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Two coherent sources have intensity ratio of 100 : 1, and are used for obtaining the phenomenon of interference. Then the ratio of maximum and minimum intensity will be _
- a)100 : 1
- b)121 : 81
- c)1 : 1
- d)5 : 1
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Two coherent sources have intensity ratio of 100 : 1, and are used for...
I1/I2 = W1/W2 = 100/1 = (a1/a2)2
a1/a2 = 10/1
a1 = 10x
a2 = x
Imax/lmin = (a1+a2/a1-a2)2
(10x+x/10x-x)2
(11x/9x)2
(11/9)2
121/81
a1/a2 = 10/1
a1 = 10x
a2 = x
Imax/lmin = (a1+a2/a1-a2)2
(10x+x/10x-x)2
(11x/9x)2
(11/9)2
121/81
This question is part of UPSC exam. View all Class 11 courses
Most Upvoted Answer
Two coherent sources have intensity ratio of 100 : 1, and are used for...
Interference of Coherent Sources
When two coherent sources are used, the phenomenon of interference is observed. The interference pattern is formed due to the superposition of the waves generated by the two sources.
Intensity Ratio
The intensity of the interference pattern depends on the phase difference between the waves generated by the two sources. The intensity ratio of the two sources is given by the square of the amplitude ratio.
Let the amplitude ratio of the two sources be a:b, then the intensity ratio is given by (a/b)^2.
In this case, the intensity ratio of the two sources is given as 100:1, which means the amplitude ratio is 10:1.
Maximum and Minimum Intensity
When two coherent sources are used for interference, the interference pattern consists of bright and dark fringes. The maximum intensity occurs at the bright fringes, and the minimum intensity occurs at the dark fringes.
Ratio of Maximum and Minimum Intensity
The ratio of maximum and minimum intensity is given by the ratio of the sum and difference of the intensities of the two sources.
Let I1 and I2 be the intensities of the two sources. Then, the maximum intensity is given by (I1 + I2 + 2√I1I2), and the minimum intensity is given by (I1 + I2 - 2√I1I2).
Substituting the intensity ratio (100:1) in the above equations, we get:
Maximum intensity = 121I1/81
Minimum intensity = I1/81
Therefore, the ratio of maximum and minimum intensity is given by:
(121I1/81)/(I1/81) = 121:1
Hence, the correct option is (b) 121:81.
When two coherent sources are used, the phenomenon of interference is observed. The interference pattern is formed due to the superposition of the waves generated by the two sources.
Intensity Ratio
The intensity of the interference pattern depends on the phase difference between the waves generated by the two sources. The intensity ratio of the two sources is given by the square of the amplitude ratio.
Let the amplitude ratio of the two sources be a:b, then the intensity ratio is given by (a/b)^2.
In this case, the intensity ratio of the two sources is given as 100:1, which means the amplitude ratio is 10:1.
Maximum and Minimum Intensity
When two coherent sources are used for interference, the interference pattern consists of bright and dark fringes. The maximum intensity occurs at the bright fringes, and the minimum intensity occurs at the dark fringes.
Ratio of Maximum and Minimum Intensity
The ratio of maximum and minimum intensity is given by the ratio of the sum and difference of the intensities of the two sources.
Let I1 and I2 be the intensities of the two sources. Then, the maximum intensity is given by (I1 + I2 + 2√I1I2), and the minimum intensity is given by (I1 + I2 - 2√I1I2).
Substituting the intensity ratio (100:1) in the above equations, we get:
Maximum intensity = 121I1/81
Minimum intensity = I1/81
Therefore, the ratio of maximum and minimum intensity is given by:
(121I1/81)/(I1/81) = 121:1
Hence, the correct option is (b) 121:81.
Community Answer
Two coherent sources have intensity ratio of 100 : 1, and are used for...
I1/I2=W1/W2=100/1=(a1/a2)2
a1/a2=10/1
a1=10x
a2=x
Imax/lmin=(a1+a2/a1-a2)2
(10x+x/10x-x)2
(11x/9x)2
(11/9)2
121/81... ans
a1/a2=10/1
a1=10x
a2=x
Imax/lmin=(a1+a2/a1-a2)2
(10x+x/10x-x)2
(11x/9x)2
(11/9)2
121/81... ans
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Two coherent sources have intensity ratio of 100 : 1, and are used for obtaining the phenomenon of interference. Then the ratio of maximum and minimum intensity will be _a)100 : 1b)121 : 81c)1 : 1d)5 : 1Correct answer is option 'B'. Can you explain this answer?
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