Two coherent sources of different intensities send waves which interfere. The ratio of maximum intensity to the minimum intensity is 25. The intensities of the sources are in the ratio ______.

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Two coherent sources of different intensities send waves which interfere. The ratio of maximum intensity to minimum intensity is 25. The intensities of the sources are in the ratio 9 : 4. Explanation: The ratio of maximum intensity and minimum intensity is given by, `I_(max) = (sqrtI_1 + sqrtI_2)^2, I_(min) = (sqrtI_1 - sqrtI_2)^2 $\therefore$ I_(max)/I_(min) = ((sqrtI_1 + sqrtI_2)/(sqrtI_1 - sqrtI_2))^2 = 25 (sqrtI_1 + sqrtI_2)/(sqrtI_1 - sqrtI_2) = 5 $\Rightarrow$ (sqrt(I_1/I_2) + 1)/(sqrt(I_1/I_2)- 1) = 5 $\Rightarrow$ sqrt(I_1/I_2) + 1 = 5sqrt(I_1/I_2) - 5 $\Rightarrow$ 6 = 4sqrt(I_1/I_2) $\Rightarrow$ sqrt(I_1/I_2) = $\frac{3}{2}$ $\Rightarrow$ I_1/I_2 = $\frac{9}{4}$`

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