In an experiment to find the focal length of a concave mirror,a graph is drawn between the magnitudes of $u$ and $v$. The graph looks like:

$A$ boy stands straight in front of a mirror at a distance of $30 \ cm$ away from it. He sees his erect image whose height is $\frac{1}{5}$ of his real height. The mirror he is using is

The shape of the image formed of an object $AB$ due to the concave mirror shown in the figure is best represented by (assume point $A$ is at the centre of curvature of the mirror):-

An object of size $7.5 \ cm$ is placed in front of a convex mirror of radius of curvature $25 \ cm$ at a distance of $40 \ cm$. The size of the image should be ........ $cm$.

If the distance between an object and its two times magnified virtual image produced by a curved mirror is $15 \,cm$, the focal length of the mirror must be:

$A$ $4.5 \;cm$ needle is placed $12 \;cm$ away from a convex mirror of focal length $15 \;cm$. Give the location of the image and the magnification. Describe what happens as the needle is moved farther from the mirror.