Two coherent monochromatic light beams of intensities 4 and 9 are superimposed. The difference between the maximum and minimum intensities in the resulting interference pattern is x. The value of x is ________. [2025]

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Solution

Q.
Two coherent monochromatic light beams of intensities 4 $I$ and 9 $I$ are superimposed. The difference between the maximum and minimum intensities in the resulting interference pattern is x $I$ . The value of x is ________. [2025]

Ans.
(24)

$I_{\max} = {(\sqrt{I_{1}} + \sqrt{I_{2}})}^{2} = {(\sqrt{4 I} + \sqrt{9 I})}^{2} = 25 I$

$I_{\min} = {(\sqrt{I_{1}} - \sqrt{I_{2}})}^{2} = {(\sqrt{4 I} - \sqrt{9 I})}^{2} = I$

$I_{\max} - I_{\min} = 24 I \Rightarrow x = 24$

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