Question

If the radius of curvature of a spherical mirror is $20{\text{ cm}}$, then its focal length is _________ cm.
A. $20\,cm$
B. $40\,cm$
C. $10\,cm$
D. None of these

Answer 1

Hint: Spherical mirrors are cut from an imaginary sphere of radius $R$ and this is known as the radius of curvature of that mirror. Focal length is the distance between the focus point and the pole of the mirror. Use the relation between these two quantities to find the focal length.

Formula used:
For a spherical mirror,
$R = 2f$
where $R$ is the radius of curvature of the mirror and $f$ is the focal length of the mirror.

Complete step by step answer:
Spherical mirrors are imagined to be cut out from a sphere and the radius of this sphere is the radius of curvature of the spherical mirror. Focal length of a mirror is the distance between the focus and the pole (center) of the mirror.

It is given that the radius of curvature of a spherical mirror is given as $R = 20{\text{ cm}}$.We know that if the radius of curvature is positive then the spherical mirror is a convex mirror. We know that for a spherical mirror the focal length is half the radius of curvature of the mirror, that is $R = 2f$.
$f = \dfrac{R}{2}$
$\Rightarrow f = \dfrac{{20}}{2}{\text{ cm}}$
$\therefore f = 10{\text{ cm}}$

Hence, the correct option is C.

Note: Remember to use the sign convention of optics to measure the distances in problems from optics. According to the type of spherical mirror, the sign of the distances also differs. The focal length, radius of curvature of a convex mirror is positive and that of a concave mirror is negative.