When an object is placed at a distance of `60 cm` from a convex spherical mirror, the magnification produced is `1//2`. Where should the object be placed to get a magnification of `1//3` ?

Answer

`- 120 cm`

Explanation

Here, `u_(1) = -60 cm, m_(1) = (1)/(2)`
`u_(2) = ?, m_(2) = (1)/(3)`
If `f` is focal length of convex mirror, then from
`m = (f)/(f - u) , (1)/(2) = (f)/(f + 60)` …(i)
`(1)/(3) = (f)/( f + u_(2))` ….(ii)
From (i), `2f = f + 60, f = 60 cm`
From (ii), `f + u_(2) = 3f`
`u_(2) = 2f = 2 xx 60 = 120 cm`