Question

A ray of light incident on a spherical mirror appears to intersect the principle axis $60\text{cm}$ behind the mirror. If the light ray retraces its path after reflection, then the focal length of the mirror is

• A. $25\text{cm}$
• B. $-30\text{cm}$
• C. $30\text{cm}$
• D. $60\text{cm}$

Answer 1

The correct option is C $30\text{cm}$

The incident ray appears to intersect the principle axis hence mirror is a convex mirror.


The light ray retracing its path after reflection indicates that incident ray strikes mirror normally and will appear to pass through center of curvature.
$PC=R=60\text{cm}$
Hence $f=R/2$
$f=60/2=30\text{cm}$

Concept involved:
Line joining any point on mirror and center of curvature is the normal to mirror at that point. if light is incident normally $\angle$i = $\angle$r = $0^{\circ }$ and light retraces its path.