The ratio of the intensities of two waves is | vedclass

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(C) Let the intensities of the two waves be $I_1$ and $I_2$. Given that $\frac{I_1}{I_2} = \frac{25}{1}$,we can write $I_1 = 25k$ and $I_2 = k$ for so

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$9 : 4$

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(C) Let the intensities of the two waves be $I_1$ and $I_2$. Given that $\frac{I_1}{I_2} = \frac{25}{1}$,we can write $I_1 = 25k$ and $I_2 = k$ for some constant $k$.The ratio of maximum intensity $(I_{\max})$ to minimum intensity $(I_{\min})$ is given by the formula:$\frac{I_{\max}}{I_{\min}} = \frac{(\sqrt{I_1} + \sqrt{I_2})^2}{(\sqrt{I_1} - \sqrt{I_2})^2}$Substituting the values:$\frac{I_{\max}}{I_{\min}} = \frac{(\sqrt{25k} + \sqrt{k})^2}{(\sqrt{25k} - \sqrt{k})^2} = \frac{(5\sqrt{k} + \sqrt{k})^2}{(5\sqrt{k} - \sqrt{k})^2}$$\frac{I_{\max}}{I_{\min}} = \frac{(6\sqrt{k})^2}{(4\sqrt{k})^2} = \frac{36k}{16k} = \frac{36}{16} = \frac{9}{4}$Thus,the ratio is $9 : 4$.

The ratio of the intensities of two waves is $25 : 1$. If interference occurs,then the ratio of the maximum and minimum intensity should be:

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