GoldBrush Academy
Why a mixed wash darkens while a glaze glows. Light, pigment, and the mathematics painters rarely see, told for the curious, with live curves for real paints.
A screen makes colour by adding light. Paint makes colour by taking light away. Every surprise in the mixing tray comes from forgetting which of the two you are working with.
Red, green and blue light add up to white. Pixels on a screen work this way.
Each pigment absorbs part of the light. Stack them, and less and less comes back, towards black.
A watercolourist works in the second world, but in two very different ways. Pigments can share one layer, or sit in separate layers. Painters feel the difference; physics explains it.
Mix Ultramarine and Burnt Sienna in the tray and the particles crowd into one layer. Light plunges in and meets them in no particular order. At every particle it is either absorbed (its energy is lost) or scattered (it bounces off in a new direction).
The appetites add up.
Let one wash dry, then lay a thin transparent wash over it. The pigments never touch. Light passes through the top layer, then the lower one, reflects off the white paper, and travels back out through both.
The filters multiply, and the paper keeps glowing through.
Choose any two paints. You'll see the mosh pit and the sandwich side by side, and underneath, what each one does to every colour of light.
Reflectance from violet (380 nm) to red (750 nm): the share of light at each wavelength that comes back to your eye. A curve near the top reflects that colour; near the bottom, it swallows it.
In 1931 Paul Kubelka and Franz Munk described a paint layer with just two numbers at each wavelength: how strongly it absorbs light, K, and how strongly it scatters it, S. They followed two streams of light, one travelling down into the layer and one travelling back up (the "two-flux" model). For a layer thick enough to hide what lies beneath, the reflectance R depends only on the ratio of the two:
A bright colour at some wavelength has a small K/S there; a dark one has a large K/S.
In 1940 D. R. Duncan showed that when pigments share a layer, their absorption and scattering simply add, each weighted by its concentration c:
This is why a mixture is darker than the average of its colours: the absorptions pile up, wavelength by wavelength, and then pass through the curved relationship above. It is also why a strong pigment such as Phthalo Blue dominates a mix: it carries much more absorption per gram.
When the pigments scatter light similarly, the law simplifies to a weighted sum of K/S values (the "single-constant" form). Our tools use that form, through the open-source spectral.js library, with each paint's weight set by its tinting strength and lightness. It is calculated separately at 38 wavelengths, from 380 to 750 nm in 10 nm steps: the readout above shows one of them.
A thin transparent glaze does not hide what lies beneath, so it behaves as a filter with a transmittance T at each wavelength. Light crosses each glaze twice, down and back, so what returns from the paper is roughly
Multiplication, not addition. Where either glaze lets a colour through, and the paper reflects it, that colour survives. This is why glazes keep their luminosity: the paper is the light source, and nothing opaque stands in its way.
An honest note: a screen colour does not contain a spectrum, so spectral.js reconstructs a plausible curve from each paint's colour. The results are a good guide, not a measurement. Measured spectra, taken with a spectrophotometer from real swatches, would make them more exact.
References: P. Kubelka and F. Munk, "Ein Beitrag zur Optik der Farbanstriche", Zeitschrift für technische Physik, 1931. D. R. Duncan, "The colour of pigment mixtures", Proceedings of the Physical Society, 1940. R. van Wijnen, spectral.js (MIT licence).
Physics decides the mechanism. You decide the art.
Colour is something we practise slowly and deliberately at GoldBrush Academy.
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