Double-slit interference (Physics HL)

The big idea: Shine one colour of light through two narrow slits that are close together, and you get a row of equally spaced bright and dark bands — called fringes.

You have seen this already: Squint at a distant streetlight through a thin curtain or a fine umbrella and it smears into a little pattern of bright dots. Two slits make the same thing happen cleanly.

New words: Fringe = one of the bright or dark bands on the screen.

Fringe spacing s = the gap from one bright fringe to the next bright fringe.

Coherent = the two slits give light of the same wavelength with a fixed phase relationship — needed for a steady pattern.

Spot it: The fringes are evenly spaced and the central one is the brightest. The spacing s is the same gap all the way across.

The set-up, step by step

The fringe spacing depends on three things: the wavelength of the light, how far away the screen is, and how close the two slits are. They combine into one equation that is given in the data booklet.

Which way each one pushes the fringes: Bigger λ or bigger D → wider fringes (s up).

Bigger slit separation d → narrower fringes (s down), because d is on the bottom.

Reading s off a picture of fringes: Count the gaps, not the fringes: if 7 bright fringes span 12 cm (centre of the first to centre of the last), there are 6 gaps, so s = 12 ÷ 6 = 2.0 cm.

Counting from the centre, the n-th dark fringe has a path difference of (n − ½)λ.

How this is tested — double-slit questions come in two flavours:

The classic trap: Mixing units — get every length into metres (mm = 10⁻³ m, nm = 10⁻⁹ m) before substituting.

Fringe angle in radians: Each bright fringe sits at an angle θ from the slits where d sin θ = nλ.

For the small angles in these experiments, sin θ ≈ θ (in radians), so neighbouring maxima are about λ/d apart, and the nearest minima either side of the centre are also λ/d apart in total.