Question

A helium-neon laser (λ = 633 nm) illuminates a single slit and is observed on a screen 1.80 mbehind the slit. The distance between the first and second minima in the diffraction pattern is 4.85 mm .

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 1.80 / d] - [1 x (633x10⁻⁹) x 1.80 / d]
= 633x10⁻⁹ x 1.80 / d
= 1139.4x10⁻⁹/d

y₂ - y₁ = = 4.85mm = 0.00485m

1139.4x10⁻⁹/d = 0.00485
d = 0.000234m (=0.234mm)