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  4. In Young's experiment, the ratio of maximum and minimum intensities in the fringe system is 9:1 . The ratio of amplitudes of coherent sources is

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Q. In Young's experiment, the ratio of maximum and minimum intensities in the fringe system is $9:1$ . The ratio of amplitudes of coherent sources is

NTA AbhyasNTA Abhyas 2020Wave Optics

Solution:

$\frac{I_{m a x}}{I_{m i n} = \frac{\left(a_{1} + a_{2}\right)^{2}}{\left(a_{1} - a_{2}\right)^{2}}}$
$\frac{9}{1}=\left(\frac{a_{1} + a_{2}}{a_{1} - a_{2}}\right)^{2}$
$\frac{a_{1} + a_{2}}{a_{1} - a_{2}}=\frac{3}{1}$
By solving this:
$a_{1}+a_{2}=3a_{1}-3a_{2}$
$4a_{2}=2a_{1}$
$\frac{a_{1}}{a_{2}}=\frac{2}{1}$