What is the spacing (in mm) between the two slits?

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

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