What will be the height of the image when an object of height $2 \ mm$ is placed on the principal axis of a convex mirror (of radius of curvature $40 \ cm$) at a distance of $20 \ cm$ from the mirror?

The primary purpose of using a parabolic mirror in a reflecting telescope is

Derive the relationship between the focal length $(f)$ and the radius of curvature $(R)$ for a spherical mirror.

An object and a concave mirror of focal length $f=10 \text{ cm}$ both move along the principal axis of the mirror with constant speeds. The object moves with speed $V_0=15 \text{ cm s}^{-1}$ towards the mirror with respect to a laboratory frame. The distance between the object and the mirror at a given moment is denoted by $u$. When $u=30 \text{ cm}$,the speed of the mirror $V_m$ is such that the image is instantaneously at rest with respect to the laboratory frame,and the object forms a real image. The magnitude of $V_m$ is . . . . . $\text{cm s}^{-1}$.

An object is placed at the principal focus of a convex mirror. The image will be at

An object is placed at $20 \ cm$ in front of a concave mirror,which produces a three times magnified real image. What is the focal length of the concave mirror (in $cm$)?