Grassmann's laws describe empirical results about how the perception of mixtures of colored lights (i.e., lights that co-stimulate the same area on the retina) composed of different spectral power distributions can be algebraically related to one another in a color matching context. Discovered by Hermann Grassmann[1] these "laws" are actually principles used to predict color match responses to a good approximation under photopic and mesopic vision. A number of studies have examined how and why they provide poor predictions under specific conditions.[2] [3]
The four laws are described in modern texts[4] with varying degrees of algebraic notation and are summarized as follows (the precise numbering and corollary definitions can vary across sources[5]):----
| Two colored lights appear different if they differ in either dominant wavelength, luminance or purity. Corollary: For every colored light there exists a light with a complementary color such that a mixture of both lights either desaturates the more intense component or gives uncolored (grey/white) light. | ||
| The appearance of a mixture of light made from two components changes if either component changes. Corollary: A mixture of two colored lights that are non-complementary result in a mixture that varies in hue with relative intensities of each light and in saturation according to the distance between the hues of each light. | ||
| There are lights with different spectral power distributions but appear identical. First corollary: such identical appearing lights must have identical effects when added to a mixture of light. Second corollary: such identical appearing lights must have identical effects when subtracted (i.e., filtered) from a mixture of light. | ||
| The intensity of a mixture of lights is the sum of the intensities of the components. This is also known as Abney's law. |
These laws entail an algebraic representation of colored light.[6] Assuming beam 1 and 2 each have a color, and the observer chooses
(R1,G1,B1)
(R2,G2,B2)
(R,G,B)
R=R1+R2
G=G1+G2
B=B1+B2
I(λ)
R=
| infty | |
| \int | |
| 0 |
I(λ)\barr(λ)dλ
G=
| infty | |
| \int | |
| 0 |
I(λ)\barg(λ)dλ
B=
| infty | |
| \int | |
| 0 |
I(λ)\barb(λ)dλ
Observe that these are linear in
I
\barr(λ),\barg(λ),\barb(λ)