Two monochromatic light beams have intensities in the ratio 1:9. An interference pattern is obtained by these beams. The ratio of the intensities of maximum to minimum is

<p>To find the ratio of the intensities of the maximum to the minimum in an interference pattern formed by two monochromatic light beams with intensity ratios of 1:9, you use the formula:</p> <p>$ \frac{I_{\max }}{I_{\min }} = \frac{\left(\sqrt{I_1} + \sqrt{I_2}\right)^2}{\left(\sqrt{I_1} - \sqrt{I_2}\right)^2} $</p> <p>Given that the intensity ratio is 1:9, we have $I_1 = 1$ and $I_2 = 9$.</p> <p><p>Calculate $\sqrt{I_1}$ and $\sqrt{I_2}$:</p> <p>$ \sqrt{I_1} = \sqrt{1} = 1 $</p> <p>$ \sqrt{I_2} = \sqrt{9} = 3 $</p></p> <p><p>Substitute these values into the formula:</p> <p>$ \frac{I_{\max }}{I_{\min }} = \frac{(1 + 3)^2}{(1 - 3)^2} = \frac{4^2}{2^2} = \frac{16}{4} = 4 $</p></p> <p>Thus, the ratio of the intensities of the maximum to the minimum is 4:1.</p>