In a Young.s double slit experiment wave length of light used is 5000 A and distance between the slits is 2mm, distance from slits is 1m. Find fringe width and also calculate the distance of `7^(th)` dark fringe from central birght fringe.

Explanation

Given = ` lamda = 5000 xx 10^(-10) m = 5 xx 10^(-7) m`
d = ` 2 xx 10^(-3) m , D = 1m `
We know that ,fringe width ` beta = ( lamdaD)/d `
i.e, ` beta = ( 5 xx 10^(-7)xx1 )/( 2 xx 10^(-3)) = 2.5 xx 10^(-4) m `
i.e,` beta = 2.5 xx 10^(-4) m`
The distance of dark fringe ` x_(4) = ((2n+1)beta)/2 `
i.e, Distance of ` 7^(th) ` dark fringe = ` ((2xx6+1)/2) ( 2.5 xx 10^(-4)) `
n = ` 1.625 xx 10^(-3) m`
Hence distance of ` 7^(th)` dark fringe = 1.625 mm.