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(A) The intensities of the two sources are $I_1$ and $I_2$. Given the ratio $I_1/I_2 = 81/1$.The maximum intensity is given by $I_{	ext{max}} = (\sqr

Vedclass · Accepted Answer

$25:16$

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(A) The intensities of the two sources are $I_1$ and $I_2$. Given the ratio $I_1/I_2 = 81/1$.The maximum intensity is given by $I_{	ext{max}} = (\sqrt{I_1} + \sqrt{I_2})^2$.The minimum intensity is given by $I_{	ext{min}} = (\sqrt{I_1} - \sqrt{I_2})^2$.The ratio of maximum to minimum intensity is:$\frac{I_{	ext{max}}}{I_{	ext{min}}} = \left( \frac{\sqrt{I_1} + \sqrt{I_2}}{\sqrt{I_1} - \sqrt{I_2}} ight)^2 = \left( \frac{\sqrt{I_1/I_2} + 1}{\sqrt{I_1/I_2} - 1} ight)^2$.Substituting $I_1/I_2 = 81$:$\frac{I_{	ext{max}}}{I_{	ext{min}}} = \left( \frac{\sqrt{81} + 1}{\sqrt{81} - 1} ight)^2 = \left( \frac{9 + 1}{9 - 1} ight)^2 = \left( \frac{10}{8} ight)^2 = \left( \frac{5}{4} ight)^2 = \frac{25}{16}$.

Two coherent sources produce interference fringes with an intensity ratio of $81:1$. Find the ratio of the maximum to the minimum intensity in the interference pattern.

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