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  4. Two waves having the intensities in the ratio 9: 1 produce interference. The ratio of maximum to minimum intensity is equal to

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Q. Two waves having the intensities in the ratio $9: 1$ produce interference. The ratio of maximum to minimum intensity is equal to

Wave Optics

Solution:

As, $\frac{I_{1}}{I_{2}}=\frac{a^{2}}{b^{2}}=\frac{9}{1}$
$\therefore \frac{a}{b}=\frac{3}{1}$
$\Rightarrow \frac{I_{\max }}{I_{\min }}=\frac{(a +b)^{2}}{(a-b)^{2}}=\left(\frac{3+1}{3-1}\right)^{2}=4: 1$