrt{2}}{1/2}=\sqrt{2}$