First slide

The lens

Question

A thin lens focal length f₁ and its aperture has diameter d. It forms an image of intensity I. Now the central part of the aperture upto diameter $\frac{d}{2}$ is blocked by an opaque paper. The focal length and image intensity will change to

Moderate

A

$\frac{f}{2} and \frac{I}{2}$
B

$f and \frac{I}{4}$
C

$\frac{3 f}{4} and \frac{I}{2}$
D

$f and \frac{3 I}{4}$

Solution

$I \propto A^{2} \Rightarrow \frac{I_{2}}{I_{1}} = {(\frac{A_{2}}{A_{1}})}^{2} = \frac{{πr}^{2} - \frac{{πr}^{2}}{4}}{{πr}^{2}} = \frac{3}{4} \Rightarrow I_{2} = \frac{3}{4} I_{1} and focal length remains unchanged$

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