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

5 years ago

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```										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.
Win exciting gifts by                  answering the questions on Discussion Forum. So help      discuss     any       query   on askiitians forum and become an Elite      Expert   League      askiitian.

Sagar Singh
B.Tech, IIT Delhi

```
5 years ago

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