Question

A convex mirror used as a rear-view mirror in a car has a radius of curvature of 3 m. If a bus is located at a distance of 5 m from this mirror, find the position of image. What is the nature of the image?

Answer 1

Given,
The mirror is convex.

Distance of the object from the mirror 'u' = -5 m
Radius of curvature of the mirror 'R' = 3 m

Focal length of the convex mirror 'f' = $\frac{\mathrm{R}}{2}$ = 1.5 m

We have to find the position of the image 'v', and its magnification 'm'.
Using the mirror formula, we get

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

$\Rightarrow \frac{1}{1.5}=\frac{1}{v}+\frac{1}{-5}$

$\Rightarrow \frac{10}{15}+\frac{1}{5}=\frac{1}{v}$

$$\begin{gathered} \Rightarrow \frac{10}{15}+\frac{3}{15}=\frac{1}{v} \\ \Rightarrow \frac{1}{v}=\frac{13}{15} \end{gathered}$$

$\Rightarrow \mathrm{v}=\frac{15}{13}=1.15\mathrm{m}$
Thus, the distance of the image 'v' is 1.15 m behind the mirror.
Now, using the magnification formula, we get

$m=\frac{-v}{u}$
$m=\frac{-\left(1.15\right)}{-5}=\frac{115}{500}=0.223$
Thus, the image is virtual, erect and smaller in size.