Question

A convex mirror with a radius of curvature of $3m$ is a used as rear view mirror for a vehicle. If a bus is located at $5m$ from this mirror, find the position, nature and size of the image.

Answer 1

$R=+3m\Rightarrow f=\frac{+3}{2}m$

$U=-5m$

By Mirror formula:

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}\Rightarrow \frac{1}{v}+\frac{1}{(-5)}=\frac{2}{5}$

$\Rightarrow \frac{1}{v}=\frac{2}{3}+\frac{1}{3}$

$\frac{1}{v}=\frac{13}{15}$

$\Rightarrow v=\frac{15}{13}\simeq 1.1538m$ behind the mirror

$m=\frac{h_I}{h_o}=-\left(\frac{v}{u}\right)\Rightarrow h_I=\left(\frac{-v}{u}\right)h_o$

$h_I=(\frac{15}{13}\times \frac{1}{\left(1.5\right)})h_o$

$h_I=\frac{3h_o}{13}$ ie. diminished & virtual & erect