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 — B, R = 2f. For a spherical mirror the focal length is half the radius of curvature, so R = 2f (equivalently f = R/2). Paraxial rays travelling parallel to the principal axis converge at the focus F, which lies midway between the pole and the centre of curvature C.
- (a)R = f — R = f would place the focus at the centre of curvature; in fact the focus is halfway between the pole and C, so R is twice f.
- (c)R = 3f — There is no 3x relation — the geometry of reflection fixes the focus at exactly half the radius of curvature.
- (d)R = 4f — R = 4f overstates the ratio; the correct paraxial relation is R = 2f.
A spherical mirror is part of a sphere of radius R (its radius of curvature), whose centre is the centre of curvature C. Under the paraxial (small-angle) approximation, rays parallel to the axis reflect through the focus F, located midway between the pole P and C — hence f = R/2.
Recall the ray diagram — pole, then focus, then centre of curvature at double the distance. The focus sits halfway to C, giving R = 2f. This holds for both concave and convex mirrors.
- Focal length is half the radius of curvature — f = R/2, i.e. R = 2f.
- The focus F lies midway between the pole P and the centre of curvature C.
- The relation follows from the paraxial approximation for spherical mirrors.
- It applies to both concave and convex spherical mirrors.
The focus is halfway to the centre of curvature, so R = 2f — option (b).
- Writing R = f (placing the focus at C) instead of R = 2f.
- Applying the wrong sign convention when using the mirror formula.
Asked directly as the f–R relation or embedded in a mirror-formula numerical — remember f = R/2.
No directly related past PYQ was found.
- practice — not a real PYQ
A concave mirror has a radius of curvature of 20 cm. Its focal length is
- (a)5 cm
- (b)10 cm
- (c)20 cm
- (d)40 cm
Answer(b) 10 cm — f = R/2 = 20/2.
- practice — not a real PYQ
For a spherical mirror, the focus lies
- (a)at the centre of curvature
- (b)midway between the pole and the centre of curvature
- (c)at the pole
- (d)beyond the centre of curvature
Answer(b) midway between the pole and the centre of curvature — so R = 2f.