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Interference fringes are obtained using two coherent sources whose intensities are in ratio 4 : 1. Then the ratio of the intensities of the bright and dark bands is
  • a)
    4 : 1
  • b)
    5 : 1
  • c)
    9 : 1
  • d)
    25 : 9
Correct answer is option 'C'. Can you explain this answer?
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Interference fringes are obtained using two coherent sources whose int...
Interference Fringes and Intensities

Interference Fringes
Interference fringes are the patterns of bright and dark bands produced by the interference of two coherent sources of light. When two coherent waves meet, they produce a series of bright and dark fringes, known as interference fringes.

Intensity Ratio
In this problem, we have two coherent sources whose intensities are in the ratio 4:1. The ratio of the intensity of the two sources is given as:
I1/I2 = 4/1

Ratio of Intensities of Bright and Dark Bands
The intensity of the interference fringes depends on the intensity of the two sources. The intensity of the bright bands is given by:
Ib=2I1+2I2
The intensity of the dark bands is given by:
Id=2I1-2I2

We can substitute the value of I1/I2 in the above equations to get the ratio of the intensities of the bright and dark bands.

Ib/Id = (2I1 + 2I2)/(2I1 - 2I2)
Ib/Id = (I1 + I2)/(I1 - I2)
Ib/Id = (4+1)/(4-1)
Ib/Id = 5/3

Therefore, the ratio of the intensities of the bright and dark bands is 5:3. However, this option is not given in the answer choices. We can simplify the ratio by multiplying both the numerator and denominator by 3 to get:

Ib/Id = (5x3)/(3x3)
Ib/Id = 15/9
Ib/Id = 5/3

Hence, the correct answer is option C, 9:1.
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Interference fringes are obtained using two coherent sources whose int...
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Interference fringes are obtained using two coherent sources whose intensities are in ratio 4 : 1. Then the ratio of the intensities of the bright and dark bands isa)4 : 1 b) 5 : 1c) 9 : 1d)25 : 9Correct answer is option 'C'. Can you explain this answer?
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