The two coherent sources with intensity ratio β produce interference. The fringe visibility will be

$\frac{2 \sqrt{β}}{1 + β}$

2 β

$\frac{2}{(1 + β)}$

$\frac{\sqrt{β}}{1 + β}$

Solution

$\frac{2 \sqrt{β}}{1 + β}$

$\frac{I_{1}}{I_{2}} = \frac{a^{2}}{b^{2}}$ = β

∴ $\frac{a}{b} = \sqrt{β}$

I_max = ( a + b )² and I_min = ( a $-$ b )²

Fringe visibility is given by

V = $\frac{I_{\max} - I_{\min}}{I_{\max} + I_{\min}}$

= $\frac{{(a + b)}^{2} - (a - b)}{{(a + b)}^{2} + (a - b)}$

V = $\frac{4 ab}{2 (a^{2} + b^{2})}$

V = $\frac{2 (\frac{a}{b})}{(\frac{a^{2}}{b^{2}} + 1)}$

V = $\frac{2 \sqrt{β}}{β + 1}$

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