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

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

Electromagnetic Waves

Solution:

$ \frac{I_1}{I_2} = \frac{a_1^2}{a_2^2} = \frac{9}{1}$
$\Rightarrow \frac{a_1}{a_2} = \sqrt{\frac{9}{1}}$
$\Rightarrow \frac{a_1}{a_2} = \frac{3}{1}$
$\therefore \frac{I_{max}}{I_{min}} = \frac{(a_1 + a_2)^2}{(a_1 - a_2)^2}$
$ = \frac{(3 + 1)^2}{(3 - 1)^2}$
$ = \frac{(3)^2}{(2)^2} = \frac{16}{4}$
$ = \frac{4}{1}$
Thus, $ I_{max} : I_{min} = 4 : 1$