Short answer
A transparent layer a few hundred nanometres thick reflects light from both its top and bottom surfaces; the two reflections add for some wavelengths and cancel for others, depending on the layer's optical thickness. Coating mica with titanium dioxide of the right thickness gives gold, red, violet, blue or green interference colours with no absorbing colourant at all. Tilting the layer shortens the effective path, shifting the colour towards blue — slightly for a high-index layer like titanium dioxide, strongly for low-index spacer layers, which is how colour-shifting security inks work.
When light meets a thin transparent film, part reflects at the top surface and part at the bottom. The second reflection travels an extra distance of twice the film thickness, multiplied by the film's refractive index and by the cosine of the angle at which light crosses the film. Where the higher-index film sits in a lower-index binder, the top reflection also picks up a half-wave phase flip. The two reflections reinforce each other at wavelengths where the extra path equals a whole number of wavelengths plus a half, and cancel where it equals a whole number. White light therefore comes back coloured: the film reflects some bands strongly and others weakly, and — because nothing is absorbed — transmits the complementary colour.
The table models a single titanium dioxide layer in a binder at normal incidence. At about 40 nm the first reflection maximum sits in the violet, and the layer reflects mostly short wavelengths weakly — in practice a silvery pearl. By 60 nm the maximum has moved into the red. Beyond that the first maximum leaves the visible and a minimum enters from the violet end, so reflection loses blue and looks gold at about 80 nm; with the minimum in the green at 100 nm, reflection looks red-violet; at 120–140 nm a new maximum enters in the blue; and by 160 nm it sits in the green. That silver, gold, red, violet, blue, green order is the familiar range of titanium dioxide–mica interference pigments. Viewed over black the reflected colour dominates; over white, the complementary transmitted colour mixes in.
Tilting shortens the interference path by the cosine of the angle inside the layer. Light entering a high-index material bends sharply towards the normal, so inside titanium dioxide (index about 2.6) the internal angle stays small and the peak moves only a few per cent even when the surface is viewed at 45°. In a low-index layer such as silica (about 1.46) the internal angle is much larger and the same tilt shifts a 550 nm peak by about 12%, far enough to change the hue name. That is why titanium dioxide–mica pearls change colour modestly, while multilayer colour-shifting pigments built around low-index spacer layers flip strongly — for example the optically variable ink on banknotes such as the US $50, whose numeral shifts between copper and green.
Nature produced interference colour long before industry: Newton described how peacock feathers owe their changing colours to structure rather than pigment, and butterflies, beetles and birds use multilayers, photonic crystals and diffraction gratings. Structural colour does not fade the way a dye does, because there is no light-absorbing molecule to break, though it disappears if the structure is crushed or wetted with a material of matching refractive index. Research into structural pigments aims to make vivid, dye-free colours from ordered nanostructures, and biomimetic surfaces are an active field, but most commercial angle-dependent colour still comes from the layered platelet pigments described here. The nature section of this site covers the biological side in detail.
| Layer thickness | Optical thickness n·d (nm) | Reflection maxima, 380–720 nm | Reflection minima, 380–720 nm |
|---|---|---|---|
| 40 nm | 104 | 417 nm (violet) | none in 380–720 nm |
| 60 nm | 157 | 626 nm (red) | none in 380–720 nm |
| 80 nm | 209 | none in 380–720 nm | 417 nm (violet) |
| 100 nm | 261 | none in 380–720 nm | 522 nm (green) |
| 120 nm | 313 | 417 nm (violet) | 626 nm (red) |
| 140 nm | 365 | 487 nm (blue) | none in 380–720 nm |
| 160 nm | 417 | 557 nm (green) | 417 nm (violet) |
| 200 nm | 522 | 696 nm (red), 417 nm (violet) | 522 nm (green) |
| Viewing angle in air | In titanium dioxide (n 2.609): shift (550 nm peak moves to) | In silica (n 1.458): shift (550 nm peak moves to) |
|---|---|---|
| 15° | 0.5% (547 nm) | 1.6% (541 nm) |
| 30° | 1.9% (540 nm) | 6.1% (517 nm) |
| 45° | 3.7% (529 nm) | 12.5% (481 nm) |
| 60° | 5.7% (519 nm) | 19.6% (442 nm) |
| 75° | 7.1% (511 nm) | 25.1% (412 nm) |
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
Thin-film interference depends on an optical path difference of 2·n·d·cos θ inside the film, with a half-wave phase shift on reflection from a medium of higher refractive index; it produces the colours of soap and oil films.
Source: Thin-film interference
Colourwise analysisModerate evidence
Viewed at 45° from air, an interference peak at 550 nm moves about 3.7% towards the blue in a titanium dioxide layer (n 2.609) but about 12.5% in a silica layer (n 1.458).
Based on: Colourwise calculation of cos θ inside the layer by Snell's law from the cited indices; see the angle table.
Caveat: Single-layer idealisation; real multilayer and absorber designs shift by different amounts.
Source: Thin-film interference; Titanium dioxide; List of refractive indices
FactModerate evidence
Optically variable ink on banknotes displays two distinct colours depending on viewing angle; the US $50 note's numeral shifts between copper and green.
Source: Optically variable ink
FactModerate evidence
Structural colour is produced by microscopically structured surfaces that interfere with light rather than by pigment; Newton described the structural origin of peacock feather colours in Opticks (1704).
Source: Structural coloration
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.