Question

Define centre of curvature of a spherical mirror. How is it related to focal length of the mirror?

Answer 1

Hint: Start by defining mirror and spherical mirror. Then define types of spherical mirrors. Tell what is the centre of curvature of the spherical mirror and also define radius of curvature. Write the expression for radius of curvature in terms of its focal length.

Complete step by step solution:
A mirror is a surface which reflects light and produces an image of the object placed in front of it. A mirror can be of any shape: plane or curved. Curved mirrors are of two types, one which converge parallel incident rays of light and second those that diverge parallel incident rays of light. Spherical mirrors are the curved mirrors which are sliced from a reflecting sphere.
Spherical mirrors which converge the parallel incident rays of light and those diverge parallel incident rays of light are known as concave and convex mirrors respectively.
Centre of curvature of a spherical mirror is defined as the centre of the sphere of which the spherical mirror is a part. In other words, it is the centre of the sphere from which the spherical mirror is sliced.
The distance from the centre of curvature of the mirror to the pole of the mirror is equivalent to radius of the sphere. The distance from the pole to the center of curvature is called the radius of curvature ($R$).
The point where reflected ray converges or appears to be diverging from is known as focus of the mirror and its distance from the pole is known as focal length ($f$). The focal length of a spherical mirror is approximately half of its radius of curvature.
$R=2f$

Note: Spherical mirrors are sliced from the sphere. Usually, such a mirror is not a complete sphere.
The focal length of a spherical mirror is approximately half of its radius of curvature.
Centre of curvature of a spherical mirror is defined as the centre of the sphere of which the spherical mirror is a part.