Q: A point light source lies on the principal axis of concave spherical mirror with radius of curvature 160 cm. Its image appears to be back of the mirror at a distance of 70 cm from mirror. Determine the location of the light source.

Sol: $\large \frac{1}{v} + \frac{1}{u} = \frac{1}{f} = \frac{2}{R}$

Here v = 70 cm, R = -160 cm

$\large \frac{1}{u} = \frac{2}{R} – \frac{1}{v} $

$\large \frac{1}{u} = \frac{2}{-160} – \frac{1}{70} = -\frac{15}{560} $

u = -560/15 cm = -37 cm

The image is at a distance of 37 cm in front of the mirror.