A 5 cm tall object is placed 1 m away from a concave mirror. If the radius of curvature of the mirror is 20 cm then find the image distance.

The radius of curvature, R = -20 cm (The radius of curvature of a concave mirror is on the left side of the mirror )
Object-distance, u = – 1m= -100cm (The object is always considered to be on the left side of the mirror)
Height = 5 cm
Image-distance (v) =?

Focal length, $\mathrm{f} = \frac{\mathrm{R}}{2} = \frac{-20}{2}= - 10 c\mathrm{m}$

Mirror formula: $\frac{1}{\mathrm{v}}+\frac{1}{\mathrm{u}}=\frac{1}{\mathrm{f}}$

$\Rightarrow \frac{1}{\mathrm{v}}=\frac{1}{\mathrm{f}}-\frac{1}{\mathrm{u}}$

$\Rightarrow \frac{1}{\mathrm{v}} =-\frac{1}{10}-\frac{1}{(-100)}$

$\Rightarrow \frac{1}{\mathrm{v}}=-\frac{1}{10}+\frac{1}{100}= \frac{-9}{100}$

$\Rightarrow \mathrm{v}=\frac{-100}{9}$

$\therefore \mathrm{v} =-11. 1 \mathrm{cm}$

Therefore, the image will be formed at a distance of -11.1 cm from the mirror. The negative sign indicates that the image will be on the left side of the mirror.