Explanation

(b) For an equilateral prism, angle of prism of refracting angle $A = 60{^\circ}$
Here, $\delta_{m} = A = 60{^\circ}$
$\therefore$ Refractive index,
$\mu = \frac{\sin{\ \left( \frac{A\ + \ \delta_{m}}{2} \right)}}{\sin\frac{A}{2}} = \frac{\sin{\ \left( \frac{60{^\circ}\ + \ 60{^\circ}}{2} \right)}}{\sin\left( \frac{60{^\circ}}{2} \right)}$
$\ \ \ = \frac{\sin{60{^\circ}}}{\sin{30{^\circ}}} = \frac{\sin{60{^\circ}}}{\cos{60{^\circ}}}$
$= \tan{60{^\circ}} = \sqrt{3}$