The figure shows a ray incident at an angle $\mathrm{i} = \mathrm{\pi }/3$. If the plot drawn shows the variation
of $\left|\mathrm{r} - \mathrm{i}\right|$versus $\frac{{\mathrm{n}}_1}{{\mathrm{n}}_2} = \mathrm{k}$, ( r = angle of refraction).

For critical ray: ${\mathrm{n}}_2\left(\frac{\sqrt{3}}{2}\right) ={\mathrm{n}}_1\sin {90}^0$

$\frac{\mathit{s}\mathit{i}\mathit{n}\mathit{ }{\mathit{60}}^{\mathit{0}}}{\mathit{s}\mathit{i}\mathit{n}\mathit{ }{\mathit{90}}^{\mathit{0}}}\mathit{ }\mathit{=}\mathit{ }\frac{{\mathit{n}}_{\mathit{1}}}{{\mathit{n}}_{\mathit{2}}}\mathit{ }\mathit{\Rightarrow }\frac{\sqrt{\mathit{3}}}{\mathit{2}}\mathit{ }\mathit{=}\mathit{ }k$

$$\begin{gathered} \left(\mathrm{r} = \mathrm{i}\right) = \left({90}^0 - {60}^0\right) = {30}^0 \\ \Rightarrow {\mathrm{n}}_1 = \frac{\sqrt{3}}{2}, {\mathrm{\theta }}_1 = {30}^0 \end{gathered}$$

Deviation is zero for ${\mathrm{k}}_2 = 1$. For large k , the angle of emergence $\approx 0^0$ .
Therefore, ${\theta }_2 = {60}^0$ .