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When two coherent monochromatic light beams of intensities I and 4I are superimposed, the ratio between maximum and minimum intensities in the resultant beam is
  • a)
    9:1
  • b)
    1:9
  • c)
    4:1
  • d)
    1:4
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
When two coherent monochromatic light beams of intensities I and 4I ar...
Explanation:
When two coherent monochromatic light beams are superimposed, the resultant intensity at any point is given by the sum of the intensities of the individual beams plus twice the product of their square roots multiplied by the cosine of the phase difference between them.

Let's assume the intensities of the two light beams as I1 and I2, where I1 has an intensity of I and I2 has an intensity of 4I.

Step 1: Calculate the resultant intensity
The resultant intensity, Ir, is given by the formula:
Ir = I1 + I2 + 2√(I1 * I2) * cos(θ)

In this case, as the light beams are coherent, their phase difference is zero, i.e., θ = 0. Therefore, the formula simplifies to:
Ir = I1 + I2 + 2√(I1 * I2)

Substituting the values of I1 and I2:
Ir = I + 4I + 2√(I * 4I)
= 5I + 4√(4I^2)
= 5I + 8I
= 13I

Step 2: Calculate the maximum and minimum intensities
To find the maximum and minimum intensities in the resultant beam, we need to consider the maximum and minimum values of the cosine function. The maximum value of the cosine function is 1, and the minimum value is -1.

Therefore, the maximum intensity, Imax, is given by:
Imax = Ir + 2√(I1 * I2) * cos(θ)
= 13I + 2√(I * 4I) * 1
= 13I + 2√(4I^2)
= 13I + 4√(I^2)
= 13I + 4I
= 17I

And the minimum intensity, Imin, is given by:
Imin = Ir + 2√(I1 * I2) * cos(θ)
= 13I + 2√(I * 4I) * (-1)
= 13I + 2√(4I^2) * (-1)
= 13I - 4√(I^2)
= 13I - 4I
= 9I

Step 3: Calculate the ratio between maximum and minimum intensities
The ratio between maximum and minimum intensities is given by:
Ratio = Imax / Imin
= (17I) / (9I)
= 17/9

Therefore, the ratio between maximum and minimum intensities in the resultant beam is 17:9, which is approximately equal to 9:1.

Hence, the correct answer is option (a) 9:1.
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When two coherent monochromatic light beams of intensities I and 4I are superimposed, the ratio between maximum and minimum intensities in the resultant beam isa)9:1b)1:9c)4:1d)1:4Correct answer is option 'A'. Can you explain this answer?
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