Question

A dentist uses a small mirror that gives a magnification of $4$ when it is held $0.60$ cm from a tooth. Find the radius of curvature of the mirror.

Answer 1

Given:

Object distance $u=-0.60cm$ (Since the dentist-mirror is a concave mirror)

Magnification $m=+4$

Radius of curvature $R=?$

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

$\Rightarrow 4=+\frac{v}{0.60}$

$\Rightarrow v=4\times 0.60$

$\Rightarrow v=2.4cm$

From mirror formula, $\frac{1}{f}=\frac{2}{R}=\frac{1}{v}+\frac{1}{u}$

$\Rightarrow \frac{2}{R}=\frac{1}{2.4}-\frac{1}{0.60}=-1.25$

$\Rightarrow R=-\frac{2}{1.25}=-1.6cm$

So, the radius of curvature of the mirror is $1.6cm$.