Question

An object is $24cm$ away from a concave mirror and its image is $16cm$ from the mirror. Find the focal length and radius of curvature of the mirror, and the magnification of the image.

Answer 1

Given

Object distance, $u=24cm$

Image distance, $v=16cm$

From mirror formula

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

$\frac{1}{f}=-\frac{1}{16}-\frac{1}{24}$

$=-\left(\frac{24+16}{16\times 24}\right)$

$-\frac{10}{24}$

$f=9.6cm$= focal length

Radius of cuvature $R=2f$

$=2\times -9.6$

$=-19.2cm$

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

$=-\frac{-16}{-24}$

$m=-\frac{2}{3}$