Question

A thin lens has focal length f and aperture radius r. It forms an image of intensity I. Now the central part of the aperture upto $\frac{r}{2}$ is blacked by an opaque material. The focal length and intensity of image will be

• A. $\frac{f}{2}\&\frac{I}{2}$
• B. $f\&\frac{I}{4}$
• C. $\frac{3f}{4}\&\frac{I}{2}$
• D. $f\&\frac{3I}{4}$

Answer 1

The correct option is B $f\&\frac{I}{4}$

There will be no change in focal length. $f^1=f$ But Intensity $I\propto A$
But Intensity $I\propto A$
$\frac{I^1}{I}=\frac{r_1^2}{r^2}=\frac{1}{4}\because r_1=\frac{r}{2}{I}^1=\frac{I}{4}$