Question

For a spherical mirror, the radius of curvature $R$ and focal length $f$are correlated as,

• A. $f=2R$
• B. $R=2f$
• C. $R=\frac{f}{2}$
• D. $R=f$

Answer 1

The correct option is B

$R=2f$

The explanation for correct option:

1. Radius of curvature of a spherical mirror is the radius of the sphere from which the mirror has been cut.
2. Focus is the point on the principal axis of the mirror where the light rays parallel to the principal axis, after reflection, converge.
3. Focal length is the distance between the pole and the focus of the mirror.
4. For a spherical mirror of a small aperture, the focus lies exactly midway between the pole and centre of curvature.
5. It means the radius of curvature is twice of the focal length.
6. Mathematically, $R=2f$.

Hence, option (b) is correct.