First slide

Coherent sources and their importance in interference

Question

Light waves from two coherent sources of amplitude ratio 9 : 1 produce interference. Find the ratio of maxima and minima intensities.

Moderate

A

5 : 4
B

9 : 1
C

25 : 16
D

5 : 8

Solution

$I n t e n s i t y \propto A m p l i t u d e^{2} \Rightarrow I_{1} = 81 k, I_{2} = k ∴ \frac{I_{\max}}{I_{\min}} = \frac{{(\sqrt{I_{1}} + \sqrt{I_{2}})}^{2}}{(\sqrt{I_{1}} - \sqrt{I_{2}})} = \frac{{(\sqrt{81 k} + \sqrt{k})}^{2}}{{(\sqrt{81 k} - \sqrt{k})}^{2}} = \frac{100}{64} = \frac{25}{16}$

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