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In the ideal double-slit experiment, when a glass-plate (refractive index 1.5) of thickness t is introduced in the path of one of the interfering beams (wave-lengh t λ), the intensity at the position where the central maximum occurred previously remains unchanged. The minimum thickness of the glass-plate is
  • a)
    2 λ
  • b)
    2 λ /3
  • c)
    λ /3
  • d)
    λ
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
In the ideal double-slit experiment, when a glass-plate (refractive in...
Path difference = (µ – 1) t = n λ;
For minimum t, n = 1; ∴ t = 2 λ
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In the ideal double-slit experiment, when a glass-plate (refractive in...
Assuming that the glass plate is introduced in the path of one of the interfering beams, the phase difference between the two beams will change due to the difference in optical path length caused by the glass plate.

The phase difference between the two beams is given by:

Δφ = 2πΔL/λ

Where ΔL is the difference in optical path length between the two beams and λ is the wavelength of the light.

In this case, the glass plate has a refractive index of 1.5 and a thickness of t. The difference in optical path length caused by the glass plate is given by:

ΔL = nt - t

Where n is the refractive index of the glass plate. Substituting in the values, we get:

ΔL = 1.5t - t = 0.5t

Therefore, the phase difference between the two beams is:

Δφ = 2π(0.5t)/λ = πt/λ

So, the phase difference between the two beams will change by πt/λ when the glass plate is introduced in the path of one of the interfering beams. This change in phase difference will affect the interference pattern observed in the double-slit experiment.
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In the ideal double-slit experiment, when a glass-plate (refractive index 1.5) of thickness t is introduced in the path of one of the interfering beams (wave-lengh t λ), theintensity at the position where the central maximum occurred previously remains unchanged. The minimum thickness of the glass-plate isa)2 λb)2 λ /3c)λ /3d)λCorrect answer is option 'A'. Can you explain this answer?
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