Why a soap bubble is rainbow
Light hitting a thin film reflects off the top surface and off the bottom surface. The two echoes interfere. Depending on the film thickness, certain colors add up and others cancel — the rainbow you see on a soap bubble is exactly this in action.
Watch the dance
Here is the reflectance of a single film at a fixed wavelength as you vary its thickness. The minima sit at 2 n d = m λ, the maxima at half-integer multiples:
Reflectance oscillates with thickness because the two echoes (top + bottom of the film) shift in phase. Minima sit where 2 nf·d = m·λ. Pile up many films with the right thicknesses and you build a Bragg mirror.
Building blocks of bigger stacks
Stack many thin films with carefully chosen thicknesses and you can engineer almost any reflectance spectrum you want. The most useful example is the distributed Bragg reflector: a designer mirror that reflects ~100% at one chosen color and is transparent everywhere else. Cascade enough thin films and you also need a smarter math tool — that's the transfer-matrix method.
- Two echoes, one wave: every thin film is an interferometer.
- Reflectance oscillates with thickness; period set by the wavelength.