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
$\pi r^{2}=\pi f^{2} \tan ^{2} \alpha$
$\Rightarrow \pi r^{2} \propto f^{2}$