In Young's experiment, the intensity ratio of the maxima and minima in an interference pattern produced by two coherent sources is 36 : 1 . The ratio of the amplitudes of the two individual sourc

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In Young's experiment, the intensity ratio of the maxima and minima in an interference pattern produced by two coherent sources is 36 : 1 . The ratio of the amplitudes of the two individual sources will be

TestHub · Accepted Answer

Let the amplitudes of the two sources be $A_{1}$ and $A_{2}$ .

The maximum intensity $I_{ma x}$ is proportional to $(A_{1} + A_{2})^{2}$ and the minimum intensity $I_{min}$ is proportional to $(A_{1} - A_{2})^{2}$ .

Given $\frac{I _{ma x}}{I _{min}} = \frac{36}{1}$

$\frac{( A _{1} + A _{2} ) ^{2}}{( A _{1} - A _{2} ) ^{2}} = \frac{36}{1}$

Taking the square root of both sides:

$\frac{A _{1} + A _{2}}{A _{1} - A _{2}} = \frac{6}{1}$

$A_{1} + A_{2} = 6 A_{1} - 6 A_{2}$

$5 A_{1} = 7 A_{2}$

$\frac{A _{1}}{A _{2}} = \frac{7}{5}$

The ratio of the amplitudes of the two individual sources is $7 : 5$ .

Answer: $7 : 5$

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