The focal length of a concave mirror is `30`cm.Find the position of the object in front of the mirror,so that the image is there times the size of the objects.

Explanation

As the object is in front of the mirror it is real and for real object the magnified image formed by concave mirror can be inverted (i.e., real) or erect (i.e., virtual), so there are two possibilities.
(a) If the image is inverted (i.e., real)
`m = (f)/(f-u) implies -3 = (-30)/(-30-u) implies u = -40` cm
Object must be at a distance of `40` cm in frond of the mirror (in between `C` and `F`).

(b) If the image is erect (i.e., virtual) `m = (f)/(f-u) implies 3 (-30)/(-30-u) implies u = -20`cm
Object must be at a distance of `20` cm in front of the mirror ( in between `F` and `P`).