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rajesh saini Grade:
`        what will happen to shape of fringes when we use slits instead of pin holes in young experiment for interference?`
7 years ago

## Answers : (1)

SAGAR SINGH - IIT DELHI
879 Points
```										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 ...)

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Sagar Singh
B.Tech, IIT Delhi

```
7 years ago
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