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

Here, `mu_1 = -60 cm, m_1 = (1)/(2)`
`mu_2 = ?, mu_1 = (1)/(3)`
As `m_1 = -(v_1)/(u_1) :. (1)/(2) = -(v_1)/(-(-60)), v_1 = 30 cm`
From `(1)/(f)=(1)/(v_1)+(1)/(u_1)=(1)/(30)-(1)/(60)=(1)/(60)`
`f = 60 cm`
Again, `m_2 = -(v_2)/(u_2) = (1)/(3), v_2 = -(u_2)/(3)`
From `(1)/(v_2)+(1)/(u_2) = (1)/(f)`
`(1)/(u_2)=(1)/(f)-(1)/(v_2)=(1)/(60)+(3)/(u_2)`
or `(1)/(u_2)-(3)/(u_2)=(1)/(60), u_2 = -120 cm`.