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Thin-film interference · a live soap film
A great variety of coloursIsaac Newton, Opticks, 1704
A soap film is a sheet of water a few hundred nanometres thick, about a hundredth of the width of a hair. Light reflects from its front and from its back, and the two reflections interfere. Which colours survive depends only on the thickness, so the colours are a live map of the film as it drains, until it turns black and bursts.
tap the bubble to pop it
I · Optics
Two reflections
To the right is a film of soapy water stretched across a wire frame, lit by daylight against black velvet. For now it is held as a perfect wedge, thin at the top and thick at the bottom, so you can read its colours like a ruler. Tap anywhere on it to measure the thickness there.
daylight
film age 0:00
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Thicknesstap the film
Reflects–
I.1
Front and back
Part of the light bounces off the front surface and part goes in, bounces off the back surface and comes out again, having travelled an extra 2nh: twice the thickness h, times the refractive index n of the water. The reflection from the front also flips upside down, because it bounces off a denser medium; the one from the back does not. Where the two meet crest to crest a wavelength is reflected strongly; where crest meets trough it cancels.
Each colour on this page is the full calculation: the reflected spectrum at every wavelength from 380 to 780 nm, weighted by the eye’s three colour sensitivities (CIE 1931), under the chosen light.
I.2
Newton’s sequence
Thin to thick, the colours repeat in orders, each a little paler than the last as more and more wavelengths are reflected at once, until above a couple of micrometres the film just looks white. In 1704 Newton listed them from the bottom of a bubble upward:
Read his list right to left, from the black, and it matches the computed strip. In 1802 Thomas Young used Newton’s own ring measurements to work out the first wavelengths of light: about 650 nm for red and 440 nm for violet.
II · Gravity
Draining
II
A film runs downhill
A fresh film is a few micrometres thick and drains under gravity, so the top thins first and coloured bands march down the film. Along the side wires, something faster happens: thin patches of film are pulled out of the meniscus and, being lighter, rise in swirling plumes while thicker film sinks. This is marginal regeneration, and it does most of the draining.
And sometimes small black Spots generated at the sides would ascend up to the larger black Spot at the top of the Bubble, and unite with it.Newton, Opticks, Book II, Obs. 17
average thickness …
III · Nanometres
The black film
III
Thinner than any colour
When the film is much thinner than a quarter of a wavelength, the extra path is almost nothing, but the flip on the front reflection is still there. The two reflections arrive almost exactly out of step and cancel at every wavelength, so the film turns black. It does not fade gradually: around a few tens of nanometres, forces between the two surfaces take over and the film jumps to a stable black film, edged sharply against the colours.
Black films come in two kinds: the common black film, from about ten to a few tens of nanometres thick, and the Newton black film, only a few nanometres, little more than two layers of soap molecules. Newton noticed darker spots inside the black, and saw a candle faintly reflected in them.
black area …reflects … of the brightest colour
IV · Milliseconds
Bursting
IV
The edge of a hole
Once a hole opens, surface tension pulls the edge back and gathers the liquid into a rim that races outward at the Taylor–Culick speed, V = √(2γ/ρh). Thinner film is lighter, so the rim moves faster through it: a few metres per second through micrometre film, tens of metres per second through black film. Watch the hole stretch toward the thin top. The whole film is gone in a few milliseconds; this replay runs 500 times slower.
rim speed in 1 µm film …in black film …
V · Measurement
Lamps and angles
V.1
One colour of light
Under a sodium lamp, which emits almost only 589 nm light, the film shows nothing but bright and dark bands. Each dark band marks a thickness where 2nh is a whole number of wavelengths, so the bands are contour lines about 221 nm apart in thickness. Monochromatic light like this is the standard way to measure a film’s thickness. Under a tungsten bulb the same film shifts warmer; under RGB LEDs some colours pull apart.
V.2
Tilt the film
Look at a film at an angle and the light crosses it on a slant, but the extra path shrinks, as 2nh cos θt, where θt is the angle inside the water. Every colour slides toward the colour of a thinner film. That is why the colours shift across a bubble from its centre toward its rim.
VI · Free play
Your film
VI
Everything is yours
Stir it, blow on it, pop it, pull a new one. The recipe controls change how the film drains.
Three centuries of bubbles
Who looked closely
Model notes
What is being computed
Reflectance of a free film (Airy), each polarisation
R = 2r²(1 − cos δ) / (1 + r⁴ − 2r² cos δ), δ = 4π n h cos θt / λ
Colour
XYZ = Σλ S(λ) R(λ) [x̄, ȳ, z̄](λ), 380–780 nm in 5 nm steps → linear sRGB
Bursting rim
V = √(2γ / ρh), γ = 30 mN/m
The colour of every pixel is computed, not painted. A table of film colours is built when the page loads: for each thickness from 0 to 3,200 nm and each viewing angle up to 80°, the film’s reflectance is worked out at 81 wavelengths with the full multiple-reflection formula for both polarisations, using water’s refractive index at each wavelength (1.343 at 400 nm, 1.333 at 589 nm, 1.330 at 700 nm). That spectrum is multiplied by the light source and the CIE 1931 colour-matching functions and converted to screen colour. The brightest possible reflection, about 8% of the light at a quarter-wave thickness, is shown as white.
The film itself is a reduced flow model. It is treated as a two-dimensional sheet of incompressible fluid, solved on the GPU, driven by its own buoyancy: thinner film weighs less per square centimetre and rises. Its thickness is carried by the flow and changes by gravity drainage with a flux that grows as the cube of the thickness, slow evaporation set by the humidity, marginal regeneration along the wires, and a jump to black film below 45 nm. These rules reproduce what real films do, with sliders standing in for real recipes; the colours from any thickness are exact.
Check
Computed here
Known
First-order red (Michel-Lévy “sensitive tint”, 550 nm retardation)
…
206 nm film
Sodium-light fringe spacing λ/2n
…
221 nm
Reflectance at a quarter wave, normal incidence
…
7.8%
Reflectance of 10 nm black film at 550 nm
…
≈ 0.20% (thin-film limit)
Rim speed at 1 µm, γ = 30 mN/m
…
7.7 m/s
At normal incidence a soap film in white light shows exactly the colours of the Michel-Lévy birefringence chart at a retardation of 2nh; I used that as an independent check of the colour engine.
Sources
R. Hooke (1665). Micrographia, Observation IX: colours in thin plates of Muscovy glass.
I. Newton (1704). Opticks, Book II, Part I, Observations 17–18 (soap bubbles).