Question

The radius of curvature of a convex mirror used on a moving automobile is $2m$. A truck is behind it at a constant distance of $3.5m$. Calculate the position, nature and size of the image relative to the size of the truck.

Answer 1

Given,

Radius of curvature, $R=2m$

object distance, $\mu =3.5m$

focal length, $f=\frac{R}{2}$

$=\frac{2}{2}$

$f=1m$

from mirror formula,

$\frac{1}{f}=\frac{-v}{\mu }$

$\frac{1}{1}=\frac{1}{v}-\frac{1}{3.5}$

$\Rightarrow \frac{1}{v}=1+\frac{1}{3.5}$

$\frac{1}{v}=\frac{9}{7}$

$v=\frac{7}{9}m=0.78m$

Magification, $m=-\frac{v}{\mu }$

$=+\frac{7}{9\times 3.5}$

$m=\frac{2}{9}=0.22$

Image will be formed at $0.78m$ & will be virtual crect and diminished.

Image will be $0.22$ times the truck.