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Two beams of light having intensities I and 4I interfere to produce a fringe pattern on a screen. The phase difference between the beams is π/2 at point A and π at point B. Then the difference between the resultant intencities at A and B is
  • a)
    2I
  • b)
    4I
  • c)
    5I
  • d)
    7I
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Two beams of light having intensities I and 4I interfere to produce a ...
To find the phase difference between the two beams of light, we need to use the formula for the intensity of the interference pattern:

I = I1 + I2 + 2√(I1I2)cos(ΔΦ)

where I1 and I2 are the intensities of the two beams, ΔΦ is the phase difference between them, and I is the intensity of the interference pattern.

In this case, we have I1 = I and I2 = 4I. Substituting these values into the formula, we get:

I = I + 4I + 2√(I×4I)cos(ΔΦ)

Simplifying this expression, we get:

1 = 5 + 4cos(ΔΦ)

Rearranging, we get:

cos(ΔΦ) = (1-5)/4 = -0.5

Using a calculator, we find that the angle whose cosine is -0.5 is 120 degrees (or 2π/3 radians). Therefore, the phase difference between the two beams is 120 degrees.
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Two beams of light having intensities I and 4I interfere to produce a ...
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Two beams of light having intensities I and 4I interfere to produce a fringe pattern on a screen. The phase difference between the beams is π/2 at point A and π at point B. Then the difference between the resultant intencities at A and B isa)2Ib)4Ic)5Id)7ICorrect answer is option 'B'. Can you explain this answer?
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