Question

A $2cm$ high object is placed at a distance of $32cm$ from a concave mirror. The image is real inverted and $3cm$ in size. Find the focal length of the mirror and the position where the image is formed.

Answer 1

Given,

Object height, $h_o=2cm$

Object distance, $u=32cm$

Image height, $h_i=3cm$

Magnification, $m=\frac{h_i}{h_o}=-\frac{v}{u}$

$\Rightarrow$ $-\frac{3}{2}=\frac{-v}{-32}$

$\Rightarrow$ $v=-\frac{32\times 3}{2}$

$v=-48cm=$ Image distance

From mirror formula,

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

$\frac{1}{f}=-\frac{1}{48}-\frac{1}{32}$

$f=-19.2cm=$ focal length