Two coherent sources of intensities I and 4I | vedclass

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(D) The resultant intensity of two interfering waves is given by $I_{res} = I_1 + I_2 + 2\sqrt{I_1 I_2} \cos \phi$.For maximum intensity,$\cos \phi =

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$9I$ and $I$

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(D) The resultant intensity of two interfering waves is given by $I_{res} = I_1 + I_2 + 2\sqrt{I_1 I_2} \cos \phi$.For maximum intensity,$\cos \phi = 1$,so $I_{max} = (\sqrt{I_1} + \sqrt{I_2})^2$.Substituting $I_1 = I$ and $I_2 = 4I$:$I_{max} = (\sqrt{I} + \sqrt{4I})^2 = (\sqrt{I} + 2\sqrt{I})^2 = (3\sqrt{I})^2 = 9I$.For minimum intensity,$\cos \phi = -1$,so $I_{min} = (\sqrt{I_1} - \sqrt{I_2})^2$.$I_{min} = (\sqrt{I} - \sqrt{4I})^2 = (\sqrt{I} - 2\sqrt{I})^2 = (-\sqrt{I})^2 = I$.Thus,the maximum and minimum intensities are $9I$ and $I$ respectively.

Two coherent sources of intensities $I$ and $4I$ interfere. The maximum and minimum intensities of the resultant wave are:

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