what is band width. derived an expression for this

Hey Lovepreet

Expression for bandwidth of interference fringes in youngs double experience : Let d be the distance between two coherent sources A and B of wavelength λ. A screen XY is placed parallel to AB at a distance D from the coherent sources. C is the mid point of AB. O is a point on the screen equidistant from A and B.P is a point at a distance x from O, as shown in figure. Waves from A and B meet at P in phase or out of phase depending upon the path difference between two waves.
Interference bandwidth
Draw AM perpendicular to BP.
The path difference S=BP−AP
AP=MP
∴ δ=BP−AP=BP−MP=BM
In right angled ABM,BM=dsinθ
If Q is small, sinθ=θ
∴ the path difference δ=θd
In right angled triangle COP,
tanθ=CPOP=Dx
For small values of θ,tanθ=θ
∴ the path difference δ=Dxd
Bright f ringes : By the principle of interference, condition for constructive interference is the path difference =nλ
∴ μDxd=λ
where n=0,1,2,..... indicates the order of the bright fringes.
∴ x=dDλ
This equation gives the distance of the nth bright fringe from the p oint O.
Dark fringes : By the principle of interference, condition for destructive interference is the path difference =(2n−1)2λ.
where n=1,2,3,.... indicate the order of the dark fringes.
∴ x=dD(2n−1)2λ
This equation gives the distance of the nth dark frin ge from the point O. Thus, on the screen alternate dark and bright bands are seen on either side of the central bright band.
Bandwidth (β) : The distance between any two consecutive bright or dark bands is called bandwidth. The distance between (n+1)th and nth order consecutive bright fringes from O is given by
x(n+1)−xn=dD(n+1)λ−dDnλ=dDλ
Bandwidth, β=dDλ.

Hope this will help you

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