If two light waves having the same frequency | vedclass

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(A) Given the ratio of intensities of two light waves is $\frac{I_1}{I_2} = \frac{4}{1}$.Let the amplitudes be $A_1$ and $A_2$. Since $I \propto A^2$,

Vedclass · Accepted Answer

$9:1$

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(A) Given the ratio of intensities of two light waves is $\frac{I_1}{I_2} = \frac{4}{1}$.Let the amplitudes be $A_1$ and $A_2$. Since $I \propto A^2$,the ratio of amplitudes is $\frac{A_1}{A_2} = \sqrt{\frac{I_1}{I_2}} = \sqrt{\frac{4}{1}} = \frac{2}{1}$.The ratio of maximum to minimum intensity is given by the formula $\frac{I_{\max}}{I_{\min}} = \left( \frac{A_1 + A_2}{A_1 - A_2} \right)^2$.Substituting the values,we get $\frac{I_{\max}}{I_{\min}} = \left( \frac{2 + 1}{2 - 1} \right)^2 = \left( \frac{3}{1} \right)^2 = \frac{9}{1}$.Thus,the ratio is $9:1$.

If two light waves having the same frequency have an intensity ratio of $4:1$ and they interfere,the ratio of maximum to minimum intensity in the pattern will be:

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