Where should an object be placed in front of a concave mirror of focal length 15 cm to have a magnification of 3 in case of
(a) real image
(b) virtual image ?

Explanation

The mirror equation is given by `(1)/(v)+(1)/(u) = (1)/(f)`
(a) In case of real image
`m = (-v)/(u) = -3`
So, v = 3u
`(1)/(3u) + (1)/(u) = (1)/(-15)`
`rArr (4)/(3u) = (1)/(-15) rArr u = -20 cm`
(b) In case of virtual image
`m = (-v)/(u) = +3 , v = -3u`
`- (1)/(3u) + (1)/(u) = (1)/(-15)`
`rArr (2)/(3u) = (1)/(-15) rArr u = -10 cm`