Question

A biconvex lens of focal length $f$ forms a circular image of sun of radius $r$ in focal plane. Then

• A. $\pi r^2\propto f$
• B. $\pi r^2\propto f^2$
• C. if the lower half part is covered by black sheet, then the area of the image is equal to $\pi r^2/2$.
• D. if $f$ is doubled, intensity will increase.

Answer 1

Answer: (B)

From the ray diagram shown here, we have
$\tan \alpha =\frac{r}{f}$
$\Rightarrow r=f\tan \alpha$
We can write the above equation as
$\pi r^2=\pi f^2{\tan }^2\alpha$
$\Rightarrow \pi r^2\propto f^2$