Explanation

(b) Here, $A = 60{^\circ},\ \mu = \ \sqrt{2}$
Now,
$\mu = \frac{\sin\left( \frac{A\ + \ \delta_{m}}{2} \right)}{\sin\left( \frac{A}{2} \right)}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ldots(i)$
Substituting given values in Eq. (i) , we get
$\sqrt{2} = \ \frac{\sin\left( \frac{60{^\circ}\ + \ \delta_{m}}{2} \right)}{\sin\left( \frac{60{^\circ}}{2} \right)}$
$Or\ \sin{\left( 30{^\circ} + \frac{\delta_{m}}{2} \right) = \sqrt{2}\ \sin{30{^\circ}}}$
$Or\ \ \sin\left( 30{^\circ} + \frac{\delta_{m}}{2} \right) = \sqrt{2} \times \frac{1}{2} = \frac{1}{\sqrt{2}}$
$Or\ \ \sin\left( 30{^\circ} + \frac{\delta_{m}}{2} \right) = 45{^\circ}$
$Or\ \left( 30{^\circ} + \frac{\delta_{m}}{2} \right) = \sin{45{^\circ}}$
$Or\ \ \delta_{m} = 30{^\circ}$
$\therefore Angle\ of\ incidnece\ i = \frac{A + \delta_{m}}{2}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{60{^\circ} + 30{^\circ}}{2} = 30{^\circ}$