Question

A beam of parallel rays is incident on a concave mirror such that they make a very small angle $\theta$ with the principle axis of the concave mirror. The distance from the focus on the focal plane where rays converge after reflection is

• A. $2f\theta$
• B. $3f\theta$
• C. $4f\theta$
• D. $f\theta$

Answer 1

The correct option is D $f\theta$


Here, focal length, $PF=f$
Parallel rays will intersect at point $F^{\prime }$ at a distance $h$ below focus in the focal plane after reflection.
In $△FP{F}^{\prime }$,
$\angle FP{F}^{\prime }=\theta$ $[\angle i=\angle r]$
and
$\tan \theta =\frac{F{F}^{\prime }}{FP}$
$\Rightarrow \tan \theta =\frac{h}{f}$
$\Rightarrow h=f\tan \theta$
Angle $\theta$ is very small.
$\tan \theta \approx \theta$
$\Rightarrow h=f\theta$