Question

A convex mirror used for rearview on an automobile has a radius of curvature of 10 m. If a bus is 5 m away from this mirror, the position of the image of the bus is _________ m behind the mirror.

• A. 2.5

Answer 1

The correct option is A 2.5
On using the sign conventions, we get,
Object distance, u = –5 m (always negative)
Radius of curvature, R = 10 m
Focal length, f = R/2 = 10/2 = 5 m
By applying the mirror formula, we get,
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\frac{1}{v}+\frac{1}{-5}=\frac{1}{5}\Rightarrow \frac{1}{v}=\frac{1}{5}+\frac{1}{5}$
$v=2.5m$
The image is formed 2.5 m behind the mirror.