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

Answer 1

The correct option is B $\pi r^2\propto f^2$

$\begin{array}{c}\tan \theta =\frac{r}{f}\\ r=f\tan \theta \\ r^2=f^2{\tan }^2\theta \\ \dot{\pi }{r}^2=\pi f^2{\tan }^2\theta \\ \text{So}\pi r^2\propto f^2\\ \text{So option}B\text{is correct}\end{array}$