The figures represent three cases of a ray passing through a prism of angle $A$. The case corresponding to minimum deviation is

$A$ monochromatic light is incident from air on a refracting surface of a prism of angle $A = 75^{\circ}$ and refractive index $n_0 = \sqrt{3}$. The other refracting surface of the prism is coated by a thin film of material of refractive index $n$ as shown in the figure. The light suffers total internal reflection at the coated prism surface for an incidence angle of $\theta \leq 60^{\circ}$. The value of $n^2$ is:

The refractive index of the material of a glass prism is $\sqrt{3}$. The angle of minimum deviation is equal to the angle of the prism. What is the angle of the prism (in $^{\circ}$)?

The angle of incidence for an equilateral prism is $45^{\circ}$. What should be the refractive index of the prism material so that the ray is parallel to the base inside the prism?

Two equilateral-triangular prisms $P_1$ and $P_2$ are kept with their sides parallel to each other,in vacuum,as shown in the figure. $A$ light ray enters prism $P_1$ at an angle of incidence $\theta$ such that the outgoing ray undergoes minimum deviation in prism $P_2$. If the respective refractive indices of $P_1$ and $P_2$ are $\sqrt{\frac{3}{2}}$ and $\sqrt{3}$,then $\theta = \sin^{-1}\left[\sqrt{\frac{3}{2}} \sin \left(\frac{\pi}{\beta}\right)\right]$,where the value of $\beta$ is:

The refractive index of a prism is $\sqrt{2}$ and the angle of the prism is $30^\circ$. One of the refracting surfaces of the prism is polished. $A$ monochromatic beam of light enters the prism and retraces its path. What is the angle of incidence at the first refracting surface of the prism in degrees (in $^\circ$)?