A colour is a thickness
A bubble's film has two faces. Light bounces back from both, and the two reflections meet in your eye. At a given thickness some colours reinforce each other and others cancel out. The colour at any point on a bubble is really a measurement: it tells you how thick the water is there, to within a few tens of nanometres, at least in its brightest colours.
The water drains downward. The top thins first, and the colours slide down in bands towards the base. Isaac Newton covered a bubble with a glass so the air could not stir it, and wrote down what he saw:
And as the Bubble grew thinner by the continual subsiding of the Water, these Rings dilated slowly and overspread the whole Bubble, descending in order to the bottom of it, where they vanish’d successively.Isaac Newton, Opticks, 1704, Book II, Observation 17
Newton’s words beside today’s physics
Newton did not know that light is a wave. He explained the rings by “fits” of the rays, now of easy reflection, now of easy transmission. Still, he measured. In the same book he printed a table of the thickness at which each colour appears, in millionths of an inch.
Below, on the left, are the colours computed today for a film of water, from the sensitivity of the eye as it was standardised in 1931. On the right are Newton’s words, at his thicknesses, converted to nanometres. The numbers in the margin are his “orders”, first to seventh.
Mostly, they match. Where Newton writes “violet”, the calculation gives violet, at 213 nm. His purple of the third order comes out purple, at 400 nm. Where they part, it is in the dull early blues and the faded high orders. Newton had a bubble, a glass cover and his eyes.
The black
Just before it bursts, the top of the bubble turns black. It is not a hole. Newton saw the faint reflection of a candle in the black spot and, inside it, spots blacker still.
One of the two reflections comes back shifted by half a wave. Once the film is far thinner than the wavelength of light, the extra path through the water is almost nothing. The two reflections then cancel for every colour at once, and almost nothing is left to see.
Newton put “very black” at three-eighths of a millionth of an inch, about 10 nanometres. Measurements today find two kinds of black film: a common one, a few tens of nanometres thick, and one of about 4 nanometres, in which the two layers of soap have nearly touched with very little water between them. A bubble’s last colour is the finest measurement it makes.
What is computed and what is imagined
Computed: the colour for every thickness and every angle. All the reflections between the two faces are summed for 81 wavelengths between 380 and 780 nm, then passed through the CIE 1931 functions into screen colours. The light is a daylight white (a black body at 6,504 K). The film has the refractive index of water, 1.333. A soap film reflects only a few per cent of the light, so the brightness is raised several times. The hue is the computed one.
Imagined: the exact shape of the draining and its swirls, the starting thickness, the window and the room. Time is compressed: here a bubble lives for 37 seconds. The burst is slowed right down; a real bubble vanishes in a few milliseconds.
Sources
- Isaac Newton, Opticks (1704). Fourth edition, 1730, on Project Gutenberg: Book II, Part I, Observations 17–18; Part II, the table of thicknesses. www.gutenberg.org
- CIE 1931 2° standard observer colour-matching functions, from the CVRL database (University College London). www.cvrl.org
- Wikipedia, “Soap film”: black spots, common black films and Newton black films. en.wikipedia.org
- Wikipedia, “Thin-film interference”: multiple reflections in a thin film. en.wikipedia.org