A beam of light of wavelength 600 nm from a distant source falls on a single slit 1 mm wide and the resulting diffraction pattern is observed on a screen 2 m away. What is the distance between the first dark fringe on either side of the central bright fringe?

Explanation

For first minimum (n = 1) on either side of central maximum.
`sin theta = (lambda)/(a)`
Where a is width of the slit
Since `theta` is very small. `(sin theta approx theta)`
`theta = (lambda)/(a)`
`sin theta approx theta = (x)/(2D)`
Where, x is distance of first dark fringe from central maximum.
D is distance between slit and screen.
From equation (1) and (2)
`(x)/(2D) = (lambda)/(a)`
`x=(2Dlamda)/(a)=(2xx2xx600xx10^(-9))/(1xx10^(-3))`
`=2400 xx 10^(-6) = 2.4 xx 10^(-3) m`
x = 2.4 mm