Question

An object is placed at a distance of (i) 20 cm (ii) 5 cm in front of a converging lens of focal length 15 cm . Find the nature, position and magnification of the image in each case.

Answer 1

$\left(i\right)$

$u=-20cm$ and $f=15cm$

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

$⟹\frac{1}{v}=\frac{-1}{20}+\frac{1}{15}$

$⟹v=60cm$

Magnification is $m=\frac{v}{u}=-3$

Image formed is real, inverted and three times magnified.

$\left(ii\right)$

$u=-5cm$ and $f=15cm$

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

$⟹\frac{1}{v}=\frac{-1}{5}+\frac{1}{15}$

$⟹v=-7.5cm$

Magnification is $m=\frac{v}{u}=1.5$

Image formed is virtual, erect and $1.5$ times magnified.