One wavelength, three experiments: grating, double slit, soap film

Three interference experiments, one number joining them. The grating goes first because it is the only one of the three that measures a wavelength well: d sin θ = mλ puts the first order 25° off axis, where a protractor is plenty, while a double slit crowds its fringes into millimetres and a soap film gives you a colour rather than a number. Once λ is pinned down, the other two become predictions — and that is the honest order of a real lab, calibrate on the instrument that resolves best, then spend the result.

Step 4 is where the marks go missing. Both thin-film conditions look like 2nt = (something)λ, and choosing between them is not a question of bright versus dark, it is a question of counting reflections that invert. Light bouncing off a denser medium flips by half a cycle; light bouncing off a rarer one does not. A soap film in air inverts at the top surface only — one flip, so the extra half-wave lands on the bright condition and 2nt = (m + ½)λ. Lay the same film on glass and both surfaces invert, the flips cancel, and the two conditions swap places; that single bookkeeping step is the difference between a quarter-wave anti-reflection coating that works and one that makes a lens shine. Notice how thin the answer is — 119 nm, about a fifth of a wavelength. Let a film drain until 2nt approaches zero and it satisfies no bright order at all, which is why the top of a bubble goes black just before it bursts. Thomas Young pointed at Newton's own rings in 1801 and said this is interference; it took most of a century for anyone to be believed saying it.