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what will happen to shape of fringes when we use slits instead of pin holes in young experiment for interference?
Dear student,
Shape will be circular........
A train of plane light waves is incident on a barrier containing two narrow slits separated by a distance’d’. The widths of the slits are small compared with wavelength of the light used, so that interference occurs in the region where the light from S1 overlaps that from S2. A series of alternately bright and dark bands can be observed on a screen placed in this region of overlap. The variation in light intensity along the screen near the centre O shown in the figure Now consider a point P on the screen. The phase difference between the waves at P is θ, where θ= 2π/λ ΔPo (where ΔPo is optical path difference, ΔPo=ΔPg; ΔPg being the geometrical path difference.) = 2π/λ [ S2P - S1P ] (here λ = 1 in air) As As, D >> d, S2P - S1P ≈ λ d sinθ sin θλ ≈ tanθ( = y/D). [for very small θ] Thus, θ = 2π/λ (dy/D) For constructive interference, θ = 2nλ (n = 0, 1, 2...) ⇒ 2π/λ (dy/D) = 2nπ ⇒ y = n λD/d Similarly for destructive interference, y = (2n - 1) λD/2d (n = 1, 2 ...)
A train of plane light waves is incident on a barrier containing two narrow slits separated by a distance’d’. The widths of the slits are small compared with wavelength of the light used, so that interference occurs in the region where the light from S1 overlaps that from S2.
A series of alternately bright and dark bands can be observed on a screen placed in this region of overlap.
The variation in light intensity along the screen near the centre O shown in the figure
Now consider a point P on the screen. The phase difference between the waves at P is θ, where
θ= 2π/λ ΔPo
(where ΔPo is optical path difference, ΔPo=ΔPg; ΔPg being the geometrical path difference.)
= 2π/λ [ S2P - S1P ] (here λ = 1 in air)
S2P - S1P ≈ λ d sinθ
sin θλ ≈ tanθ( = y/D).
[for very small θ]
Thus, θ = 2π/λ (dy/D)
θ = 2nλ (n = 0, 1, 2...)
⇒ 2π/λ (dy/D) = 2nπ ⇒ y = n λD/d
y = (2n - 1) λD/2d (n = 1, 2 ...)
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Sagar Singh
B.Tech, IIT Delhi
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