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  4. The ratio of intensities of two waves is 16: 9. If they produce interference, then ratio of maximum and minimum intensities will be

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Q. The ratio of intensities of two waves is $16 : 9$. If they produce interference, then ratio of maximum and minimum intensities will be

AFMCAFMC 2005Electromagnetic Waves

Solution:

Since, $\frac{I_1}{I_2} = \frac{16}{9} = \frac{a_1^2}{a_2^2}$
$\Rightarrow \frac{a_1}{a_2} = \sqrt{\frac{16}{9}} = \frac{4}{3}$
or $a_1 = \frac{4}{3} a_2$
$\therefore \frac{I_{max}}{I_{\min}} = \frac{(a_1 + a_2)^2}{(a_1 - a_2)^2}$
$= \frac{\left(\frac{4}{3}a_2 + a_2 \right)^2}{\left(\frac{4}{3}a_2 - a_2 \right)^2} = 49 : 1$