 # what will happen to shape of fringes when we use slits instead of pin holes in young experiment for interference?

12 years ago

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 ...)

All the best.

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