Grassmann's law

Grassmann's law describes how the human visual system perceives colour as a linear combination of primary stimuli. In practical terms: if you mix two coloured lights and adjust their intensities, you can match the appearance of a third colour to an observer, and this relationship holds predictably across different lighting conditions. The law is empirical, built on direct observation of how people actually perceive colour matches, not derived from the physics of light itself.

The law rests on three key principles. First, a colour sensation can be reproduced by mixing three primary lights in appropriate proportions, which is why RGB colour systems work in displays. Second, if two colour mixtures look identical to an observer, then adding the same light to both will still leave them identical: colour perception is additive. Third, the proportions needed to match a colour remain consistent; they do not depend on what other colours are present in the visual field. This linearity makes colour prediction tractable in imaging systems.

Application and limits

Grassmann's law underpins the design of colour television, computer monitors, and colour matching in printing and photography. CIE colour space standards and tristimulus values all depend on this principle. However, the law breaks down in extreme conditions: at very low light levels, colour discrimination deteriorates and additivity fails; at very high intensities, nonlinear responses emerge; and large colour fields produce adaptation effects that violate the linearity assumption. For practical work in imaging, these exceptions matter most at the extremes of the tonal and dynamic range.

The law is named after Hermann Grassmann, a 19th-century mathematician and physicist who published his observations on colour mixing in 1853. Although Grassmann formulated it, the principle had been observed by earlier natural philosophers including Newton and Young. The term persists because Grassmann gave it explicit mathematical structure and tested it rigorously across different observer populations.

In contemporary practice, Grassmann's law is treated as an engineering foundation rather than an absolute truth. When setting up colour management workflows, profiling displays, or specifying colour tolerances in manufacturing, technicians assume linearity within the relevant range. Deviations are known and corrected through calibration curves and lookup tables. The law is reliable enough for consumer and professional imaging, but critical work in spectrophotometry or colour science often requires more sophisticated models that account for context and adaptation.