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  4. Two waves of equal amplitude and frequency interfere each other. The ratio of intensity when the two waves arrive in phase to that when they arrive 90° out of phase is

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Q. Two waves of equal amplitude and frequency interfere each other. The ratio of intensity when the two waves arrive in phase to that when they arrive $90^{\circ}$ out of phase is

Wave Optics

Solution:

Resultant intensity $I=4 I_{0} \cos ^{2}(\phi / 2)$
$\Rightarrow \frac{I_{1}}{I_{2}}=\frac{\cos ^{2}\left(\phi_{1} / 2\right)}{\cos ^{2}\left(\phi_{2} / 2\right)}$
$=\frac{\cos ^{2} 0}{\cos ^{2}(90 / 2)}=\frac{2}{1}$