Velocity of light in diamond is \(\left(\frac{5}{12}\right)^{\text {th }}\) times that in air. Velocity of light in water is \(\left(\frac{3}{4}\right)^{\text {th }}\) times that in air. The angle of incidence of ray of light travelling from water to diamond is (angle of refraction \(\left.(r)=30^{\circ}\right)\left\lceil\right.\) Given \(\left.\rightarrow \sin 30^{\circ}=\frac{1}{2}\right\rceil\)

Given,
\(\mathrm{v}_{\mathrm{d}}=\frac{5}{12} \mathrm{c} \Rightarrow \frac{\mathrm{v}_{\mathrm{d}}}{\mathrm{c}}=\frac{5}{12}\) and \(\mathrm{v}_{\mathrm{w}}=\frac{3}{4} \mathrm{c} \Rightarrow \frac{\mathrm{v}_{\mathrm{w}}}{\mathrm{c}}=\frac{3}{4}\)
\({ }_w \mathrm{n}_{\mathrm{d}}=\frac{\mathrm{n}_{\mathrm{d}}}{\mathrm{n}_{\mathrm{w}}}=\frac{\frac{\mathrm{c}}{\mathrm{v}_{\mathrm{d}}}}{\frac{\mathrm{c}}{v_{\mathrm{w}}}}=\frac{\frac{12}{5}}{\frac{4}{3}}=\frac{12}{5} \times \frac{3}{4}=\frac{9}{5}\)
Using, \({ }_w \mathrm{n}_{\mathrm{d}}=\frac{\sin \mathrm{i}}{\sin \mathrm{r}}\)
\(\therefore \sin i={ }_w n_d \times \sin r=\frac{9}{5} \times \sin 30^{\circ}=\) \(\frac{9}{5} \times \frac{1}{2}=\frac{9}{10}\)
\(\therefore \quad i=\sin ^{-1}\left(\frac{9}{10}\right)\)