Question

An object is placed at 20 m in front of a concave mirror. If its radius of curvature is 40 m, then the image distance is equal to ___ m.

Answer 1

Given,
Distance of the object from the mirror, $u=20m$ and radius of curvature, $R=40m$
Let image distance $=v$.
We know, focal length, $f=\frac{radiusofcurvature}{2}$ = $\frac{40}{2}$
$\Rightarrow f=20m$.

Using sign conventions we have $u=-20m$ and $f=-20m$ ( for concave mirror)
Using mirror formula
$\frac{1}{\text{v}}$ + $\frac{1}{\text{u}}$ = $\frac{1}{\text{f}}$
$\frac{1}{\text{v}}$ + $\frac{1}{-20}$ = $\frac{-1}{20}$
$\frac{1}{\text{v}}$ = 0
$v=\frac{-1}{0}$ = $\infty$
So the image will form at infinity.