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  4. Two coherent sources whose intensity ratio is 64: 1 produce interference fringes. The ratio of intensities of maxima and minima is

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Q. Two coherent sources whose intensity ratio is $64: 1$ produce interference fringes. The ratio of intensities of maxima and minima is

EAMCETEAMCET 2010

Solution:

The ratio of intensities of maxima and minima
$\frac{I_{\max }}{I_{\min }} =\frac{\left(\sqrt{I_{1}}+\sqrt{I_{2}}\right)^{2}}{\left(\sqrt{I_{1}}-\sqrt{I_{2}}\right)^{2}}$
$=\frac{(\sqrt{64}+\sqrt{1})^{2}}{(\sqrt{64}-\sqrt{1})^{2}}$
$\frac{I_{\max }}{I_{\min }}=\frac{(8+1)^{2}}{(8-1)^{2}}=\frac{81}{49}$