First slide

Young's double slit Experiment

Question

The ratio of intensities of two coherent sources is p. In the interference pattern, visibility of fringes will be

Difficult

A

$\sqrt{p / (1 + p)}$
B

$2 \sqrt{p} / (1 + p)$
C

$p / (1 + p)$
D

$2 p / (1 + p)$

Solution

The fringe visibility V is given by
$V = \frac{I_{max} - I_{min}}{I_{max} + I_{min}} Given \frac{I_{1}}{I_{2}} = p = {(\frac{a_{1}}{a_{2}})}^{2} or \frac{a_{1}}{a_{2}} = \sqrt{p} V = \frac{2 \sqrt{I_{1} I_{2}}}{(I_{1} + I_{2})} = \frac{2 \sqrt{I_{1} / I_{2}}}{(I_{1} / I_{2} + 1)} = \frac{2 \sqrt{p}}{(p + 1)}$

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