Question

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

Answer 1

Answer: 0.33

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

$\Rightarrow v=60cm$
As triangles $OPC$ and $ABC$ are similar
$\Rightarrow \frac{2}{60}=\frac{x}{10}$
$\Rightarrow x=\frac{1}{3}=0.33cm$