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Intensity Explanation in YDSE

The intensity...

Question

The intensity of the light coming from one of the slits in YDSE is double the intensity from the other slit. Find the ratio of the maximum intensity to minimum intensity in the interference fringe pattern observed

A

32

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B

34

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C

36

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D

38

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Solution

The correct option is A $34$
Given that $\frac{I_{1}}{I_{2}} = 2$

$I_{m a x} = I_{1} + I_{2} + 2 \sqrt{I_{1} . I_{2}} I_{m i n} = I_{1} + I_{2} - 2 \sqrt{I_{1} . I_{2}}$

$∴ \frac{I_{m a x}}{I_{m i n}} = \frac{I_{1} + I_{2} + 2 \sqrt{I_{1} . I_{2}}}{I_{1} + I_{2} - 2 \sqrt{I_{1} . I_{2}}}$

$= \frac{I_{2} (I_{1} / I_{2} + 1 + 2 \sqrt{I_{1} / I_{2}})}{I_{2} (I_{1} / I_{2} + 1 - 2 \sqrt{I_{1} / I_{2}})} = \frac{2 + 1 + 2 \sqrt{2}}{2 + 1 - 2 \sqrt{2}} \approx 34$

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