Two coherent sources of intensity ratio 100 : 1, interfere. What is the ratio of the intensity between the maxima and minima in the interference pattern?

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$10 : 1$

$11 : 9$

$121 : 81$

$5 : 2$

answer is C.

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Detailed Solution

Given $\frac{I_{1}}{I_{2}} = 100$ , i.e. $I_{1} = 100$ units and $I_{2} = 1$ unit.

Intensity at maxima is:
$I = I_{1} + I_{2} + 2 \sqrt{I_{1} I_{2}} = 100 + 1 + 2 \sqrt{100 \times 1} = 121$
Intensity at minima is:
$I^{'} = I_{1} + I_{2} - 2 \sqrt{I_{1} I_{2}} = 81$
$∴ \frac{I}{I^{'}} = \frac{121}{81}$

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