The focal length of a concave mirror is $50 \ cm$. At what distance (in $cm$) should an object be placed to obtain a real and inverted image of double the size?

If the lateral magnification is $-2$ for a virtual object in a spherical mirror,then:

Two objects $A$ and $B$ are placed at $15\,cm$ and $25\,cm$ from the pole in front of a concave mirror having a radius of curvature $40\,cm$. The distance between the images formed by the mirror is $..........\,cm$.

$A$ 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 $cm$)?

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

$A$ diminished virtual image can be formed only in