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  4. Two coherent sources produce waves of different intensities which interfere. After interference, the ratio of the maximum intensity to the minimum intensity is 16. The intensity of the waves are in the ratio:

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Q. Two coherent sources produce waves of different intensities which interfere. After interference, the ratio of the maximum intensity to the minimum intensity is $16$. The intensity of the waves are in the ratio:

JEE MainJEE Main 2019Wave Optics

Solution:

$\frac{I_{\max}}{I_{\min}} = 16 $
$ \Rightarrow \frac{A_{\max }}{A_{\min }} = 4 $
$ \Rightarrow \frac{A_{1} + A_{2}}{A_{1} - A_{2}} = \frac{4}{1} $
Using componendo & dividendo.
$ \frac{A_{1} }{A_{2}} = \frac{5}{3} \Rightarrow \frac{I_{1}}{I_{2}} = \left(\frac{5}{3}\right)^{2} = \frac{25}{9} $