$A$ ray of light incident on a glass sphere (refractive index $\sqrt{3}$) suffers total internal reflection before emerging out exactly parallel to the incident ray. The angle of incidence was (in $^{\circ}$)

$A$ ray is incident on a prism $ABC$ and travels as shown in the figure. The minimum refractive index of the material of the prism should be .......

As shown in the figure,a light ray $P$ enters a slab at an angle of $60^{\circ}$ with the normal. Inside the slab,the light ray $Q$ undergoes total internal reflection at the vertical face. Find the minimum refractive index of the slab.

Total internal reflection of light is possible when light enters from

The phenomenon utilised in an optical fibre is

At the interface between two materials having refractive indices $n_1$ and $n_2$,the critical angle for reflection of an electromagnetic wave is $\theta_{1C}$. The $n_2$ material is replaced by another material having refractive index $n_3$,such that the critical angle at the interface between $n_1$ and $n_3$ materials is $\theta_{2C}$. If $n_3 > n_2 > n_1$,$\frac{n_2}{n_3} = \frac{2}{5}$,and $\sin \theta_{2C} - \sin \theta_{1C} = \frac{1}{2}$,then $\theta_{1C}$ is: