(i) Calculation of speed of light (ii) Calculation of angle of incidence at face AB (i) $\mu = \frac{ \sin\; \left( \frac{A+\delta_m}{2} \right) }{ \sin\; \left( \frac{A}{2} \right) }$ $\;=\; \frac{ \sin\; \left( \frac{60^{\circ}+30^{\circ}}{2} \right) }{ \sin\; \left( \frac{60^{\circ}}{2} \right) } = \sqrt{2}$$\;\text{ Also }\; \;\; \mu\;=\;\frac{c}{v} \Rightarrow v = \frac{3 \times 10^8}{\sqrt{2}} \text{m/s}$$v\;= 2.122 \times 10^8 \text{m/s}$ (ii) At face $AC$, let the angle of incidence be $r_2$. For grazing ray, $e = 90^{\circ}$ $\Rightarrow \;\; \mu = \frac{1}{\sin\; r_2} \Rightarrow r_2 = \sin^{-1}\left( \frac{1}{\sqrt{2}} \right) = 45^{\circ}$ Let angle of refraction at face $AB$ be $r_1$. Now $r_1 + r_2 = A$ $\therefore \;\; r_1 = A - r_2 = 60^{\circ} - 45^{\circ} = 15^{\circ}$ Let angle of incidence at this face be $i$ $\;\mu\;=\;\frac{ \sin\; i }{ \sin\; r_1 }$ $\Rightarrow \;\; \mu = \sqrt{2} = \frac{ \sin\; i }{ \sin\; 15^{\circ} }$ $\therefore \; i = \sin^{-1}\left( \sqrt{2} \cdot \sin\; 15^{\circ} \right)$