The correct relation between the radius of curvature R and focal length f of a spherical mirror is
- A.R = f
- B.R = 2f
- C.R = 3f
- D.R = 4f
Correct answer
Explanation
The correct answer is B, R = 2f. For a spherical mirror of small aperture, the radius of curvature is twice the focal length, so f = R/2.
The centre of curvature C is the centre of the sphere of which the mirror is a part, and the radius of curvature R is the distance from the pole P to C. Rays parallel to the principal axis, after reflection, meet at (or seem to come from) the principal focus F, which lies midway between P and C. So a concave mirror with R = 40 cm has a focal length of 20 cm. The relation holds for both concave and convex mirrors.
A is wrong because the focus is not at the centre of curvature; it is halfway to it.
C is wrong because R = 3f puts the focus at one-third of the radius, which does not happen.
D is wrong because R = 4f would put the focus at a quarter of the radius.
Exam tip: f = R/2; the principal focus lies midway between the pole and the centre of curvature.
Practice Questions
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