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 ΔP_o

(where ΔP_o is optical path difference, ΔP_o=ΔP_g; ΔP_g  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 ...)

Please feel free to ask your queries here. We are all IITians and here to help you in your IIT JEE preparation.

All the best.

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B.Tech, IIT Delhi