Question

A spherical surface of radius of curvature R separates two media of refractive indices n₁ and n₂. A point object is placed in front of the surface at distance u in medium of refractive index n₁ and its image is formed by the surface at distance v, in the medium of refractive index n₂. Derive a relation between u and v.

A solid glass sphere of radius 6·0 cm has a small air bubble trapped at a distance 3·0 cm from its centre C as shown in the figure. The refractive index of the material of the sphere is 1·5. Find the apparent position of this bubble when seen through the surface of the sphere from an outside point E in air.

A lens is a transparent optical medium bounded by two surfaces; at least one of which should be spherical. Considering image formation by a single spherical surface successively at the two surfaces of a lens, lens maker's formula is obtained. It is useful to design lenses of desired focal length using surfaces of suitable radii of curvature. This formula helps us obtain a relation between u, v and f for a lens. Lenses form images of objects and they are used in a number of optical devices, for example microscopes and telescopes.

A point source in air is kept 24 cm in front of a concave spherical glass surface (ₐμg = 1.5) and radius of curvature 60 cm. Find the nature of the image formed and its distance from the point source.