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Q.

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 $\frac{2 α + 1}{β + 3}, then \frac{α}{β}$ will be :

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a

2

b

1

c

1.5

d

0.5

answer is B.

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Detailed Solution

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$\begin{array}{l} \frac{I_{1}}{I_{2}} = \frac{1}{4} \\ I_{2} = 4 I_{1} \\ I_{max} = I_{1} + 4 I_{1} + 2 \sqrt{I_{1} 4 I_{1}} = 9 I_{1} \\ I_{min} = I_{1} + 4 I_{1} - 2 \sqrt{I_{1} 4 I_{1}} = I_{1} \\ ∴ \frac{9 I_{1} + I_{1}}{9 I_{1} - I_{1}} = \frac{10}{8} = \frac{5}{4} = \frac{2 α + 1}{β + 1} \\ α = 2 β = 1 \\ ∴ \frac{α}{β} = \frac{2}{1} = 2 \end{array}$

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Two coherent sources of light interfere. The intensity ratio of two sources is 1 : 4. For this interference pattern if the value of Imax+IminImax−Imin is equal to 2α+1β+3, then αβ will be :