First slide

Ray optics

Question

A lens having focal length f and aperture of diameter d forms an image of intensity I. Aperture of diameter d/2 in central region of lens is covered by a black paper. Focal length of lens and intensity of image now will be respectively

Moderate

A

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

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

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

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

Solution

focal length does not change, f ' = f
$\Rightarrow But I \propto A, ∴ \frac{I_{1}}{I_{2}} = \frac{A_{1}}{A_{2}} ∴ \frac{I}{I_{2}} = \frac{π {(d)}^{2}}{[π {(d)}^{2} - π {(d / 2)}^{2}]} ∴ I_{2} = \frac{3 I}{4}$

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