Light from a helium-neon laser (λ=633nm) is used to illuminate two narrow slits. The interference pattern is observed on a screen 3.1mbehind the slits. Twelve bright fringes are seen, spanning a distance of 51mm .

experiment is given by the spanning distance / order of the interference

=51 / 12 mathrm{~mm}

=51 / 12

this is equal to lambda { }^{*} mathrm{D} / mathrm{d}

=mathrm{d} the gap beteween the slits

= lambdaD { }^{*}(12 / 51)

=633 times 10^{wedge}-6 times 3.1 times 10^{wedge} 3 times 12 / 51 mathrm{~mm}

so the gap between the slits is

=0.462 mathrm{~mm}

Y = mLR/d

where Y = fringe width

m = no. of fringes

L = wavelength

R = distance between slit and the screen

d = slit width

so here

d = mLR/Y

d = 12 * 633*10^-9 * 3.1/51*10^-3

d = 0.461 mm