Question

An object is placed at 60 m in front of a concave mirror. If its radius of curvature is 40 m, then the image distance is equal to _____ m.

• A. -30
• B. 30
• C. 20
• D. -20

Answer 1

The correct option is A -30

Given, distance of the object from the mirror, $u=-60m$ (object is on the left side of the mirror) and radius of curvature, $R=40m$
We know, focal length, $f=\frac{R}{2}$ = $\frac{40}{2}$ $=20m$
For concave mirror, $f$ is negative, i.e $f=-20m$
Let the image distance be $v$

Using mirror formula
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\frac{1}{v}+\frac{1}{-60}=\frac{-1}{20}$
$\frac{1}{v}=\frac{1-3}{60}$
$v=-30m$
Negative sign represents that object and image are on the same side of mirror.