Two coherent sources of intensities $I_{1}$ and $I_{2}$ produce an interference pattern,. The maximum intensity in the interference pattern will be-

I_{1} + I_{2}

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I_{1}^{2} + I_{2}^{2}

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(I_{1} + I_{2})^{2}

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(\sqrt{I_{1}} + {\sqrt{I_{2})}}^{2}

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Solution

The correct option is D $(\sqrt{I_{1}} + {\sqrt{I_{2})}}^{2}$
Resultant intensity $I_{R} = I_{1} + I_{2} + 2 \sqrt{I_{1} I_{2}} cos ϕ$
For maximum $I_{R}, ϕ = 0^{o}$
$\Rightarrow I_{R} = I_{1} + I_{2} + 2 \sqrt{I_{1} I_{2}} (\sqrt{I_{1}} + {\sqrt{I_{2})}}^{2}$

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