In Young’s double-slit experiment, the two coherent sources have different intensities. If the ratio of the maximum intensity to the minimum intensity in the interference pattern produced is 25:1, what is the ratio of the intensities of the two sources?

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KollegeApply · Accepted Answer

9:4 Explanation: Given: The ratio of maximum intensity to minimum intensity is I_"max"/I_"min" = $\frac{25}{1}$ Apply the formula to calculate the ratio I_"max"/I_"min" `I_"max"/I_"min" = (a_1 + a_2)^2/(a_1 - a_2)^2 Where, a_1^2/a_2^2 = I_1/I_2 Substitute I_"max"/I_"min" = $\frac{25}{1}$ for I_"max"/I_"min" = $\frac{25}{1}$ in the above relation. $\frac{25}{1}$ = (a_1 + a_2)^2/(a_1 - a_2)^2 $\frac{5}{1}$ = (a_1 + a_2)/(a_1 - a_2)` $\Rightarrow$ a1 = 3; a2 = 2 Substitute 3 for a1 and 2 for a2 in the relation a_1^2/a_2^2 = I_1/I_2 I_1/I_2 = 3^$\frac{2}{2}$^2 I_1/I_2 = $\frac{9}{4}$ I1 : I2 :: 9 : 4

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