Size of an object formed by …

We have to do calculations for both the concave and convex mirror as the type of mirror is not specified here.
For concave mirror:
Focal length, f = -20cm
Magnification, m = {tex} - \frac{1}{3}{/tex}
Since, magnification, m = {tex} - \frac{v}{u}{/tex}
Magnification, m = {tex} - \frac{1}{3} = - \frac{v}{u}{/tex}
{tex}\Rightarrow{/tex} v {tex} = \frac{u}{3}{/tex}
By mirror formula,
{tex}\frac{1}{f} = \frac{1}{v} + \frac{1}{u}{/tex}
{tex}\frac{1}{f} = \frac{3}{u} + \frac{1}{u} = \frac{4}{u}{/tex}{tex}\Rightarrow{/tex} u = 4f
= 4(-20) = -80cm
The placement of object should be at 80cm in front of the concave mirror.
For convex mirror:
Focal length, f = +20cm
Magnification, m = {tex}+\frac{1}{3}{/tex}
Since, magnification, m = {tex} - \frac{v}{u}{/tex}
Magnification, m = {tex}\frac{1}{3} = - \frac{v}{u}{/tex}
{tex}\Rightarrow{/tex} v = {tex} - \frac{u}{3}{/tex}
By mirror formula,
{tex}\frac{1}{f} = \frac{1}{v} + \frac{1}{u}{/tex}
{tex}\frac{1}{f} = \frac{{ - 3}}{u} + \frac{1}{u} = \frac{{ - 2}}{u} \Rightarrow - 2f{/tex}
= -2(20) = -40cm
The placement of an object should be at 40cm in front of the concave mirror, to get a diminished, virtual and erect image.