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

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

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1 Answers

SAGAR SINGH - IIT DELHI
878 Points
13 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.

1915_Deubleslit.JPG

 

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

226_fringe-width.JPG

 

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.)

 1679_YOUNG’S DOUBLE SLIT EXPERIMENT.JPG

 

= 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 ...)

 

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All the best.

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Askiitians Expert

Sagar Singh

B.Tech, IIT Delhi

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