Question

Define:
(a) Radius of curvature of a spherical mirror (b) Focal length of a spherical mirror.

Answer 1

Hint: The radius of curvature of a spherical mirror relates the closeness of the centre of curvature and the pole of the mirror. Focal length of a spherical mirror relates to the closeness of the focus of the mirror to the pole of the mirror.

Complete step-by-step answer:
The radius of curvature of a spherical mirror is the radius of the circle of which the spherical mirror is a part. It can also be defined as the distance between the centre of curvature of the mirror and the pole of the mirror on the principal axis. The radius of curvature is also a measure of how curved the mirror is. A spherical mirror with a smaller radius of curvature will be more curved than one with a larger radius of curvature.
The focal length of a spherical mirror is the distance between the pole of the mirror and the focus of the mirror on the principal axis. Rays parallel to the principal axis converge on the focus (for a concave mirror) or appear to diverge from the focus (for a convex mirror).
Note: Students must keep in mind that the focal length is half of the radius of curvature for spherical mirrors and lenses. This property comes in very handy in many numerical problems. For a plane mirror, the radius of curvature can be said to be infinity and hence, a plane mirror does not curve at all. The focus for a concave mirror is in front of the mirror (real focus) while for a convex mirror, it is behind the mirror (virtual focus) and hence, the respective focal lengths radii of curvatures of the two mirrors are measured in front and behind the mirrors respectively.