Question

The focal length of a convex mirror is 20cm, its radius of curvature will be:
(A) 10cm
(B) 20cm
(C) 30cm
(D) 40cm

Answer 1

Hint
We know that focal length is the point on the principle axis of a spherical mirror where the light rays coming from infinity parallel to the axis meet. We also know that focal length is the half the numerical value of the radius of curvature.

Complete step by step answer
We know that the radius of curvature is the radius of the spherical mirror if it were a whole sphere. The radius of curvature is double the numerical value of the focal length of a spherical mirror.
(The focal length is a point on the principal axis where rays coming parallel to the axis from infinity meet.)
Therefore, the radius of curvature $ = 2x$ (focal length) $ = 2x20 = 40cm$
Therefore, the answer is option (D); 40 cm.

Note
If the mirror might have been concave, the value of focal length would have been negative, in that case the radius of curvature is also negative.
Also, one sometimes instead of doubling the value half it, therefore one should be alert while calculating.