Question

If refractive index of a material of equilateral prism is $\sqrt{3}$, then angle of minimum deviation of the prism is

• A. $30^{\circ}$
• B. $45^{\circ}$
• C. $60^{\circ}$
• D. $75^{\circ}$

Answer 1

Answer: (C)

$\mu=\frac{\sin \left(\frac{A+\delta_{m}}{2}\right)}{\sin \frac{A}{2}}$
$\sqrt{3}=\frac{\sin \left(\frac{60^{\circ}+\delta_{m}}{2}\right)}{\sin \frac{60^{\circ}}{2}}$
$\Rightarrow \frac{\sqrt{3}}{2}=\sin \left(30^{\circ}+\frac{\delta_{m}}{2}\right)$
$\Rightarrow \delta_{m}=60^{\circ}$