Thin-film interference

A thin film has two surfaces — top and bottom — and light striking it partially reflects off each one. The two reflected waves travel slightly different distances: light reflecting off the bottom surface has to travel into the film and back out again, an extra distance that depends directly on the film's thickness. When those two reflected waves recombine on their way back to your eye, they interfere, and whether that interference is constructive or destructive at a given wavelength depends on how that extra path length compares to the wavelength involved.

Because the condition for constructive interference depends on wavelength, different colours of light are reinforced or cancelled at different film thicknesses. White light contains every visible wavelength at once, so at any point where the film has a particular thickness, some wavelengths interfere constructively (and appear bright) while others interfere destructively (and vanish from the reflection) — the surviving mixture is what you perceive as colour, entirely without any pigment or dye. A soap film has no fixed thickness at all: gravity drains it thinner at the top, air currents disturb it, and its thickness changes continuously across its surface and over time, which is exactly why the colours swirl and shift rather than sitting still.

This same mechanism, engineered rather than accidental, is what anti-reflective coatings on camera lenses and eyeglasses exploit: a coating of carefully chosen thickness is designed so that reflected light in the visible range interferes destructively, cancelling most of the reflection and letting more light through the lens instead of bouncing back off its surface. The iridescent sheen of an oil slick on wet pavement is the same physics again, just with an oil film of varying thickness sitting on water instead of a soap film in air.