Thin-Film Interference: Where Soap-Bubble Colours Come From

Two reflections, one interference pattern

A soap film or an oil slick is thin enough that light hitting it produces two distinct reflected beams: one that bounces straight off the top surface, and one that travels into the film, bounces off the bottom surface, and travels back out. Because both beams originate from the same incoming wave and end up travelling in the same direction toward your eye, they overlap and interfere. Whether that interference is constructive (bright) or destructive (dark, or missing that colour) depends entirely on the extra distance the second beam travelled inside the film, compared to the wavelength of the light.

Because that path difference depends on wavelength, different colours of white light interfere constructively at different film thicknesses. A film of one exact thickness reinforces red and cancels blue; a slightly thicker or thinner patch reinforces a different colour — which is exactly the swirling rainbow pattern you see on the surface of a soap bubble, where the film's thickness is constantly changing under gravity and evaporation.

The optical path difference and the half-wave shift

The condition for constructive or destructive interference depends on the film's refractive index n, its physical thickness t, and the angle of refraction θ the light takes inside the film — plus one subtlety that trips people up constantly: a reflection off a boundary where the refractive index increases flips the wave by half a wavelength (exactly like a wave on a rope reflecting off a wall it can't move), while a reflection off a boundary where the index decreases does not. For a soap film in air (low-high-low index), only the top reflection is flipped, so the two reflected beams start out already half a wavelength out of step before either has travelled any extra distance:

optical path difference (extra distance travelled inside the film):

  delta = 2 * n * t * cos(theta)

one reflection flipped by half a wavelength (soap film in air):

  constructive (bright):   delta = (m + 1/2) * lambda      m = 0, 1, 2, ...
  destructive  (dark):     delta =  m * lambda

zero or two flips (e.g. anti-reflection coating on glass):

  constructive (bright):   delta =  m * lambda
  destructive  (dark):     delta = (m + 1/2) * lambda

That is also why a soap film always looks dark (not bright) right before it pops: once the film is thinner than about a quarter of the shortest visible wavelength, the path difference from thickness alone becomes negligible, and the single unmatched half-wave flip forces destructive interference for every colour at once, so almost no light reflects back at all — you're looking straight through it.

Anti-reflection coatings run the effect in reverse

Engineers deliberately deposit a thin coating on camera lenses and eyeglasses, chosen with a refractive index between air and glass and a thickness of a quarter-wavelength, so that the reflection from the top of the coating and the reflection from the coating-glass boundary destructively cancel for the wavelength of interest (usually tuned toward the middle of the visible spectrum, green-yellow, which is why coated lenses often show a faint purple tint — the leftover, imperfectly cancelled red and blue). Multi-layer coatings stack several such films tuned to different wavelengths to suppress reflection across almost the whole visible range at once, which is standard practice in modern camera and telescope optics.

Newton's rings and measuring nanometres with visible light

Press a slightly curved lens down onto a flat glass plate and you get a thin, wedge-shaped air gap between them whose thickness increases outward from the point of contact — shine light through it and you see concentric bright and dark rings, Newton's rings, each ring marking a contour of constant path difference. Because visible light has a wavelength around 500 nanometres, and interference is sensitive to path differences of a fraction of that, thin-film interference is one of the most precise and low-tech ways to measure extremely small thicknesses and surface flatness — the same principle, refined into laser interferometry, underlies precision manufacturing metrology and, at the extreme end, gravitational-wave detectors.

Frequently asked questions

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