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Question
Choose the correct option:
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?
Options
5:1
25:1
3:2
9:4
Solution
9:4
Explanation:
Given: The ratio of maximum intensity to minimum intensity is `I_(max)/I_(min) = 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) = 25/1` for `I_(max)/I_(min) = 25/1` in the above relation.
`25/1 = (a_1 + a_2)^2/(a_1 - a_2)^2`
`5/1 = (a_1 + a_2)/(a_1 - a_2)`
⇒ `a_1 = 3; a_2 = 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 = 3^2/2^2`
I1 : I2 :: 9 : 4
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