$(a)$ Define radius of curvature and focal length of a spherical mirror and show it on a figure.
$(b)$ Write the relation between the radius of curvature and the focal length of a spherical mirror.

(N/A) Radius of curvature: The radius of the hollow sphere of which the reflecting surface of the spherical mirror forms a part is called the radius of curvature. It is denoted by $R$.
Focal length: The distance between the pole $(P)$ and the principal focus $(F)$ of a spherical mirror is called its focal length. It is denoted by $f$.
In the figure,$P$ is the pole,$F$ is the principal focus,and $C$ is the center of curvature. The distance $PC$ represents the radius of curvature $(R)$,and the distance $PF$ represents the focal length $(f)$.
$(b)$ Relation: For a spherical mirror of small aperture,the radius of curvature is twice the focal length. The mathematical relation is given by:
$f = \frac{R}{2}$ or $R = 2f$