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Q.

The intensity ratio of the two interfering beams of light is $β$ What is the value of $[(I_{max} - I_{min}) / (I_{max} + I_{min})] ?$

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a

$2 \sqrt{β}$

b

$2 \sqrt{β} / (1 + β)$

c

$(1 + β) / 2 \sqrt{β}$

d

$2 / (1 + β)$

answer is B.

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Detailed Solution

${(a_{1} / a_{2})}^{2} = β or a_{1} / a_{2} = \sqrt{β} I_{max} = {(a_{1} + a_{2})}^{2} and I_{min} = {(a_{1} - a_{2})}^{2} so \frac{I_{max} - I_{min}}{I_{max} + I_{min}} = \frac{4 a_{1} a_{2}}{2 (a_{1}^{2} + a_{2}^{2})} = \frac{4 a_{1} / a_{2}}{2 (1 + a_{1}^{2} / a_{2}^{2})} = \frac{2 \sqrt{β}}{(1 + β)}$

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