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.

Light of wavelength 6000Å is incident on a slit of width 0.30 mm. The

1.	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.
Answer» 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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