Soap Bubble Interference - 2D Thin-Film Colours, Reflectance Spectrum and Drainage

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Speed

Live readouts

Graphs

Numerical checks

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How to use

The bubble is coloured from the true reflectance of its film at each height. Drag inside the bubble to place the yellow probe line and read the spectrum, optical path and colour at that thickness. Try: (1) Fresh bubble - bands of colour stack up while the film drains; (2) Almost black top film - when the film is much thinner than a wavelength the reflected waves cancel and the top turns black; (3) Grazing view - raise the viewing angle and every band shifts toward blue; (4) Thick film - many overlapping fringes average to near-white. Space pauses, R restarts drainage.

The science

Two reflections. Light reflects from the front surface (air to film, phase flip of half a wave) and from the back surface (film to air, no flip). Their path difference is 2 n t cos(theta_t) so with the half-wave flip, reflection is bright when 2 n t cos(theta_t) = (m + 1/2) lambda and dark when 2 n t cos(theta_t) = m lambda.

Exact reflectance. Summing all multiple reflections (Airy) with Fresnel amplitudes r (s and p polarised): R = |r(1 - e^(i d))|^2 / |1 - r^2 e^(i d)|^2, d = 4 pi n t cos(theta_t) / lambda At normal incidence the first maximum is 4r^2/(1+r^2)^2 which for n = 1.33 is only about 8%, so bubbles look pale.

Colour. The reflectance spectrum is weighted by the CIE 1931 colour-matching functions (analytic multi-lobe fit), converted to sRGB and white-balanced for an equal-energy light source.

Drainage. Gravity pulls liquid down: the film is a wedge, thinnest at the top. The top thickness decays roughly exponentially until it goes below about 10-20 nm (a black film) and the bubble bursts shortly after. Marangoni flows add the swirling turbulence.

Checks. (1) R is zero at t = lambda/(2n); (2) the first maximum equals 4r^2/(1+r^2)^2; (3) the Airy formula equals an independent characteristic-matrix calculation to 1e-9 over 200 random cases; (4) zero thickness is black; (5) a very thick film is near-white.

Simplifications. Constant refractive index (no dispersion), no surfactant layer structure, wedge plus sinusoidal swirl instead of a fluid solver, a spherical shading cue instead of true 3D reflection of the environment, and one fixed illuminant.