Question

The distance CP is the:

(A). Center of curvature
(B). Radius of curvature
(C). Focal length
(D). None of these

Answer 1

Hint: There are three main types of mirrors: plane mirror, concave mirror, convex mirror. The mirror in which the reflecting surface is curved inwards is called the concave mirror. Different parameters associated with mirrors describe different image formations and image positions like pole, focus, radius of curvature etc.

Complete solution:
A concave mirror is curved inwards. The outer surface is polished while the inner surface acts as the surface for reflection. The different parameters which describe image formation are-pole, focus, radius of curvature and focal length etc.

The pole is the midpoint of the reflecting surface. It lies in the mirror.

The focus is a point on the axis of the mirror where rays travelling parallel to the axis, after reflection passes through the focus.
Focal length is the length of the line joining the pole and focus.

The radius of curvature is the radius of the circle of which the curved surface of the mirror forms a part of.

In the figure shown-

Since F or focus is the midpoint of CP, then CP is the radius of curvature as radius is two times the focal length. Therefore,
$R=2f$
Here,
$R$ is the radius of curvature
$f$ is the focal length
$\Rightarrow CP=2FP$

Therefore, the distance CP is the radius of curvature. Hence the correct option is (B).

Note:
By convention, all distances to the left of the mirror are taken as negative. Therefore, the focal length, object distance and radius of curvature of the concave mirror are negative. When it forms real images, the image distance is also taken as negative. For different positions of the object, concave mirrors can form real as well as virtual images.