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Physics Question on wave interference

The intensity ratio of the maxima and minima in an interference pattern produced by two coherent sources of light is 9 : 1. The intensities of the used light sources are in ratio

A

3:01

B

4:01

C

9:01

D

10:01

Answer

4:01

Explanation

Solution

ImaxImin=(a+b)2(a−b)2\frac{I_{max}}{I_{min}}=\frac{\left(a+b\right)^{2}}{\left(a-b\right)^{2}} 91=(a+b)2(a−b)2\frac{9}{1}=\frac{\left(a+b\right)^{2}}{\left(a-b\right)^{2}} or 31=a+ba−b\quad \frac{3}{1}=\frac{a+b}{a-b} or 3a-3b = a+b or \quad 2a = 4b or a = 2b ∴I1I2=a2b2=41\therefore\quad \frac{I_{1}}{I_{2}}=\frac{a^{2}}{b^{2}}=\frac{4}{1}