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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...
Given:
- Two coherent monochromatic light beams of intensities I and 4I are superimposed.

To find:
- The ratio between maximum and minimum intensities in the resultant beam.

Solution:
- When two coherent light beams are superimposed, the resultant intensity is given by I_r = I_1 + I_2 + 2√(I_1*I_2)*cos(φ), where φ is the phase difference between the two beams.
- Since the two beams are coherent, their phase difference is constant and φ = 0 or 2π.
- When φ = 0, the two beams are in phase and add up constructively to give maximum intensity.
- When φ = 2π, the two beams are out of phase and add up destructively to give minimum intensity.
- Therefore, the ratio between maximum and minimum intensities in the resultant beam is given by (I_1 + I_2 + 2√(I_1*I_2)) / (I_1 + I_2 - 2√(I_1*I_2)).
- Substituting I_1 = I and I_2 = 4I, we get the ratio as (I + 4I + 2√(I*4I)) / (I + 4I - 2√(I*4I)) = (5 + 2√4) / (5 - 2√4) = 9:1.

Therefore, the correct answer is option 'A'.
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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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