Question

Sol. [Key Concept: $\mu = \frac{c}{v} = \sqrt{2}$; the prism relation $\mu = \frac{\sin\frac{\delta_{m} + A}{2}}{\sin\frac{A}{2}}$ with $A{= 60}^{\circ}$ gives $\delta_{m}$.]

$${\mu = \frac{sin\left\lbrack \frac{\delta_{\text{min}\text{~}} + A}{2} \right\rbrack}{sin\frac{A}{2}} }{\mu = \frac{C}{V} = \frac{3 \times 10^{8}}{2.12 \times 10^{8}} = \sqrt{2} }{\sqrt{2} = \frac{sin\left\lbrack \frac{\delta_{\text{min}\text{~}} + 60^{\circ}}{2} \right\rbrack}{sin30^{\circ}} }{sin\left\lbrack \frac{\delta_{\text{min}\text{~}} + 60^{\circ}}{2} \right\rbrack = \frac{1}{\sqrt{2}} }{\delta_{\text{min}\text{~}} + 60^{\circ} = 90^{\circ} \Rightarrow \delta_{\text{min}\text{~}} = 30^{\circ} }$$