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 light sources used are in the ratio

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Let the intensities of the two coherent sources be $I_{1}$ and $I_{2}$ .

The maximum and minimum intensities in the interference pattern are given by:

$I_{ma x} = (I_{1} + I_{2})^{2}$

$I_{min} = (I_{1} - I_{2})^{2}$

Given that $\frac{I _{ma x}}{I _{min}} = \frac{9}{1}$

$\frac{( I _{1} + I _{2} ) ^{2}}{( I _{1} - I _{2} ) ^{2}} = \frac{9}{1}$

Taking the square root on both sides:

$\frac{I _{1} + I _{2}}{I _{1} - I _{2}} = \frac{3}{1}$

$I_{1} + I_{2} = 3 I_{1} - 3 I_{2}$

$4 I_{2} = 2 I_{1}$

$\frac{I _{1}}{I _{2}} = \frac{2}{1}$

Squaring both sides:

$\frac{I _{1}}{I _{2}} = \frac{4}{1}$

The intensities of the light sources are in the ratio $4 : 1$ .

Answer: $4 : 1$

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