An automobile's rear-view convex mirror has a 4.00m radius of curvature. Find the location of the image if a bus is 5.00m away from this mirror.

Radius of curvature, R = + 3.00 m
Object distance, u = – 5.00 m (The object is always considered to be on the left side of the mirror)
Image distance (v) =?

Focal length, $\mathrm{f} = \frac{\mathrm{R}}{2} = \frac{4}{2}= + 2 \mathrm{m}$

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

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

$\Rightarrow \frac{1}{\mathrm{v}} =+\frac{1}{2}-\frac{1}{(-5.00)}$

$\Rightarrow \frac{1}{\mathrm{v}}=\frac{1}{2}+\frac{1}{5.00}$

$\Rightarrow \mathrm{v}=\frac{10}{7}$

$\therefore \mathrm{v} =+1.47 \mathrm{m}$

Therefore, the image will be formed at a distance of 1.47 m from the mirror. The positive sign indicates that the image will be on the right side of the mirror.