The refractive index of the material of a prism is $\sqrt{2}$ and the angle of the prism is $30^\circ$. One of the two refracting surfaces of the prism is made a mirror inwards with a silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface) if the angle of incidence on the prism is:

A horizontal ray of light is incident on a right-angled prism with a prism angle of $6^{\circ}$. If the refractive index of the material of the prism is 1.5, then the angle of emergence will be:

A concave lens with a focal length of $-25 \text{ cm}$ is sandwiched between two convex lenses, each with a focal length of $40 \text{ cm}$. The power (in diopters) of the combined lens system would be:

The refracting angle of a prism is $A$, and the refractive index of the material of the prism is $\cot(A/2)$. The angle of minimum deviation is:

A small telescope has an objective of focal length $140\text{ cm}$ and an eyepiece of focal length $5.0\text{ cm}$. The magnifying power of the telescope for viewing a distant object is:

An astronomical telescope has an objective and eyepiece of focal lengths $40\text{ cm}$ and $4\text{ cm}$ respectively. To view an object $200\text{ cm}$ away from the objective, the lenses must be separated by a distance of:

A plano-convex lens fits exactly into a plano-concave lens. Their plane surfaces are parallel to each other. If lenses are made of different materials of refractive indices $\mu_1$ and $\mu_2$ and $R$ is the radius of curvature of the curved surface of the lenses, then the focal length of the combination is:

A double convex lens has a focal length of 25 cm. The radius of curvature of one of the surfaces is double of the other. What would be the radii if the refractive index of the material of the lens is 1.5?

The power of a biconvex lens is 10 dioptre and the radius of curvature of each surface is 10 cm. The refractive index of the material of the lens is: