Short answer
Unless a layer hides completely, some light passes through it, reflects off what is underneath and comes back through it, so the substrate becomes part of the colour. Thin, weakly scattering layers — stains, washes, glazes, inks, the first coat of a pale paint — show the most substrate; thick, strongly scattering or dark layers show the least. How much comes through depends on the layer's scattering and absorption, its thickness and how different the substrate is.
Kubelka and Munk's two-flux model, published in 1931 and still used in paint and paper, treats a coloured layer as something that scatters and absorbs light as it passes through. A layer hides its background when almost no light reaches the background and returns. Strong absorption does this quickly, which is why dark colours cover in one coat. Strong scattering does it too, which is why titanium dioxide, with a very high refractive index, is the basis of opaque whites. Pale, clean colours are the hard case: they must absorb little by definition, so they depend on scattering alone and need more film to hide. Yellows and bright reds made with transparent organic pigments are notorious for needing extra coats or a tinted primer.
The table on this page evaluates the Kubelka–Munk equations for a pale and a mid-dark coating, each over a white and a black background, as the layer's scattering thickness builds up. The mid-dark coating is effectively hidden — its colour over black and over white within a fraction of a lightness unit — by the time the pale coating still shows a difference of several units. The ratio of the two reflectances is the contrast ratio that paint makers use as a measure of hiding. In practice that is why a pale colour over a darker old colour needs an extra coat or a primer tinted towards the topcoat, and why a patch-primed repair can 'ghost' through a pale finish.
Wood stains, oils, limewash, glazes and washes are chosen precisely because they let the substrate through. A stain adds its colour to the wood's own, so the same stain looks different on oak, pine and beech, and differently again on sapwood and heartwood of one board; blotchy species absorb it unevenly. Limewash over a warm render looks warmer than over a cold one. A glaze on a red earthenware body is darker and warmer than the same glaze on white stoneware. Printing inks are transparent by design, so the paper white is the lightest colour in the image and a warm or bluish paper tints every colour printed on it. For these finishes the substrate is not a problem to be hidden but an ingredient to be specified.
Designers talk about a colour's 'undertone' to describe a subtle cast — a white that leans pink, a grey that leans green — which is often invisible alone and obvious beside another. Some undertones are in the pigment mix; many come from the substrate showing through a nominally opaque finish, or from the finish adding to a warm or cool base. Plaster pink under thin white paint, the yellowish cast of an old oil-based undercoat under a new white, the grey of cement showing through limewash and the brown of kraft under white-lined board all create undertones. Checking the substrate with the finish over it, beside the reference colour, is the only reliable way to see them before the whole wall or run is done.
| Coating | Scattering thickness SX | L* over white (R = 0.85) | L* over black (R = 0.03) | Contrast ratio |
|---|---|---|---|---|
| Pale coating (R∞ = 0.80) | 0.5 | 93.5 | 65.2 | 41% |
| Pale coating (R∞ = 0.80) | 1 | 93.2 | 75.9 | 60% |
| Pale coating (R∞ = 0.80) | 2 | 92.7 | 84.2 | 78% |
| Pale coating (R∞ = 0.80) | 4 | 92.1 | 89.3 | 92% |
| Pale coating (R∞ = 0.80) | 8 | 91.8 | 91.3 | 99% |
| Mid-dark coating (R∞ = 0.30) | 0.5 | 72.3 | 56.5 | 56% |
| Mid-dark coating (R∞ = 0.30) | 1 | 64.3 | 60.6 | 87% |
| Mid-dark coating (R∞ = 0.30) | 2 | 61.8 | 61.6 | 99% |
| Mid-dark coating (R∞ = 0.30) | 4 | 61.7 | 61.7 | 100% |
| Mid-dark coating (R∞ = 0.30) | 8 | 61.7 | 61.7 | 100% |
Why: Pale colours hide poorly; the film is not thick enough to mask the contrast.
Fix: Prime with a primer tinted towards the topcoat and allow for an extra coat.
Why: Different species, sapwood content or absorbency under a translucent stain.
Fix: Test on offcuts of the actual timber; use a conditioner on blotch-prone species.
Why: A thin white coating over a grey or brown recycled back lets the substrate through.
Fix: Proof on the production board; specify a heavier white coating if needed.
Each statement is labelled by kind — established fact, a standard’s requirement, observed market data, a convention, or Colourwise’s own interpretation or analysis — with the strength of the evidence behind it.
FactModerate evidence
The Kubelka–Munk model, published in 1931, describes a coating by its absorption and scattering coefficients and predicts how much of the substrate's colour shows through at a given thickness, including hiding and contrast ratio.
Source: Kubelka–Munk theory
Colourwise analysisModerate evidence
In a Kubelka–Munk calculation a mid-dark coating hides a black–white background within a fraction of a lightness unit at a scattering thickness where a pale coating still shows a difference of several units.
Based on: Colourwise evaluated the Kubelka–Munk layer-over-background equation for coatings with R∞ of 0.80 and 0.30 over backgrounds of 0.85 and 0.03 reflectance, converting luminance factor to CIE L*; see the table on this page.
Caveat: Illustrative single-wavelength calculation; real paints have wavelength-dependent coefficients and surface reflection not modelled here.
Source: Kubelka–Munk theory; CIE (International Commission on Illumination) publications
FactModerate evidence
Rutile titanium dioxide has a refractive index of about 2.6, far above the roughly 1.5 of typical binders, which is why it scatters strongly and is used to make coatings and plastics opaque.
Source: List of refractive indices; Effects of UV radiation on natural and synthetic materials (Photochem. Photobiol. Sci.)
FactStrong evidence
Early stucco often took its colour mostly from the sand in the mix, sometimes with natural pigments or a limewash or colourwash over it, so the substrate materials set the finished tone.
Source: Preservation Brief 22: The Preservation and Repair of Historic Stucco
Reviewed 29 September 2026. Colourwise summarises its sources in its own words and does not reproduce standards text or proprietary colour data. Spotted an error? Tell us.