A transparent solid cylindrical rod (refractive index $\displaystyle \frac{2}{\sqrt{3}}$ ) is kept in air. A ray of light incident on its face travels along the surface of the rod, as shown in figure. Calculate the angle $\displaystyle \theta$.

For critical Angle \[\begin{aligned} & \frac{\mathrm{n}_{2}}{\mathrm{n}_{1}}=\frac{1}{\sin \theta_{c}} \\ & \mathrm{n}_{1}=1 \quad \mathrm{n}_{2}=\frac{2}{\sqrt{3}} \quad \text { (given) } \\ & \frac{2}{\sqrt{3}}=\frac{1}{\sin \theta_{c}} \\ & \sin \theta_{c}=\frac{\sqrt{3}}{2} \\ & \theta_{c}=60^{\circ} \\ & r=90-\theta_{c} \\ & =30^{\circ} \end{aligned} \] From Snell's law at air rod interface \(\displaystyle \mathrm{n}_{1} \sin i=\mathrm{n}_{2} \sin r\)