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Two light beams of intensities 4I and 9I interfere on a screen. The phase difference between these beams on the screen at point A is zero and at point B is $π$ . The difference of resultant intensities, at the point A and B, will be _________ I.

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answer is 24.

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Detailed Solution

$\begin{array}{l} I_{net} = I_{1} + I_{2} + 2 \sqrt{I_{1}} \sqrt{I_{2}} \cos ϕ \\ I_{max} for ϕ = 0 & I_{min} for ϕ = π \\ I_{max} = {(\sqrt{I_{1}} + \sqrt{I_{2}})}^{2} = (\sqrt{91} - \sqrt{41})^{2} = 25 I \\ I_{min} = {(\sqrt{I_{1}} - \sqrt{I_{2}})}^{2} = (\sqrt{91} - \sqrt{41})^{2} = I \\ I_{max} - I_{min} = 25 I - I = 24 I \end{array}$

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