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Wave Optics

Question

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Two coherent light beams of intensities I and 4I are superposed. The maximum and minimum possible intensities in the resulting beam are

5I and I

5 I and 3 I

9 I and I

9 I and 3 I

Solution

C.

9 I and I

Given: $I_{1} = I, I_{2} = 4 I$

$I_{\max} = {(\sqrt{I_{1}} + \sqrt{I_{2}})}^{2}$

= ${(\sqrt{I} + \sqrt{4 I})}^{2}$

$I_{\max} = {(3 \sqrt{I})}^{2}$

$I_{\max} = 9 I$

$I_{\max} = {(\sqrt{I_{1}} - \sqrt{I_{2}})}^{2}$

$I_{\min} = {(\sqrt{I_{1}} - \sqrt{4 I})}^{2}$

= ${(- \sqrt{I})}^{2}$

I_min = I

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