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(B) Given the intensity ratio of two coherent sources is $\frac{I_1}{I_2} = \frac{1}{4}$,so $I_2 = 4I_1$.The maximum intensity is given by $I_{\max} =

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$2$

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(B) Given the intensity ratio of two coherent sources is $\frac{I_1}{I_2} = \frac{1}{4}$,so $I_2 = 4I_1$.The maximum intensity is given by $I_{\max} = I_1 + I_2 + 2\sqrt{I_1 I_2} = I_1 + 4I_1 + 2\sqrt{I_1(4I_1)} = 5I_1 + 4I_1 = 9I_1$.The minimum intensity is given by $I_{\min} = I_1 + I_2 - 2\sqrt{I_1 I_2} = I_1 + 4I_1 - 2\sqrt{I_1(4I_1)} = 5I_1 - 4I_1 = I_1$.Now,calculate the ratio $\frac{I_{\max} + I_{\min}}{I_{\max} - I_{\min}} = \frac{9I_1 + I_1}{9I_1 - I_1} = \frac{10I_1}{8I_1} = \frac{5}{4}$.Comparing this with the given expression $\frac{2\alpha + 1}{\beta + 3} = \frac{5}{4}$,we have $2\alpha + 1 = 5 \implies 2\alpha = 4 \implies \alpha = 2$ and $\beta + 3 = 4 \implies \beta = 1$.Therefore,$\frac{\alpha}{\beta} = \frac{2}{1} = 2$.

Two coherent sources of light interfere. The intensity ratio of two sources is $1:4$. For this interference pattern,if the value of $\frac{I_{\max} + I_{\min}}{I_{\max} - I_{\min}}$ is equal to $\frac{2\alpha + 1}{\beta + 3}$,then the value of $\frac{\alpha}{\beta}$ will be:

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