Question

A thin lens forms image of intensity $I$. If the central part of the lens diameter half the diameter of the lens is black polished, then what will be the intensity of the image formed by the remaining part?

Answer 1

Intensity is directly proportional to the area of the aperture of the lens receiving the light.

Total area of the aperture is,

$A=\frac{\pi d^2}{4}..........\left(i\right)$

Remaining area after covering,

$A^{\prime }=\frac{\pi d^2}{4}-\frac{\pi d^2}{16}=\frac{3\pi d^2}{16}.........\left(ii\right)$

$\frac{I}{I^{\prime }}=\frac{A}{A^{\prime }}=\frac{4}{3}{I}^{\prime }=\frac{3}{4}I$