The distance of an object from a spherical mirror is equal to the focal length of the mirror. Then the image:

An object is placed at a distance of $f$ from the pole of a convex mirror of focal length $f$. Where will the image be formed?

$A$ short object of length $L$ is placed along the principal axis of a concave mirror away from focus. The object distance is $u$. If the mirror has a focal length $f,$ what will be the length of the image? You may take $L << |u-f|$.

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 . . . . . $\text{cm s}^{-1}$.

$A$ virtual image larger than the object can be obtained by

Obtain the mirror equation for the real image formed by a concave mirror.