An object is placed at a distance of 30 cm from a convex mirror. The magnification produced is 12. What should be the position of the object to get the magnification of 13?

The object should be placed

60 cm

from the convex mirror to get a magnification of

\frac{1}{3}

.
Given,

u_{1} = - 30 cm

m = \frac{1}{2}

The formula of magnification is given as

m = - \frac{v_{1}}{u_{1}}

\Rightarrow \frac{1}{2} = - \frac{v_{1}}{- 30}

\Rightarrow v_{1} = + 15 cm

Using mirror formula

\frac{1}{f} = \frac{1}{u_{1}} + \frac{1}{v_{1}}

\Rightarrow \frac{1}{f} = \frac{1}{- 30} + \frac{1}{15}

\Rightarrow

f = + 30 cm

………..(1)
Again,

m' = - \frac{v_{2}}{u_{2}}

\Rightarrow \frac{1}{3} = - \frac{v_{2}}{u_{2}}

\Rightarrow v_{2} = - \frac{u_{2}}{3}

………….(2)
Using mirror formula again

\frac{1}{f} = \frac{1}{u_{2}} + \frac{1}{v_{2}}

Using equations (1) and (2)

\frac{1}{30} = \frac{1}{u_{2}} - \frac{3}{u_{2}}

\Rightarrow \frac{1}{30} = - \frac{2}{u_{2}}

\Rightarrow

u_{2} = - 60 cm

An object is placed at a distance of $30 cm$ from a convex mirror. The magnification produced is $\frac{1}{2}$ . What should be the position of the object to get the magnification of $\frac{1}{3}$ ?