Refraction at a Spherical Surface and Lenses - Refraction at Spherical Surfaces

A convex lens has a focal length of 10 cm. Find the location and nature of the image if a point object is placed on the principal axis at a distance of (a) 9.8 cm, (b) 10.2 cm from the lens.

A point object in the air is placed symmetrically at a distance of 60 cm in front of a concave spherical surface with a refractive index of 1.5. If the radius of curvature of the surface is 20 cm, find the position of the image formed.

A converging lens of focal length 15 cm and a converging mirror of focal length 10 cm are placed 50 cm apart with common principal axis. A point source is placed in between the lens and the mirror at a distance of 40 cm from the lens. Find the locations of the two images formed.

What type of wavefront will emerge from a (i) point source, and (ii) distance light source?

A ball is kept at a height h above the surface of a heavy transparent sphere made of a material of refractive index μ. The radius of the sphere is R. At t = 0, the ball is dropped to fall normally on the sphere. Find the speed of the image formed as a function of time for \[t < \sqrt{\frac{2h}{g}}\] . Consider only the image by a single refraction.

Define the critical angle for a given pair of media and total internal reflection. Obtain the relation between the critical angle and refractive index of the medium.

Use the above relation to obtain the condition on the position of the object and the radius of curvature in terms of n₁and n₂ when the real image is formed.

A point source of light is placed at a distance of 2 f from a converging lens of focal length f. The intensity on the other side of the lens is maximum at a distance