Question

Find the size of the image formed by a concave lens of focal length 20 cm when an
object having 4 cm height placed at a distance of 60 cm from it.

Answer 1

Given,

focal length, $f=20cm$

Object distnace, $u=60cm$

Object height, $h_0=4cm$

Lens is concave

Image height, $h_i=$?

From lens formula

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

$\because$ lens is concave; $f=-20cm$

$u=-60cm$

$-\frac{1}{20}=\frac{1}{v}-\frac{1}{(-60)}$

$\Rightarrow \frac{1}{v}=-\frac{1}{60}-\frac{1}{20}$

$=\frac{-4}{60}=\frac{-1}{15}$

$v=-15cm$

magnification, $m=\frac{h_i}{h_0}=+\frac{v}{u}$

$\Rightarrow h_i=+\left(\frac{-15}{-60}\right)4$

$h_i=1cm$