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  4. Two coherent sources of intensity ratio 1:4 produce an interference pattern. The fringe visibility will be

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Q. Two coherent sources of intensity ratio $ 1:4 $ produce an interference pattern. The fringe visibility will be

J & K CETJ & K CET 2004

Solution:

Fringe visibility $V=\frac{2 \sqrt{I_{1} I_{2}}}{I_{1}+I_{2}}$
where $I_{1}$ and $I_{2}$ are intensities of coherent sources.
Given, $\frac{I_{1}}{I_{2}}=\frac{1}{4}$
$\therefore I_{2}=4 I_{1}$
$\therefore $ Fringe visibility
$=\frac{2 \sqrt{I_{1} \times 4 I_{1}}}{\left(I_{1} \times 4 I_{1}\right)}$
$=\frac{2 \times 2 I_{1}}{5 I_{1}}=\frac{4}{5}$
$\Rightarrow V=0.8$