Home > musing > Mixing colors: pigment vs. light

Mixing colors: pigment vs. light

July 1, 2012

Today we will address another topic in a list of “things I’m kind of ashamed I don’t understand considering I am a professional scientist of sorts” (please make suggestions!).

Why is it that when you mix light blue (cyan) and yellow paint you get green paint, but when you mix cyan and yellow light you get white light?

Unlike with yesterday’s analemma post, where I couldn’t find a satisfactory write-up on another blog, today’s blog is actually pretty nicely explained and beautifully illustrated here. I will crib their illustrations and summarize the explanations but it’s really out-and-out plagiarism for the moment.

First, you’ve got the so-called “hue wheel” (which sounds more sophisticated than “color wheel”, don’t you agree?):

This is illustrating the following. There are three basic pigments: yellow, cyan and magenta. There are three basic colors of light, namely green, blue, and red. And if you mix the fundamental pigments pair-wise (as in, you get paints and mix them) you get the fundamental colors of lights.

And vice versa as well, although this time you’re mixing as in splicing them together but keeping them separate, like we use pixels on our screen. This means, specifically, that you can combine green and red to get yellow. That’s majorly unbelievable until you see this miraculous picture, also from this webpage:

See how that works? I just can’t get over this picture. The little piece of yellow on the left is just stripes of green and red. Really incredible. The purple I get because it’s blue and red just like it’s supposed to be.

So, why?

The first thing to understand is that this isn’t just a relationship between us and the object we are looking at. It is instead a three-part relationship between us (or more specifically, our eyes), the object, and the sun (or some other source of light, but it’s more traditional in explanations like this to use fundamental, macho objects of nature like the sun).

Nothing can happen without a source of light. Which begs the question, what is light anyway? Again a picture stolen from here:

The prism separates the white light into various wavelengths, where red is at 700 nanometers and violet at 400 nanometers. More on the visible spectrum here. Note that the hidden difficulty here is why a prism does this, which is explained here.

So when an apple looks red to us, we have to imagine white light from the sun hitting that apple, and the key is that the skin of the apple is absorbing everything except the red light:

That thing on top is the sun, and the thing on bottom is your eyeball. The point is the red part of the light is reflected off the apple skin into your eye. And even though white light from the sun is the whole spectrum, we are denoting it when just the fundamental three colors of light because other colors can be made from those. And this can be corroborated by looking at your computer screen with a magnifying glass, where you will see that the white background is actually made up of little pixels of green, red, and blue.

By the way, we are again sidestepping the actual hard part here, namely why some surfaces such as apple skins reflect some colors like red. I have no idea. But I don’t feel as guilty about not understanding that.

Finally, back to the first question, of why cyan and yellow paint make green whereas cyan and yellow light make white. Turns out the light one is actually easier, since our second picture above shows us that yellow light is actually a mix of red and green, and when you add cyan, you now have all three fundamental colors of light, which gives us white light.

If you have cyan paint, then it is reflecting blue and green light, so absorbing red light. If you have yellow paint then that’s a material which is reflecting both green and red, so absorbing blue. For some weird reason (a third moment of stuffing things under the rug), the mixture of the paint is additive on absorbing things, so absorbs both blue and red, leaving only green reflected.

In the end we get a kind of mini De Morgan’s Law for color.

I’ve convinced myself that, modulo the following three questions I understand this explanation:

  1. How does a prism separate white light into the colors really?
  2. How do different surfaces decide which lights to reflect and which to absorb? And a related question from Aaron, why do colors fade when they’ve been in the sun?
  3. Why is “absorbing light” an additive procedure when you mix materials? I feel like if I understood 2 then I’d get 3 for free.
Categories: musing
  1. July 1, 2012 at 7:34 am

    The statement that there are three basic colors of light is misleading. There are, of course, infinitely many colors of light. What is true is that the human eye processes color using cells which respond to three different characteristic ranges of frequencies which roughly peak at “the three basic colors” (or something along these lines); in other words, the human eye projects an infinite-dimensional vector space down to a three-dimensional one when processing light.

    From the perspective of light, rather than the perspective of what the human eye sees, you really do need to distinguish between light that is a mixture of two colors that looks like a third color and light that actually is, physically, that third color.

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    • July 1, 2012 at 7:36 am

      In quantum mechanics I might have to replace “infinitely many” with “lots of.” I admit I don’t have this stuff completely straight in my head either.

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    • July 28, 2012 at 6:00 pm

      There’s a truly wonderful discussion of color vision, in terms of this projection from infinite dimensions to three dimensions (or two, or perhaps even four), in the Feynman Lectures on Physics.

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  2. None
    July 1, 2012 at 8:41 am

    1) white light = light containing differing wavelengths. Waves of differing wavelengths refract at different angles when incident at an angle on a surface and hence the constituent waves get spread out
    2) the electrons in the atoms/molecules of the absorbing get excited into different energy bands, but there are only set energy bands available so specific wavelengths (corresponding to those exact energy levels) can get absorbed corresponding to the available energy bands. This means that if you know the available electron bands in a material you can tell in advance what wavelengths it will absorb and therefor which ones it will reflect (ie what colour it will appear)
    3) It isnt always, as long as the materials dont chemically combine (thus changing their available electron bands) its additive because you will still get the reflected light from each of the independent pigments, though in a reduced intensity since theres proportionally less of it per unit area

    4) Things fade in the sun because, the chemical composition of the material changes, chemical reaction being precipitated by increase in incident energy (ie sunlight), which results in fewer energy bands available for absorption: causing more frequencies to be reflected and making the material appear paler, or more white. So obviously more chemically stable materials (with fewer energy levels available for chemical activity, or light absorption) would be whiter, this made me wonder immediately why gold (very inert) is yellow, so I googled that for myself, the answer is interesting:
    http://www.physicsforums.com/showthread.php?t=310479

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  3. None
    July 1, 2012 at 8:47 am

    “since our second picture above shows us that yellow light is actually a mix of red and green”

    Yellow light is yellow. A mix of red and green light looks yellow because the green and red receptors in our eyes are both excited when hit with yellow light, and our brain interprets that as yellow. When a mix of red and green light hits the red and green receptors then again both get excited and our brain interprets that, as before, as yellow.

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  4. July 1, 2012 at 10:17 am

    Can’t resist adding a few things that I think are really cool about this topic. One is that it’s not just the light source, the object, and our eyes…it’s definitely also our minds because we will “see” the same frequency of light as different colors in different contexts (many optical illusions exploit this fact). Another…have you ever noticed that if you look at a blue sheet of paper, you see blue everywhere…even where your blind spot is. But if you look at a white sheet of paper, you see white everywhere…even where your blind spot is. So your mind is filling in the blind spot with a best guess. You can put a blue dot on white paper and if that blue dot is where your blind spot is, you’re going to see white there instead. (And try looking at a piece of graph paper…) Just how much of what we see is an illusion created by our minds? Finally, some humans have less than 3 color receptor types (color blind people)…but there’s evidence that some have more…and these people can tell the difference between purple (which is the mix of red and blue) and violet (which is a pure frequency and is reflected by some flowers). There’s also an article on additive color in the Oct. 2010, vol. 4, no. 1 of the Girls’ Angle Bulletin.

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    • July 1, 2012 at 1:33 pm

      Fascinating topic! A color-vision researcher suggests that there may be 99 million women in the world who have four color receptors (“tetrachromats”) and the number of hues one can perceive grows exponentially.

      http://www.post-gazette.com/stories/news/health/some-women-may-see-100-million-colors-thanks-to-their-genes-450179/

      Apparently butterflies and some birds are believed to be pentachromats, presumably because ability to make such distinctions conferred evolutionary advantages in finding food and/or mates. Butterflies and birds are already so beautiful to us humans, so it is mind blowing to think what they might look like to one another!

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  5. July 1, 2012 at 1:40 pm

    I think “None”‘s comment above is the one that misled me for the longest time — people telling me “red and blue make purple” instead of “red and blue look purple”. There’s no physics involved in these color mixings, there’s eye physiology (namely, that we don’t have color receptors tuned to very many different wavelengths). I wish that people in science and art classes would at least say enough to young kids to make this distinction clear. “Your eyes see three basic colors” instead of “there are three primary colors”, and things like that.

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  6. Scott Carnahan
    July 1, 2012 at 6:43 pm

    Questions 1 and 2a are partly answered in Feynman’s non-specialist book QED. Absorption, transmission, and reflection are governed by the interactions between the electronic structure of the surface and the incoming light, which you might view as chunks of electromagnetic energy that can behave like waves and interfere. A post-hoc reason for the separation of light by a prism is that some frequencies of light travel faster in glass than others, and light always follows the paths that are local minima with respect to travel time.

    The primary answer to question 2b is that solar radiation has an ultraviolet component, that is energetic enough to knock electrons out of atoms and break chemical bonds. When pigments suffer such chemical changes, they tend to turn into chemicals with less distinguishing optical properties.

    For question 3, absorbing as a lack of reflection is less an additive property, and more of an averaging process. You can approximate it by assuming a given tiny chunk of surface is either one pigment or the other. Absorbing light under transmission (like for slides or movie projectors or sunglasses) is additive.

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  7. Cliff
    July 2, 2012 at 7:06 am

    For an exhaustive, indeed exhausting, treatment of the phenomena of color, especially as it pertains to pigments used by artists, check out Bruce MacEvoy’s splendid web site:

    http://www.handprint.com/HP/WCL/color18a.html.

    Mr. MacEvoy is both a scientist and an artist, so he digs deep into the physical properties of pigments and color more generally.

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  8. ed
    July 2, 2012 at 11:25 am

    Next step: realizing that some of the colors you see don’t exist, e.g. pink.

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    • araybold
      July 8, 2012 at 9:52 am

      Pink is not found in the spectrum of visible light because it stimulates the photoreceptors of the eye in a ratio that no single frequency can achieve.

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  9. FogOfWar
    July 2, 2012 at 9:17 pm

    Totally awesome post–always wondered about that myself!

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  10. araybold
    July 8, 2012 at 10:35 am

    Describing absorption an additive process is only an approximation that is most true when considering the transmission of light through a series of filters, each of which completely absorbs a part of the spectrum and completely transmits the rest. In this case, the combined filter absorbs all the light at any of the frequencies absorbed by any of its components, so what is being added are the notches that each filter takes out of the spectrum (where a spectrum is intensity as a function of frequency).

    More generally, each component filter would be modeled by the ratio of transmitted to incident intensity as a function of the frequency of light, and also of some measure of its ‘density’, which would account for such matters as the thickness of the component and its dilution by a transparent medium. In this model, the component functions are multiplied to get the composite function.

    From this model, we can expect that dilute pigments will result in reduced saturation, ‘washed-out’ colors, and if the dilution is unequal between filters, the color will be different. As pointed out by Scott, exposure to ultraviolet light may cause such a dilution.

    Things get more complicated when we consider reflection and scattering. A layer of pigment that is a thin, purely transmissive compound filter on top of a bright white scattering layer (e.g. paper) will, I believe, give the same resulting color (after allowing for the light taking two passes through the filter). On the other hand, if the surface is a two-dimensional microscopic, pointillist mosaic of colored spots, where the incident light is either absorbed or scattered out of the medium, so that only an insignificant amount of reflected light has scattered from one spot to another, then the additive rule would apply. The color of a mixture of real pigments is affected by both absorption and scattering.

    Because of these complications, the subtractive rule cannot necessarily tell us what the mixture of two pigments will look like when used to paint with, and the color of a pigment in bulk is not necessarily its color when used as paint. This, and much more, is explained by Bruce MacEvoy in the link given by Cliff. Mr. MacEvoy carefully separates two issues: how the perception of color arises from a spectrum, and the various effects of pigments on a spectrum: “There are two surprises when we learn about color mixture. The first is that subtractive color mixture is nothing more than additive color mixture, in an expanded form that tries to compensate for the light absorbing effects of material mixtures. The second is that additive color mixture is a rigorous explanation of color vision, a true scientific theory; but subtractive color mixture is only an idealized and unreliable approximation of the actual complexity and diversity of material color mixture.”

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  11. July 23, 2012 at 12:34 pm

    “In order to match the value of the majority of the colours we see in the world around us with oil paint, large amounts of white must be mixed into the paint in order to lighten it – to raise its value.” – Paul Foxton on mixing paint colors

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  1. September 20, 2012 at 10:35 am
  2. September 20, 2012 at 11:46 am
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