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Two coherent sources of intensity ratio 100:1 interfere. The ratio of interference at the maxima and minima
- a)120:81 cm
- b)121:81 cm
- c)3:1 cm
- d)121:85 cm
Correct answer is option 'B'. Can you explain this answer?
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Interference of Coherent Sources
When two coherent sources interfere, the resultant intensity is given by
I = I1 + I2 + 2√(I1I2)cos(δ)
where I1 and I2 are the intensities of the individual sources, δ is the phase difference between them.
Intensity Ratio
The intensity ratio of two coherent sources is given by
R = I1/I2
Squaring both sides, we get
R^2 = I1/I2
R^2 - 1 = (I1 - I2)/I2
(I1 - I2)/I2 = (R^2 - 1)
(I1 - I2) = I2(R^2 - 1)
(I1 - I2)/I1 = (1 - 1/R^2)
(1 - 1/R^2) is the fractional difference in the intensities of the two sources.
Ratio of Interference at Maxima and Minima
At the maxima, cos(δ) = 1, so the interference term is at its maximum value. At the minima, cos(δ) = -1, so the interference term is at its minimum value. Thus, the ratio of interference at the maxima and minima is given by
(I1 + I2 + 2√(I1I2))/(I1 + I2 - 2√(I1I2)) = [(1 + √R)/(1 - √R)]^2
Substituting R = 100, we get
[(1 + √100)/(1 - √100)]^2 = (121/81)
Therefore, the correct option is B, 121:81 cm.
When two coherent sources interfere, the resultant intensity is given by
I = I1 + I2 + 2√(I1I2)cos(δ)
where I1 and I2 are the intensities of the individual sources, δ is the phase difference between them.
Intensity Ratio
The intensity ratio of two coherent sources is given by
R = I1/I2
Squaring both sides, we get
R^2 = I1/I2
R^2 - 1 = (I1 - I2)/I2
(I1 - I2)/I2 = (R^2 - 1)
(I1 - I2) = I2(R^2 - 1)
(I1 - I2)/I1 = (1 - 1/R^2)
(1 - 1/R^2) is the fractional difference in the intensities of the two sources.
Ratio of Interference at Maxima and Minima
At the maxima, cos(δ) = 1, so the interference term is at its maximum value. At the minima, cos(δ) = -1, so the interference term is at its minimum value. Thus, the ratio of interference at the maxima and minima is given by
(I1 + I2 + 2√(I1I2))/(I1 + I2 - 2√(I1I2)) = [(1 + √R)/(1 - √R)]^2
Substituting R = 100, we get
[(1 + √100)/(1 - √100)]^2 = (121/81)
Therefore, the correct option is B, 121:81 cm.
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Two coherent sources of intensity ratio 100:1 interfere. The ratio of interference at the maxima and minimaa)120:81 cmb)121:81 cmc)3:1 cmd)121:85 cmCorrect answer is option 'B'. Can you explain this answer?
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