Question

The intensity ratio of maximum and minimum in an interference pattern is 4 : 1. find the ratio of slit widhts​

Answer 1

Explanation:

$given, \\ \frac{I_{1 }}{I_{2}} = \frac{W_{1}}{W_{2}} = \frac{4}{1} \\ Therefore, \\ \frac{I_{max}}{I_{min}} = \frac{ {( \sqrt{I_{2}} + \sqrt{I_{1}} )}^{2} }{ {( \sqrt{I_{2}} - \sqrt{I_{1}} )}^{2} } = \frac{ {( \frac{\sqrt{I_{2}}}{\sqrt{I_{1}}} + 1 )}^{2} }{ {( \frac{\sqrt{I_{2}}}{\sqrt{I_{1}}} - 1 )}^{2} } \\ Substitute \:all\: values \:in \:above\: equation:\\</p><p>\frac{I_{max}}{I_{min}} = \frac{ {( \frac{\sqrt{1}}{\sqrt{4}} + 1 )}^{2} }{ {( \frac{\sqrt{1}}{\sqrt{4}} - 1 )}^{2} } \\ = \frac{ {(1 + 2)}^{2} }{ {(1 - 2)}^{2} } \\ = \frac{ {(3)}^{2} }{ {( - 1)}^{2} } \\ = \frac{9}{1} \\ = > 9 : 1$

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