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Draw a neat labelled diagram of Young.s ...

Draw a neat labelled diagram of Young.s Double Slit experiment. Show that `beta= (lamda D)/(d)`, where the terms have their usual meaning (either for bright or dark fringe).

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Let .S. be the monochromatic source of light and `S_(1),S_(2)` be the two parallel narrow slits close to each other. According to Huygen.s principle, `S_(1)` and `S_(2)` act as new wave source from which secondary wave originate. Let `S_(1)A` is the perpendicular drawn on `S_(2)P` from `S_(1)`. Path difference is given by

In right angled `DeltaS_(1),S_(2)A,sintheta=(S_(2)A)/(S_(1)S_(2))`
In right angled `DeltaPCO,tantheta=(OP)/(CO)`
If `theta` is small, then `(S_(2)A)/(S_(1)S_(2))=(OP)/(CO)`
`(S_(2)A)/(d)=(x)/(D)`
So, Path difference `=S_(2)A=(xd)/(D)`
The intensity of light will be maximum at those places where the path difference between the interfering waves is zero or integral multiple of `lamda`.
So, `(xd)/(D)=mlamda`
or `x=(mDlamda)/(d)`
Now, distance between two consecutive bright fringes or dark fringes is called fringe width `(beta)`.
`:.beta=x_(n+1)-x_(n)`
`=((n+1)Dlamda)/(d)=(nDlamda)/(d)`
`impliesbeta=(DDeltalamda)/(d)`
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