Derive the relationship between the focal length and radius of curvature of a concave mirror.

Establish the relation between the radius of curvature $R$ and focal length $f$ of the spherical concave mirror.

An object is placed beyond the centre of curvature $C$ of the given concave mirror. If the distance of the object is $d_1$ from $C$ and the distance of the image formed is $d_2$ from $C,$ the radius of curvature of this mirror is:

An object is placed at $10 \mathrm{cm}$ distance infront of a concave mirror of radius of curvature $40 \mathrm{cm}$. Find the position, nature and magnification of the image.

An object is placed at a distance of $12 \mathrm{cm}$ from a convex lens. A convex mirror of focal length $15 \mathrm{cm}$ is placed on another side of the lens at $8 \mathrm{cm}$ as shown in the figure. The image of the object coincides with the object.

When the convex mirror is removed, a real and inverted image is formed at a position. The distance of the image from the object will be $\_\_\_ \mathrm{cm}$

A point object is moving uniformly towards the pole of a concave mirror of focal length $25 \mathrm{cm}$ along its axis as shown below. The speed of the object is $1 {\mathrm{ms}}^{-1}$. At $t=0$, the distance of the object from the mirror is $50 \mathrm{cm}$. The average velocity of the image formed by the mirror between time $t=0$ and $t=0.25 \mathrm{s}$ is: