Question

An object placed 12 cm from the pole of a concave mirror produces a real image magnified four times. Find the radius of curvature of the mirror. $(f-9.6cm,R=-19.2cm)$

Answer 1

Given,

Object distance, $u=12cm$

magnification, $m=4$

We know,

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

$-4=\frac{-v}{-12}$

$v=-48cm$

from mirror formula

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

$=-\frac{1}{48}-\frac{1}{12}$

$=-\left[\frac{12+48}{12\times 48}\right]$

$=-\left[\frac{5}{48}\right]$

$f=-9.6cm$

Radius of curvature, $R=2f$

$=-2\times 9.6$

$R=-19.2cm$