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Q.

The ratio of maximum to minimum intensity in the interfernce pattern is 25 : 1.Then the ratio of intensities of
interfering beams is

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a

4 : 9

b

3 : 2

c

2 :3

d

9 : 4

answer is A.

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Detailed Solution

$\begin{array}{l} \frac{I_{max}}{I_{min}} = {(\frac{\sqrt{I_{1}} + \sqrt{I_{2}}}{\sqrt{I_{1}} - \sqrt{I_{2}}})}^{2} = \frac{25}{1}; \frac{\sqrt{I_{1}} + \sqrt{I_{2}}}{\sqrt{I_{1}} - \sqrt{I_{2}}} = \frac{5}{1} \\ \Rightarrow \frac{\sqrt{I_{1}}}{\sqrt{I_{2}}} = \frac{5 + 1}{5 - 1} \Rightarrow \frac{I_{1}}{I_{2}} = {(\frac{6}{4})}^{2} = \frac{9}{4} \end{array}$

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The ratio of maximum to minimum intensity in the interfernce pattern is 25 : 1.Then the ratio of intensities ofinterfering beams is