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S1 and S2 are the two coherent point sources of light located in the xy-plane at points (0,0) and (0,3λ) respectively.Here λ is the wavelength of light. At which one of the following points (given as coordinates), the intensity of interference will be maximum?
  • a)
    (3λ, 0)
  • b)
    (4λ, 0)
  • c)
    (5λ/4, 0)
  • d)
    (2λ/3, 0)
Correct answer is option 'B'. Can you explain this answer?
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S1 and S2 are the two coherent point sources of light located in the x...
), respectively. The distance between the two sources is 3 units. The two sources emit light waves with a wavelength of 2 units.

When two coherent sources emit light waves, they interfere with each other. This interference can be either constructive or destructive, depending on the phase difference between the waves.

In this case, the phase difference between the waves from S1 and S2 can be calculated using the formula:

Δφ = (2π/λ) * d * sin(θ)

Where Δφ is the phase difference, λ is the wavelength, d is the distance between the sources, and θ is the angle between the line connecting the two sources and the point of interest.

Let's consider a point P located at coordinates (x, y) in the xy-plane. The angle θ can be calculated using the formula:

θ = atan((y-3)/x)

Now, we can calculate the phase difference between the waves from S1 and S2 at point P. Assuming x and y are known, we can substitute the values into the formulas to get the phase difference.

Δφ = (2π/2) * 3 * sin(atan((y-3)/x))

The phase difference determines the interference pattern observed at point P. If the phase difference is an integer multiple of 2π, the waves will interfere constructively, creating bright fringes. If the phase difference is an odd multiple of π, the waves will interfere destructively, creating dark fringes.

By analyzing the phase difference at different points in the xy-plane, we can determine the interference pattern created by the two coherent sources S1 and S2.
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