Assertion :Ratio of maximum intensity and minimum intensity in interference is 25 : 1. Hence amplitude ratio of two waves should be 3 : 2. Reason: $\frac{I_{m a x}}{I_{m i n}} = {(\frac{A_{1} + A_{2}}{A_{1} - A_{2}})}^{2}$

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Assertion is incorrect but Reason is correct

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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
Assume there are two waves of amplitudes $A_{1}$ and $A_{2}$ with no loss of generality assume $A_{1} > A_{2}$ .
These two waves upon being superimposed would give us waves:
Maximum amplitude = $A_{1} + A_{2}$
Minimum amplitude = $A_{1} - A_{2}$
Since intensity is proportional to the square of amplitude.
$\frac{I_{m a x}}{I_{m i n}} = (\frac{A_{1} + A_{2}}{A_{1} - A_{2}})^{2}$
Upon substituting this ratio = 25 and solving,
We get, $\frac{A_{1}}{A_{2}} = \frac{3}{2}$
Hence both assertion and reason are true, reason is the correct explanation,
Hence option A.

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