Question

A concave mirror has a radius of curvature of 24 cm. How far is the object from the mirror if the image formed is 3 times the size of object?

Answer 1

Given,

Radius of curvature, $R=24cm$

magnification, $m=3$

focal length, $f=\frac{R}{2}$

$=\frac{24}{2}$

$f=12cm$

We know

$m=-\frac{v}{u}$

$3=-\frac{v}{u}$

$\Rightarrow$ $v=-3u......\left(1\right)$

from mirror formula

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

$\frac{1}{-12}=\frac{1}{-3u}+\frac{1}{u}$ (from (1))

On solving

$u=-8cm$

The object will be $8cm$ from the mirror