Question

An object of size $3cm$ is placed $14cm$ in front of a convex lens of focal length $21cm$. Find the nature and size of image.

Answer 1

Object height, $h_0=3cm$

Object distance, $u=-14cm$

Focal length, $f=21cm$

from lens formula,

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

$\frac{1}{21}=\frac{1}{v}-\frac{1}{-14}$

$\frac{1}{v}=\frac{1}{21}-\frac{1}{14}$

$\Rightarrow$ $\frac{1}{v}=\frac{14-21}{14\times 21}$

$=\frac{-7}{14\times 21}$

$v=-42cm$

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

$\Rightarrow$ $h_i=\frac{-42}{-14}\times 3$

$h_i=9cm$