A ray of light is incident on one face of an equilateral glass prism having refractive index \(\sqrt{2}\). It produces the emergent ray which just grazes along the adjacent face. The value of angle of incidence is

The emergent ray just grazes the second face.
Hence angle of emergence, \(\mathrm{e}=90^{\circ}\)
\(\begin{aligned} & \mu=\frac{\sin \mathrm{e}}{\sin r_2}=\frac{\sin 90^{\circ}}{\sin r_2}=\frac{1}{\sin r_2} \\ & \therefore \frac{1}{\sin r_2}=\sqrt{2} \text { or } \sin r_2=\frac{1}{\sqrt{2}}\end{aligned}\)
\(\begin{aligned} & \therefore \mathrm{r}_2=45^{\circ} ; \mathrm{A}=\mathrm{r}_1+\mathrm{r}_2 \\ & \therefore \mathrm{r}_1=\mathrm{A}-\mathrm{r}_2=60-45=15^{\circ}\end{aligned}\)
Also, \(\frac{\sin i}{\sin r_1}=\mu\)
\(\begin{aligned} & \therefore \sin \mathrm{i}=\mu \sin \mathrm{r}_1=\sqrt{2} \sin 15^{\circ} \\ & \therefore \mathrm{i}=\sin ^{-1}\left(\sqrt{2} \sin 15^{\circ}\right)\end{aligned}\)