The Physics
Opus in profectus


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Color is a function of the human visual system, and is not an intrinsic property. Objects don't "have" color, they give off light that "appears" to be a color. Spectral power distributions exist in the physical world, but color exists only in the mind of the beholder.

Color is determined first by frequency and then by how those frequencies are combined or mixed when they reach they eye. This is the physics part of the topic. Light falls on specialized receptor cells (called rods) at the back of the eye (called the retina) and a signal is sent to the brain along a neural pathway (called the optic nerve). This signal is processed by the part of the brain near the back of the skull (called the occipital lobe). Here's where the biology kicks in, or maybe it's the psychology, or maybe it's both. They eye is very much like a camera, but the brain is not like a video recorder. The brain is not like a computer with fixed hardware of transistors and capacitors executing some sort of software code. The neurons of the brain are probably best thought of as wetware — a fusion of hardware and software or maybe something completely different. I don't feel qualified to say much about that end of this process. Once the visual information leaves the eye, basic physics ends and neurocognition takes over.

Color is determined first by frequency. Let's start by determining what a typical person would see when looking at electromagnetic radiation of a single frequency. Physicists call this monochromatic light. (The literal meaning of this word is "single color", but the actual meaning is "single frequency".) Low frequency radiation is invisible. With an adequately bright source, starting somewhere around 400 THz (1 THz = 1012 Hz) most humans begin to perceive a dull red. As the frequency is increased, the perceived color gradually changes from red to orange to yellow to green to blue to violet. The eye doesn't perceive violet so well. It always seems to look dark compared to other sources at equal intensity. Somewhere between 700 THz and 800 THz the world goes dark again.

A continuous spectrum running horizontally across the page

How many colors are there in the spectrum above? How many did I name?

red orange yellow green blue violet

The simple named colors are mostly monosyllabic English words — red, green, brown, black, white, gray. Brevity indicates an Old English (Anglo-Saxon) origin. Monosyllabic words are generally the oldest words in the English language — head, eye, nose, foot, cat, dog, cow, eat, drink, man, wife, house, sleep, rain, snow, sword, sheath, God…. These words go back more than fifteen centuries. Yellow, purple, and blue are exceptions to the one-syllable-equals-English rule. Yellow and purple are Old English color words with two syllables. Blue is a one syllable French word (bleu) that replaced a two syllable Old English word (hǽwen) eight hundred years ago.

Some of the names for colors are loan words from French (many of which are loan words from other languages). Since the ʒ (zh) sound doesn't exist in Old English, orange and beige are obviously French. (Garage is also a very French word.) The words violet and orange were the names of plants (nouns) before they were the names of colors (adjectives). Violet came from 14th Century French, which came from Latin. Orange came from 16th Century French, which came from Italian, which came from Arabic, which came from Persian, which came from Sanskrit.

English arose when three Germanic tribes — the Angles, The Saxons, and the Jutes — migrated from continental Europe to the British Isles in the Fifth Century. The language they spoke is called Anglo-Saxon or Old English. You would hardly recognize this language if you heard it spoken or saw it written today. Danes probably have the best chance of understanding spoken Old English, Icelanders the best chance of understanding written Old English. Of the six named colors in my spectrum, only four were known to the Anglo-Saxons: reád, geolu, grÉne, hǽwen. Do you recognize any of them?

réad geolu grÉne hǽwen

In the year 1066, an invasion of French speaking peoples — the Normans, the Bretons, and the French — swept over the British Isles. The last Anglo-Saxon King of England, King Harold II, was succeeded by the first Norman king, William the Conqueror. The Normans had an odd empire (if that's the word for it) that included the British Isles, northern France (appropriately named Normandy), southern Italy, Sicily, Syria, Cyprus, and Libya. William was a Norman, descended from Norsemen, but he spoke French not Swedish or Norwegian or Danish. One factor leading to the rise of the Normans in their scattered empire is their ability to quickly integrate themselves into the culture of the peoples they conquered. For purposes of this discussion, we care about language. When the Normans got to northern France, they started speaking French. When the Normans got to England they got the Anglo-Saxons to start speaking French too (sort of). In about a hundred years, Anglo-Saxon had mutated into something closer to what we would recognize as English today — neither French nor Anglo-Saxon. Old English became Middle English. This is when English acquired the words blue (which replaced hǽwen) and violet (which never existed as an English color word before).

rede ȝeoluw grene blu violet

The next change in the English language was one of pronunciation — the Great Vowel Shift (1350–1700). This is when silent e and other spelling rules that frustrate both native and second language speakers arose. The notion of long and short vowels also changed. At one time a long vowel was one that was pronounced for a longer time than a short vowel. Take the words pan and pane. Before the Great Vowel Shift, pan was pronounced "pan" and pane was pronounced "paaaneh" with a literal looong vowel and a non-silent "eh" at the end. Being mostly a change in pronunciation, the rise of Modern English around 1550 doesn't affect our discussion of color words. Movable type printing invented in Germany around 1445 is probably more important. Books became relatively plentiful, spelling became standardized, and tracking down the first occurrence of a word became easier. The Modern English period is when the words orange and indigo were first used to identify colors.

red orange yellow green blue indigo violet

I have issues with indigo. More on that later.

The first written occurrence of some color names in English Primary source: Oxford English Dictionary. Translations: Sean Crist, et al's Bosworth-Toller Anglo-Saxon Dictionary, Phil Barthram's Old English to Modern English Translator, University of Michigan's Middle English Dictionary.
modern english
(old english)
representative quote (year)
on ðæs sacerdes hrægle scoldon hangigan bellan & ongemang ðæm bellum reade apla.
on the priest's robe should hang bells and among the bells, red apples.
King Alfred's West-Saxon version of Pope Gregory's Pastoral Care (~870)
Uyrmas mec ni auefun uyrdi cræftum, ða ði geolu godueb geatum frætuath.
Worms did not weave me with the skills of the fates, those that decorated the yellow cloth garment.
The Leiden Riddle (~900)
siððan adam stop on grene græs, gaste geweorðad.
since Adam stepped on green grass, possessed of life.
The Genesis A, B story from the Cædmon Manuscript (~950)
þou schalt þeos þreo cloþes do a non ech of heom in o Caudroun, for ich þe wolle segge sothþ þat þis on schal beo fair blu cloth, þis oþur grene, onder stond þis!
[I am unable to translate this from Middle English to modern English.]
Altenglische legenden a.k.a. Old English Legends compiled by Carl Horstmann (~1300)
In Inde also may men fynd dyamaundz of violet colour and sum what browne, þe whilk er riȝt gude and full precious.
The Buke of John Maundeuill a.k.a. Mandeville's Travels (1425)
no Person or Persons shall put to sale by Retail within this Realm any Cloth or Clothes … of other Colour or Colours than is hereafter expressed; that is to say, Scarlet, Red, Crimson, Murry, Violet, Puke, Brown-blue, Blacks, Greens, Yellows, Blues, Orange-tauny, Russet, Marble-gray, Sad new Colour, Azure, Watchet, Sheeps-colour, Lion-colour, Motley or Iron gray
Great Britain Statutes at Large (1552)
For a deepe and sad Greene, as in the inmost leaves of Trees, mingle Indico and Pinke.
The Compleat Gentleman by Henry Peacham (1622)

There is no physical significance in color names. It's all a matter of culture and culture depends on where you live, what language you speak, and what century it is. A given wave of light has the same frequency no matter who is viewing it, but the person perceiving the color will call it a word appropriate to their culture.

Color discrimination is probably the same for all people in all cultures (all people with properly working eyeballs). Did the English see orange or violet before the French told them about it? Of course they could. They probably called orange reád (red) or geolo-reád (yellow-red) and violet hǽwen (blue) or blæc-hǽwen (dark blue) because those were the words they had available.

Why is an orange called an orange but a lemon not called a yellow and a lime not called a green?

What would you call indigo if I showed it to you? Most certainly blue. I don't know anyone who uses the word indigo in everyday conversation. Maybe some painters do. That'd be about it for indigo as far as Modern English speakers were concerned. In some languages blue and indigo are equally significant color words. Maybe the real question is do we need blue, indigo, and violet?

…World Color Survey…

Frequency determines color, but when it comes to light, wavelength is the easier thing to measure. A good approximate range of wavelengths for the visible spectrum is 400 nm to 700 nm (1 nm = 10−9 m) although most humans can detect light just outside that range. Since wavelength is inversely proportional to frequency the color sequence gets reversed. 400 nm is a dull violet (but violet always appears dull). 700 nm is a dull red.

Wavelength varies with the speed of light, which varies with medium. The speed of light is about 0.03% slower in air than in vacuum. If you're trying to understand color, wavelength is just as good as frequency.

We humans who speak English and live at the dawn of the 21st Century have identified six wavelength bands in the electromagnetic spectrum as significant enough to warrant a designation with a special name. They are: red, orange, yellow, green, blue, and violet. Where one color ends and another begins is a matter of debate as you will see in the table below.

Wavelength ranges for monochromatic light (nm) 1 CRC Handbook of Chemistry and Physics. 1966. 2 Hazel Rossotti. Color. Princeton University Press, 1983. 3 Edwin R. Jones. Physics 153 Class Notes. University of South Carolina, 1999. 4 Deane B. Judd. Goethe's Theory of Colors. MIT Press, 1970.
color   1 2 3 4
red   647–700 647–760 630–700 620–800
orange   585–647 585–647 590–630 590–620
yellow   575–585 575–585 570–590 560–590
green   491–575 491–575 500–570 480–560
blue   424–491 424–491 450–500 450–480
violet   400–424 380–424 400–450 400–450

Which brings us to indigo. How many of you reading this learned about "Roy G. Biv" (Americans, I presume) or that "Richard of York Gave Battle In Vain" (Britons, I presume)? Who among you learned that between blue and violet there was this special color called indigo?

Indigo. The only time I ever hear it is when students recite the visible spectrum. Indigo is a color of relatively little importance. If indigo counts as a color then so should canary, and mauve, and puce, and brick, and teal, and so on. Where is their place in the spectrum?

A continuous spectrum running horizontally across the page

How many colors are there in this swatch? How many were you taught in elementary school? The inclusion of indigo in the spectrum goes back to Isaac Newton. More on this after the data table. If you believe that indigo is an important color, then here's a set of spectral tables for you.

Wavelength ranges for monochromatic light (nm) with indigo 5 Howard L. Cohen. AST 1002 Study Guide. University of Florida, 1999–2003. 6 J.L. Morton. Color Matters, 1995–2002. 7 A Dictionary of Science. Oxford University Press, 2000. 8 Thomas Young. Theory of Light and Colours, 1802.
color   5 6 7 8
red   630–750 650–750 620–740 624–675
orange   590–630 590–640 585–575 598–624
yellow   570–590 550–580 575–858 557–598
green   490–570 490–530 500–575 515–557
blue   450–490 460–480 445–500 480–515
indigo   420–450 440–450 425–445 460–480
violet   380–420 390–430 390–425 425–460

Did Richard of York give battle in vain so that future citizens in the dismantled British Empire would forever remember indigo? Did Mr. and Mrs. Biv conceive little Roy G. so that future generations of Americans might learn the true nature of light? Where did indigo come from?

When Newton attempted to reckon up the rays of light decomposed by the prism and ventured to assign the famous number seven, he was apparently influenced by some lurking disposition towards mysticism, If any unprejudiced person will fairly repeat the experiment, he must soon be convinced that the various coloured spaces which paint the spectrum slide into each other by indefinite shadings: he may name four or five principal colors, but the subordinate spaces are evidently so multiplied as to be incapable of enumeration. The same illustrious mathematician, we can hardly doubt, was betrayed by a passion for analogy, when he imagined that the primary colours are distributed over the spectrum after the proportion of the diatonic scale of music, since those intermediate spaces have really no precise defined limits.

John Leslie, 1838


rubeus aureus flavus viridis cæruleus indicus violaceus



The human eye can distinguish something on the order of 7 to 10 million colors — that's a number greater than the number of words in the English language (the largest language on earth).

The retina…

The rods, which far outnumber the cones, respond to wavelengths in the middle portion of the spectrum of light. If you had only rods in your retina, you would see in black and white. The cones in our eyes provide us with our color vision. There are three types of cone, identified by a capital letter, each of which responds primarily to a region of the visible spectrum: L to red, M to green, and S to blue.

The peak sensitivities are 580 nm for red (L), 540 nm for green (M), and 440 nm for blue (S). Red and green cones respond to nearly all visible wavelengths, while blue cones are insensitive to wavelengths longer than 550 nm. The total response of all three cones together peaks at 560 nm — somewhere between yellow and green in the spectrum.


Commission Internationale de l'Eclairage

The relative response of the red and green cones to different colors of light are plotted on the horizontal and vertical axes, respectively. Values on the tongue shaped perimeter are for light of a single wavelength (in nanometers). Values within the curve are for light of mixed frequency. The point in the center labeled D65 corresponds to light from a blackbody radiator at 6500 K — the effective temperature of daylight at midday, a generally accepted standard value of white light.

white & black

Continuous, thermal spectra

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additive color mixing

The absence of light is darkness. Add light and human eyes to the darkness and you get color — a perception of the human visual system. The retina at the back of the human eye has three types of neurons called cones, each sensitive to a different band of wavelengths — one long, one medium, and one short. The long wavelength cones are most stimulated by light that appears red, the medium wavelength cones by light that appears green, and the short wavelength cones by light that appears blue. A monochromatic wavelength of light (or a narrow band of wavelengths) can be selected as a representative for each of these colors. These become the primary colors of a system that can be used to reproduce other colors in a process known as additive color mixing.

Additive Primary Colors
black  +  red  =  red
black  +  green  =  green
black  +  blue  =  blue

When no light or not enough light falls on the retina, the brain perceives this nothing as the color black. When the light from two or more sources falls on adjacent rods in the retina, the brain percives the combination as a different color. The rules for combinations of the primary colors are as follows…

Additive Color Mixing Rules
nothing  =  black
red  +  green  =  yellow
green  +  blue  =  cyan
blue  +  red  =  magenta
red + green  +  blue  =  white

Most of us with typical human eyes and a basic knowledge of the English language are familar with the color yellow. This is probably not the case for cyan and magenta. Because inkjet printers (which have cyan, magenta, yellow, and black cartridges) are commonplace nowadays, it's not uncommon for people to recognise the words cyan and magenta, but not know how to pronounce them (ˈsīˌan and məˈjentə). As you'd expect given that it's a combination of blue and green light, cyan appears blue-green — something like the blue of the sky but not exactly. I'd say more like the semiprecious stone turquois than anything else. Magenta is often confused with pink, but magenta is much more vibrant. Pink is desaturated red. Magenta is considered a pure color. (More on this later.) A close relative of magenta is fuschia, which is a synthetic dye. I can't think of anything natural that looks like magenta.

These rules are better understood with a diagram than a series of equations.

Color mixing is not an all or nothing process. Red light and green light together appear yellow, it's true, but they can also appear orange when mixed if the red light is brighter than the green light. Red light and green light can be combined in other proportions to produce light that appears to be a color halfway between red and orange, and orange and yellow, and yellow and green. We can keep dividing and subdividing like this to produce new, distinct colors.

red red-orange orange orange-yellow yellow yellow-green green

One convenient way to represent some of the possibilities is with a continuous color wheel. Starting on the right side and going counterclockwise as is the tradition in mathematics, red is placed on the circumference at 0°, green at 120°, and blue at 240°. The complimentary colors are halfway between the primaries — yellow at 60°, cyan at 180°, and magenta at 300°. These numbers are called hue angles. White is at the origin. The distance from the origin to any point on the colorwheel stated as a fraction of the radius is known as the saturation. White is completely desaturated. Its saturation is 0%. Colors with low saturation are often identified as pale or pastel. Colors with a high saturation are bright or vibrant. Colors with 100% saturation are said to be pure.

more talk

[insert image - pixels?]

Purple and violet are similar, though purple is closer to red. In optics, there is an important difference; purple is a composite color made by combining red and blue, while violet is a spectral color, with its own wavelength on the visible spectrum of light.

subtractive color mixing

The absence of pigment is white paper. (The absence of pigment is paper that appears white when illuminated with white light.)

Add pigment to it. (Subtract certain wavelength ranges.)

Subtractive Primary Colors
white  −  red  =  cyan
white  −  green  =  magenta
white  −  blue  =  yellow

Mix them.

Subtractive Color Mixing Rules
nothing  =  white
cyan  +  magenta  =  blue
magenta  +  yellow  =  red
yellow  +  cyan  =  green
cyan + magenta  +  yellow  =  black

the subtractive color wheel

more talk

A five color press: yellow, magenta, cyan, black, spot color.

historical junk

The painter's color wheel is a convenient way to understand how to mimic some colors by mixing red, yellow, and blue pigments. This does not make red, yellow, and blue the primary colors of the human visual system. They do not satisfy the definition of primary. They can't reproduce the widest variety of colors when combined. Cyan, magenta, and yellow have a greater chromatic range as evidenced by their ability to produce a reasonable black. No combination of red, yellow, and blue pigments will approach black as closely as do cyan, magenta, and yellow. The primary colors are red, green, and blue — not red, yellow, and blue.

more talk

Johann Wolfgang von Goethe (1749–1832), student of the arts, theatrical director, and author (Iphigenia at Taurus, Egmont, Faust). Lots of interesting descriptive information on the subjective nature of color, which many physicists of his day ignored, but does not propose a physical model of color.

The theory of colors, in particular, has suffered much, and its progress has been incalculably retarded by having been mixed up with optics generally, a science which cannot dispense with mathematics; whereas the theory of colors, in strictness, may be investigated quite independently of optics.

Colour is a law of nature in relation with the sense of sight… [It] is an elementary phenomenon in nature adapted to the sense of vision…

It is not light, in an abstract sense, but a luminous image that we have to consider.

Yellow, blue, and red, may be assumed as pure elementary colors, already existing; from these, violet, orange, and green, are the simplest combined results.

That all the colours mixed together produce white, is an absurdity which people have credulously been accustomed to repeat for a century, in opposition to the evidence of their senses.

Johann Wolfgang von Goethe, 1810

Hmmm. Alright then.

Now, as it is almost impossible to conceive each sensitive point of the retina to contain an infinite number of particles, each capable of vibrating in perfect unison with every possible undulation, it becomes necessary to suppose the number limited, for instance, to the three principal colours, red, yellow, and blue, of which the undulations are related in magnitude nearly as the numbers 8, 7, and 6; and that each of the particles is capable of being put in motion less or more forcibley by undulations differing less or more from a perfect unison; for instance the undulations of green light being nearly in the ratio of 6½, will affect equally the particles in unison with yellow and blue, and produce the same effect as a light composed of these two species: and each sensitive filament of the nerve may consist of three portions, one for each principal colour.

Thomas Young, 1802

color production


color spaces