Question

A helium-neon laser (λ=633nm) illuminates a single slit and is observed on a screen 1.35 m behind the slit. The distance between the first and second minima in the diffraction pattern is 4.70 mm . Part A What is the width (in mm) of the slit?

Answer 1

The standard formula for the position of the m-th minimum from a single slit diffraction pattern is:
yₘ = mλD/d
where
m = the order of minimum
yₘ = distance on the screen of the minimum from central axis
λ = wavelength
D = screen-to-slit distance
d = slit width

The difference in y values between the 1st and 2nd minima is
y₂ - y₁ = [2 x (633x10⁻⁹) x 1.35 / d] - [1 x (633x10⁻⁹) x 1.35 / d]
= 633x10⁻⁹ x 1.35/ d
= 854.55 x10⁻⁹/d

y₂ - y₁ = = 4.70mm = 0.00470m

854.55x10⁻⁹/d = 0.00470
d = 0.00018m (=0.18mm)

Hope this helps.

please thumbs up!