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`?

Explanation

`u=-60 cm`
`m=+1/2`
`m=-v/u`
`1/2 =-v/60`
v = 30 cm
Using mirror formula, `1/u + 1/v = 1/f`
`-1/60 + 1/30 =1/f`
`1/f =(-1 +2)/60 = 1/60`
`rArr f = 60 cm`
To get the magnification 1/3
`m =-v/u =1/3`
`rArr v =-u/3`
Again using the mirror formula,
`1/u + 1/v = 1/f`
`1/u +1/(-u//3) = 1/60`
`1/u-1/3 =1/60`
`(1-3)/u =1/60`
`=-2/u =1/60` `rArr u=-120 cm`