Question

An object is placed at 30 m in front of a concave mirror. If its radius of curvature is 20 m, then what will be its image distance?

• A. -7 m
• B. +15 m
• C. -15 m
• D. +7 m

Answer 1

The correct option is C -15 m

Given, distance of the object from the mirror, $u=-30m$ (as the object is on the left side of the mirror, the sign of u is negative) and radius of curvature, $R=20m$
We know, focal length, $f=\frac{R}{2}$ = $\frac{20}{2}$ $=10m$
For concave mirror, $f$ is negative, i.e $f=-10m$
Let the image distance be $v$

Using mirror formula
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\frac{1}{v}+\frac{1}{-30}=\frac{-1}{10}$
$\frac{1}{v}=\frac{1-3}{30}$
$v=-15m$
Negative sign indicates that object is in the left side of mirror.