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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0.5

1.5

answer is B.

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Detailed Solution

$\frac{I_{1}}{I_{2}}$ = $\frac{1}{4}$ $\Rightarrow$ I2 = 4I1
Imax= $I_{1} + 4 I_{1} + 2 \sqrt{I_{1}} \sqrt{4 I_{1}} = 9 I_{1}$
Imin = $I_{1} + 4 I_{1} - 2 \sqrt{I_{1}} \sqrt{4 I_{1}} = I_{1}$
$\frac{Im a x + Im i n}{Im a x - Im i n} = \frac{9 I_{1} + I_{1}}{9 I_{1} - I_{1}} = \frac{10}{8} = \frac{5}{4} \Rightarrow \frac{2 α + 1}{β + 3} = \frac{5}{4}$
$α$ = 2, $β$ = 1 $\frac{α}{β} = \frac{2}{1} = 2$