Two coherent light sources of intensity ratio n are employed in an interference experiment. The ratio of the intensities of the maxima and minima in the interference pattern is:

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$(\frac{n + 1}{n - 1})$

${(\frac{n + 1}{n - 1})}^{2}$

$(\frac{\sqrt{n} + 1}{\sqrt{n} - 1})$

${(\frac{\sqrt{n} + 1}{\sqrt{n} - 1})}^{2}$

answer is D.

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Detailed Solution

Given $\frac{I_{1}}{I_{2}} = n$

Therefore, the amplitude ratio will be:

$\frac{A_{1}}{A_{2}} = \sqrt{n}$

Now $I_{m a x}$ = ${(A_{1} + A_{2})}^{2}$ and $I_{m i n} = {(A_{1} - A_{2})}^{2}$

$∴ \frac{I_{m a x}}{I_{m i n}} = \frac{{(A_{1} + A_{2})}^{2}}{{(A_{1} - A_{2})}^{2}} =$ $\frac{{(\frac{A_{1}}{A_{2}} + 1)}^{2}}{{(\frac{A_{1}}{A_{2}} - 1)}^{2}}$ = $\frac{{(\sqrt{n} + 1)}^{2}}{{(\sqrt{n} - 1)}^{2}}$

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