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  4. Two coherent sources of different intensities send waves which interfere. The ratio of the maximum intensity to the minimum intensity is 25. The intensities are in the ratio:

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Q. Two coherent sources of different intensities send waves which interfere. The ratio of the maximum intensity to the minimum intensity is $25.$ The intensities are in the ratio:

Waves

Solution:

$\frac{a_{1}+a_{2}}{a_{1}-a_{2}}=5$
$\Rightarrow a_{1}+a_{2}=5\left(a_{1}-a_{2}\right)$
$\frac{a_{1}}{a_{2}}=\frac{3}{2} $
$\frac{I_{1}}{I_{2}}=\left(\frac{a_{1}}{a_{2}}\right)^{2}=\frac{9}{4}$