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The two light beams having intensities I and 9I interfere to produce a fringe pattern on a screen. The phase difference between the beams is $π / 2$ at point P and π at point Q . Then the difference between the resultant intensities at P and Q will be____

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answer is A.

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Detailed Solution

$\begin{array}{l} I = I_{1} + I_{2} + 2 \sqrt{I_{1} I_{2}} \cos ϕ \\ I_{P} = I + 9 I + 2 \sqrt{I \cdot 9 I} \cdot \cos π / 2 = 10 I \\ I_{Q} = I + 9 I + 2 \sqrt{I \cdot 9 I} \cdot \cos (π) = 4 I \\ I_{P} - I_{Q} = 6 I \end{array}$

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