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Light of wavelength 6000Å is incident on...

Light of wavelength 6000Å is incident on a slit of width 0.30 mm. The screen is placed 2 m from the slit. Find (a) the position of the first dark fringe and (b). The width of the central bright fringe.

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The first fringe is on either side of the central bright fringe.
here `n=+-1,D=2m,lamda=6000Å=6xx10^(-7)m`
`thereforesintheta=(x)/(D)impliesa=0.30mm=3xx10^(-4)m`
`impliesasintheta=nlamdaimplies(ax)/(D)=nlamda`
(a). `x=(nlamdaD)/(a)impliesx=+-[(1xx6xx10^(-7)xx2)/(3xx10^(-4))]=+-4xx10^(-3)m`
The positive and negative signs corresponds to the dark fringes on either side of the central bright fringe.
(b). The width of the central bright fringe `y=2x=2xx4xx10^(-3)=8xx10^(-3)m=8mm`
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