A cubical block of glass of refractive index ${\mathrm{n}}_1$ is in contact with the surface of water of refractive index ${\mathrm{n}}_2$. A beam of light is incident on vertical face of the block (see figure). After refraction, a total internal reflection at the base and refraction at the opposite vertical face, the ray emerges out at an angle $\mathrm{\theta }$. The value of $\mathrm{\theta }$ is given by-

 

A beam of diameter $\text{'}\mathrm{d}\text{'}$ is incident on a lass hemisphere as shown. If the radius of curvature of the hemisphere is very large in comparison to $\mathrm{d}$, then the diameter of the beam at the base the hemisphere will be:

A light ray hits the pole of a thin biconvex lens as shown in figure. The angle made by the emergent ray with the optic axis will be nearly 

The diagram shown five isosceles right angled prism. A light ray incident at $90°$ at the first face emerges at same angle with the normal from the last face. Which of the following relations will hold regarding the refractive indices?

A ray incident at an angle $53°$ on a prism emerges at an angle $37°$ as shown. If the angle of incidence is made $50°$, which of the following is a possible value or the angle of emergence?