Question

Paraxial rays parallel to each other but not parallel to the principal axis making an angle of $1^{\circ }$ falls on a concave mirror of focal length $f=10\text{cm}$ as shown in the figure. Find the perpendicular distance of the image from the principal axis.

• A. $\frac{\pi }{8}$
• B. $\frac{\pi }{18}$
• C. $\frac{\pi }{180}$
• D. $\frac{\pi }{36}$

Answer 1

The correct option is B $\frac{\pi }{18}$

Since rays are parallel to each other but not parallel to principal axis, they meet on the focal plane upon reflection.


Let $I$ be the image formed on the focal plane.

From $△POI$:

$\tan \alpha =\frac{h}{f}....\left(1\right)$
Since rays are paraxial, $\alpha$ is very small $\therefore \tan \alpha \approx \alpha$

So, we can rewrite $\left(1\right)$ as

$\alpha \approx \frac{h}{f}\Rightarrow h\approx \alpha f=\frac{\pi }{180}\left(10\right)=\frac{\pi }{18}$

Hence, option (b) is the correct answer.

Let's try :- If two paraxial rays are parallel to each other as well as parallel to principal axis, where does the rays meet on the principal axis?