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(A) Given the ratio of amplitudes $\frac{a_1}{a_2} = \frac{1}{3}$.We know that the intensity $I$ is proportional to the square of the amplitude $a$,so

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$4$

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(A) Given the ratio of amplitudes $\frac{a_1}{a_2} = \frac{1}{3}$.We know that the intensity $I$ is proportional to the square of the amplitude $a$,so $\frac{I_1}{I_2} = \left(\frac{a_1}{a_2}\right)^2 = \left(\frac{1}{3}\right)^2 = \frac{1}{9}$.Let $a_1 = x$ and $a_2 = 3x$.The maximum intensity $I_{\max}$ is proportional to $(a_1 + a_2)^2 = (x + 3x)^2 = (4x)^2 = 16x^2$.The minimum intensity $I_{\min}$ is proportional to $(a_2 - a_1)^2 = (3x - x)^2 = (2x)^2 = 4x^2$.The ratio of maximum to minimum intensity is $\frac{I_{\max}}{I_{\min}} = \frac{16x^2}{4x^2} = 4$.

In an interference experiment,the ratio of amplitudes of coherent waves is $\frac{a_1}{a_2} = \frac{1}{3}$. The ratio of maximum and minimum intensities of fringes will be

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