The minimum distance between the object and its real image for a concave mirror is

$A$ concave mirror is used to focus the image of a flower on a nearby wall $120 \ cm$ from the flower. If a lateral magnification of $16$ is desired,the distance of the flower from the mirror should be $... \ cm$.

The focal length of a concave mirror is $50 \, cm$. Where should an object be placed so that its image is two times magnified and inverted?

$A$ mirror is used to produce an image with magnification of $\frac{1}{4}$. If the distance between the object and its image is $40 \ cm$,then the focal length of the mirror is . . . . . . . (in $cm$)

$A$ concave mirror has a focal length of $30 \, cm$. If the image formed is erect (virtual),at what distance from the mirror should an object be placed so that the image is three times the size of the object (in $, cm$)?

$A$ concave mirror of radius of curvature $R$ has a circular outline of radius $r$. $A$ circular disc is to be placed normal to the axis at the focus,so that it collects all the light that is reflected from the mirror from a beam parallel to the axis. For $r \ll R$,the area of this disc has to be at least