Question

At what distance from a concave mirror of focal length 10cm should an object be placed so that:
(a) its real image is formed 20 cm from the mirror?
(b) its virtual image is formed 20cm from the mirror?

Answer 1

(a) $f=10cm$
$v=20cm$ (real image)
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\frac{1}{-20}+\frac{1}{u}=\frac{1}{-10}$
$\frac{1}{u}=\frac{-1}{10}+\frac{-1}{20}=\frac{-1}{20}$
$u=-20cm$
(b)$f=10cm$
$v=20cm$ (virtual image)
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\frac{1}{20}+\frac{1}{u}=\frac{1}{-10}$
$\frac{1}{u}=\frac{-1}{10}+\frac{-1}{20}=\frac{-3}{20}$
$u=-\frac{20}{3}cm$