A concave mirror having a radius of curvature 40 cm is placed in front of an illuminated point source at a distance of 30 cm from it. Find the location of the image.

#### Solution

Using sign conventions, given,

Distance of object from mirror, *u* = − 30 cm,

Radius of curvature of concave mirror *R* = − 40 cm

Using the mirror equation,

\[\frac{1}{v} + \frac{1}{u} = \frac{2}{R}\]

\[ \Rightarrow \frac{1}{v} = \frac{2}{R} - \frac{1}{u}\]

\[ \Rightarrow \frac{1}{v} = \frac{2}{- 40} - \frac{1}{- 30} = \frac{1}{- 20} + \frac{1}{30}\]

\[ \Rightarrow \frac{1}{v} = \frac{- 30 + 20}{30 \times 20} = \frac{- 10}{30 \times 20}\]

\[ \Rightarrow \frac{1}{v} = - \frac{1}{60}\]

or, *v* = − 60 cm

Hence, the required image will be located at a distance of 60 cm in front of the concave mirror.