Question

How far should an object be placed from the pole of converging mirror of focal length $20cm$ to from a real image of the size exactly $\frac{1}{4}th$ the size of the object?

Answer 1

For converging mirror we know that magnification $m=-v/u$ and real images formed by concave mirror are inverted so, $-1/4=v/-u\Rightarrow v=u/4$

Using these in the mirror formula : $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

$\frac{-4}{u}+\frac{-1}{u}=\frac{-1}{20}$

$\frac{5}{u}=\frac{1}{20}$

This gives $u=5\times 20=100cm$