Two coherent waves of intensities I_1 and I_2 | vedclass

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(D) The intensity of a wave is proportional to the square of its amplitude,i.e.,$I \propto A^2$. Thus,$A \propto \sqrt{I}$.For two coherent waves with

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$(\sqrt{I_1} + \sqrt{I_2})^2$

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(D) The intensity of a wave is proportional to the square of its amplitude,i.e.,$I \propto A^2$. Thus,$A \propto \sqrt{I}$.For two coherent waves with amplitudes $A_1$ and $A_2$,the resultant amplitude $A_{res}$ is given by $A_{res} = \sqrt{A_1^2 + A_2^2 + 2A_1A_2 \cos \phi}$,where $\phi$ is the phase difference.For maximum intensity,the phase difference $\phi = 0, 2\pi, 4\pi, ...$,which implies $\cos \phi = 1$.Therefore,the maximum resultant amplitude is $A_{max} = \sqrt{A_1^2 + A_2^2 + 2A_1A_2} = A_1 + A_2$.Since $A_1 = \sqrt{I_1}$ and $A_2 = \sqrt{I_2}$,the maximum amplitude is $A_{max} = \sqrt{I_1} + \sqrt{I_2}$.The maximum intensity $I_{max}$ is proportional to the square of the maximum amplitude:$I_{max} \propto (A_{max})^2 = (\sqrt{I_1} + \sqrt{I_2})^2$.

Two coherent waves of intensities $I_1$ and $I_2$ produce an interference pattern. The maximum intensity of the interference pattern is .....

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