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(D) The resultant intensity $I_R$ in an interference pattern is given by the formula: $I_R = I_1 + I_2 + 2\sqrt{I_1 I_2} \cos \phi$. For maximum inten

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$9I$ and $I$

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(D) The resultant intensity $I_R$ in an interference pattern is given by the formula: $I_R = I_1 + I_2 + 2\sqrt{I_1 I_2} \cos \phi$. For maximum intensity $(I_{\max})$,the phase difference $\phi = 0$,so $I_{\max} = I_1 + I_2 + 2\sqrt{I_1 I_2} = (\sqrt{I_1} + \sqrt{I_2})^2$. Given $I_1 = I$ 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 $(I_{\min})$,the phase difference $\phi = \pi$,so $I_{\min} = I_1 + I_2 - 2\sqrt{I_1 I_2} = (\sqrt{I_1} - \sqrt{I_2})^2$. $I_{\min} = (\sqrt{I} - \sqrt{4I})^2 = (\sqrt{I} - 2\sqrt{I})^2 = (-\sqrt{I})^2 = I$. Thus,the maximum and minimum intensities are $9I$ and $I$ respectively.

Two monochromatic beams of intensities $I$ and $4I$ respectively are superposed to form a steady interference pattern. The maximum and minimum intensities in the pattern are

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