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Intensity Amplitude Relationship

Two coherent ...

Question

Two coherent monochromatic light beams of intensities $I$ and $4 I$ superimpose. The maximuma and minimum possible intensities in the resulting beam are.

A

5 I

and

I

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B

5 I

and

3 I

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C

3 I

and

I

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D

9 I

and

I

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Solution

The correct option is D $9 I$ and $I$
$I_{m a x} = (I_{1} + I_{2})^{2} = (\sqrt{I} + \sqrt{4 I})^{2} = 9 I$
$I_{m i n} = (I_{1} - I_{2})^{2} = (\sqrt{I} - \sqrt{4 I})^{2} = I$

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