Question

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

• A. $20m$
• B. $30m$
• C. $60m$
• D. $120m$

Answer 1

The correct option is B

$30m$

Given:
Radius of curvature, $R=-40m$
Object distance, $u=-60m$

Let the sign convention be such that the object distance is negative i.e. positive direction is taken along the direction of the incident ray.

From mirror formula,
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
where:
$v:$ Position of image
$f:$ Focal length

But focal length is half of the radius.
$⟹f=\frac{R}{2}=-20m$

$⟹\frac{1}{v}+\frac{1}{-60}=\frac{1}{-20}$
$v=-30m$

Negative sign represents that object and image are on the same side of mirror.