The Colors of a Soap Film

A soap film’s changing colors arise from interference between light reflected at its front and back surfaces. Because reflection from air into water reverses the wave’s phase while reflection from water into air does not, the two returning beams have opposite signs. Their extra travel through the film creates a wavelength-dependent phase delay, so the reflected brightness follows a cosine of the light’s wavenumber. The film’s optical path difference is twice the water’s refractive index times its thickness. A two-beam calculation captures the effect closely; additional internal reflections make only a small correction.

To turn the reflected spectrum into perceived color, the analysis combines it with standard CIE color-matching functions and a daylight illuminant, then converts the resulting tristimulus values to display color. This yields a simple description: the color is proportional to a fixed white point minus the cosine transform of three spectral weighting curves. At zero thickness the reflections cancel, producing black; a very thin film reflects a faint bluish gray. As the film thickens, brightness minima recur about every 208 nanometers, producing purple bands that separate color orders. The predicted sequence - including the first-order shift from white toward yellow and red, and later bands of blue, green, and other hues - matches Newton’s recorded thicknesses. The calculations also explain why vertical films show moving color bands as they drain and grow thinner at the top.