Light of wavelength 580 nm is incident on a slit having a width of `0.300` nm The viewing screen is 2.00 m from the slit. Find the positions of the first dark fringe and the width of the central bright fringe.

Explanation

For first dark fringe,
`sintheta=+-(lambda)/(a)=+-(5.8xx10^(-7)m)/(0.3xx10^(-3)m)=+-1.9xx10^(-3)`
The positions of the first minima, measured from the central axis are
`y_(1)=+-D tantheta~~+-D sin theta`
As `theta` is small, `tan theta=sintheta`
`impliesy_(1)=+-D((lambda)/(a))=+-2(1.9xx10^(-3)m)=+-3.8xx10^(-3)m`
The positive and negative signs correspond to the first dark fringes on either side of the central bright fringe is given by `2 |y_(1)|=7.6xx10^(-3)m=7.6mm`.
Note that this value is much greater than the width of the slit `(0.3mm)`