Question

What is the refractive index of a prism whose angle $A={60}^o$ and angle of minimum deviation $d_m={80}^o?$

• A. $\sqrt{2}$
• B. ${\sin }^{-1}\left(\sqrt{3}\right)$
• C. ${\tan }^{-1}\left(\sqrt{2}\right)$
• D. ${\tan }^{-1}\left(\sqrt{3}\right)$

Answer 1

Answer: (A)

$\sqrt{2}$

Refractive index of prism

$\mu =\frac{\sin \frac{A+\sigma m}{2}}{\sin A/2}$

$=\frac{\sin \frac{{60}^o+{30}^o}{2}}{\sin \frac{60}{2}}$

$=\frac{\sin {45}^o}{\sin {30}^o}=\frac{\frac{1}{\sqrt{2}}}{\frac{1}{2}}=\sqrt{2}$