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Question
Two coherent sources of different intensities send waves which interfere. The ratio of maximum intensity to the minimum intensity is 25. The intensities of the sources are in the ratio ______.
Options
25 : 1
5 : 1
9 : 4
625 : 1
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Solution
Two coherent sources of different intensities send waves which interfere. The ratio of maximum intensity to minimum intensity is 25. The intensities of the sources are in the ratio 9 : 4.
Explanation:
The ratio of maximum intensity and minimum intensity is given by,
`I_(max) = (sqrtI_1 + sqrtI_2)^2, I_(min) = (sqrtI_1 - sqrtI_2)^2`
∴ `I_(max)/I_(min) = ((sqrtI_1 + sqrtI_2)/(sqrtI_1 - sqrtI_2))^2 = 25`
`(sqrtI_1 + sqrtI_2)/(sqrtI_1 - sqrtI_2) = 5`
⇒ `(sqrt(I_1/I_2) + 1)/(sqrt(I_1/I_2)- 1) = 5`
⇒ `sqrt(I_1/I_2) + 1 = 5sqrt(I_1/I_2) - 5`
⇒ `6 = 4sqrt(I_1/I_2)`
⇒ `sqrt(I_1/I_2) = 3/2`
⇒ `I_1/I_2 = 9/4`
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