Question

A lens of focal length $20.0 \,cm$ and aperture radius $2.0 \, cm$ is placed at a distance $30.0 \, cm$ from a point source of light. On the other side a screen is placed at a distance $50.0 \,cm$ from the lens. Find the radius of spot of light formed on screen (in $cm )$. (Neglect spherical aberration through lens)

Answer 1

By lens formula, we have $\frac{1}{v}-\frac{1}{u}=\frac{1}{f} $
$\Rightarrow \frac{1}{20}=\frac{+1}{+30}+\frac{1}{v}$
$\Rightarrow \frac{1}{v}=\frac{1}{20}-\frac{1}{30}=\frac{1}{60}$

$\Rightarrow v=60 \,cm$
As triangles $O P C$ and $A B C$ are similar
$\Rightarrow \frac{2}{60}=\frac{x}{10}$
$ \Rightarrow x=\frac{1}{3}=0.33\, cm$