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  4. Two waves of same frequency and same amplitude from two monochromatic sources are allowed to superpose at a certain point. If in one case the phase difference is 0° and in other case is π /2, the ratio of the intensities in the two cases will be

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Q. Two waves of same frequency and same amplitude from two monochromatic sources are allowed to superpose at a certain point. If in one case the phase difference is $0^°$ and in other case is $\pi /2$, the ratio of the intensities in the two cases will be

Wave Optics

Solution:

From $I_{R}=I_{1}+I_{2}+2\sqrt{I_{1}I_{2}}\,cos\phi$
When $\phi=0^{°}, I_{R}=I+I+2\sqrt{II} \,cos0^{°}=4I$
When $\phi=90^{°}, I '_{R}=I+I+2\sqrt{II}\,cos90^{°}=2I$
$\therefore \frac{I_{R}}{I '_{R}}=\frac{4I}{2I}=2 : 1$