The image formed by a convex mirror of focal length $30 \,cm$ is a quarter of the size of the object. The distance of the object from the mirror is (in $\,cm$)

$A$ thin rod of length $f/3$ lies along the axis of a concave mirror of focal length $f$. One end of its magnified image touches an end of the rod. The length of the image is

Consider a light source placed at a distance of $1.5 \ m$ along the axis facing the convex side of a spherical mirror of radius of curvature $1 \ m$. The position $(s^{\prime})$,nature and magnification $(m)$ of the image are

The graph between $u$ and $v$ for a convex mirror is

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

$A$ person wants a real image of his own,$3$ times enlarged. Where should he stand in front of a concave mirror of radius of curvature $30 \ cm$ (in $cm$)?