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Thread: The math behind mixing colors

  1. #1
    Natural Philosopher RJBeery's Avatar
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    Whatever The math behind mixing colors

    So I'm coloring with my daughter yesterday and I start thinking about the Physics behind the mixing of colors. There isn't really a "connection' that should bring the violet end of the spectrum back to the red in a color wheel when thought of in terms of wavelengths...or is there?

    My first thought is that maybe the frequency of red mixed with the frequency of yellow might make a phase-differential on the order of the true orange range. But if this were true couldn't we do the same with any EM source (i.e. mixing radiowaves with x-rays and "seeing" green). I haven't researched this in any way, and I apologize for my sloppily-written post. I'm sure the answer is well-established, does anyone know it?

  2. #2
    Valued Senior Member Rhaedas's Avatar
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    I don't think so. When the retina receives two different colors mixed, it's the brain that combines the effect to give us a new color. Since our retina is only sensitive to a small section of the EM band, we couldn't use a higher or lower frequency to move the combined result up or down, as our retina won't see it, only the other color.

    Another thing is that if mixing was possible, then we couldn't separate colors from sunlight, nor could we utilize fiber optics to send millions of different signals down the same line.

  3. #3
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    Quote Originally Posted by RJBeery View Post
    So I'm coloring with my daughter yesterday and I start thinking about the Physics behind the mixing of colors. There isn't really a "connection' that should bring the violet end of the spectrum back to the red in a color wheel when thought of in terms of wavelengths...or is there?

    My first thought is that maybe the frequency of red mixed with the frequency of yellow might make a phase-differential on the order of the true orange range. But if this were true couldn't we do the same with any EM source (i.e. mixing radiowaves with x-rays and "seeing" green). I haven't researched this in any way, and I apologize for my sloppily-written post. I'm sure the answer is well-established, does anyone know it?
    I cannot give a full explanation at present, however it involves the difference between using pigments to create color and using a light emitting source. The yellow pigment in this case absorbs red light and the red absorbs yellow. What is reflected is a combination rather than a pure frequency. The "mind" interprets the mixture ....

    With emission sources it winds up differently. Mix all pigments properly and you get black or more realistically a brown. Mix all emitted wavelengths and you get white light. So it is difficult to compare pigment created colors with the same light spectrum obtained from an emitted light source.

    I know that was ackward....

  4. #4
    Natural Philosopher RJBeery's Avatar
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    Yes, I wondered if it was an effect purely in the brain but cameras pick it up as well. How does a digital camera record "orange" for a pixel if the incident photons are all red and yellow? There clearly isn't any internal interpretation going on, it's a simple measurement.

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    Quote Originally Posted by RJBeery View Post
    Yes, I wondered if it was an effect purely in the brain but cameras pick it up as well. How does a digital camera record "orange" for a pixel if the incident photons are all red and yellow? There clearly isn't any internal interpretation going on, it's a simple measurement.
    Cameras and TV or computer displays use a "usually" RGB color system. They record and project colors much in the same way as pigments absorb and reflect light. The mind once again interprets specific color from the mixture.

  6. #6
    Valued Senior Member scheherazade's Avatar
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    Quote Originally Posted by RJBeery View Post
    Yes, I wondered if it was an effect purely in the brain but cameras pick it up as well. How does a digital camera record "orange" for a pixel if the incident photons are all red and yellow? There clearly isn't any internal interpretation going on, it's a simple measurement.
    My experience with cameras, film and digital variety, is that the color portrayed in the result is not how my eyes/brain perceive it. With digital, it is easy to compare immediately.

    This seems especially noticeable with violet/blue and reds. Hard colors to capture with any accuracy, at least for me.

  7. #7
    Natural Philosopher RJBeery's Avatar
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    Quote Originally Posted by OnlyMe
    Cameras and TV or computer displays use a "usually" RGB color system. They record and project colors much in the same way as pigments absorb and reflect light. The mind once again interprets specific color from the mixture.
    This just doesn't seem right to me. If this were true then a digital picture of an object composed of a mixture of red and yellow would be composed of discrete pixels of either red or yellow, with no orange detected, wouldn't it? If you're saying that the RGB sensor might "combine" the incoming photons to interpret orange for an individual pixel then that's exactly what I'm asking...how does it do that?

    Maybe I'm mistaken here but I have a problem with accepting the "it's all an illusion created by the brain" explanation...

  8. #8
    Natural Philosopher RJBeery's Avatar
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    Quote Originally Posted by RJBeery
    Maybe I'm mistaken here but I have a problem with accepting the "it's all an illusion created by the brain" explanation...
    Continuing this thought, if red and yellow make orange because our brains "average out" the energy (or whatever explanation I'm being fed here) that still doesn't explain why violet reconnects with red in the color wheel. Also, if that's the real answer, WHY does the brain do such a thing? If it's all about averaging why doesn't mixing red and violet produce green (or whatever color would exist between ANY two colors...I don't believe color mixing behaves in this manner).

  9. #9
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    Quote Originally Posted by RJBeery View Post
    This just doesn't seem right to me. If this were true then a digital picture of an object composed of a mixture of red and yellow would be composed of discrete pixels of either red or yellow, with no orange detected, wouldn't it? If you're saying that the RGB sensor might "combine" the incoming photons to interpret orange for an individual pixel then that's exactly what I'm asking...how does it do that?

    Maybe I'm mistaken here but I have a problem with accepting the "it's all an illusion created by the brain" explanation...
    You cannot think of this as an illusion. For a great deal of what we "see" in the world around us, the color we "see" is reflected and that reflection in most circumstances works just like pigments in a paint or crayon. A green leaf is green because it absorbs red light, leaving the blue and yellow to be reflected and mixed by our optical process (eye and brain) to be green. And yes there are some situations where only green light is reflected and we see green.

    The point is that a large portion of what we see as color, is a composite of more than one color that we see the same as if it were a single wavelength of emitted light. Look at a painters color pallet and compare the variations with a spectrograph. There will be variations in the painter's pallet that are not duplicated in an emitted light spectrum. While at the same time a painter will have a difficult time exactly matching some individual wavelengths.

    There was another unrelated thread a short while back discussing the Charles Bennet Syndrome (CBS), http://www.sciforums.com/showthread.php?t=109558 that involves how the brain fills in missing information. That syndrome is not the same as color perception but in some respects it does speak to the mind's ability to interpret and fill in where necessary. While CBS does involve to varying extents illusion and imagination, it is an example to some extent what our mind's do in everyday experiences. They make best guesses based on past experience.

    When you mix two pigments, red and yellow, each pigment particle reflects either red or yellow absorbing other wavelengths. The eye and mind "see".., perceive the red and yellow as orange. However if you could put the reflected light through a prism you would get red and yellow not orange, while you can hava discrete emission of orange light that would not be separated by the prism into red and orange.

  10. #10
    Valued Senior Member Rhaedas's Avatar
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    It's a good question raised, when a camera records red and yellow, presumably it's recording orange, so when it's re-emitted on a screen, is it now truly orange, or is it sent out as red and yellow again in the appropriate levels?

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    Quote Originally Posted by RJBeery View Post
    Continuing this thought, if red and yellow make orange because our brains "average out" the energy (or whatever explanation I'm being fed here) that still doesn't explain why violet reconnects with red in the color wheel. Also, if that's the real answer, WHY does the brain do such a thing? If it's all about averaging why doesn't mixing red and violet produce green (or whatever color would exist between ANY two colors...I don't believe color mixing behaves in this manner).
    Mixing pigments and mixing light are two very different things. As I mentioned earlier if you mix all visible wavelengths of light you get white light, while if you mix all colors of pigments you get a muddy brown.

    Why not black? Because light is still being reflected by the individual particles of pigment and we "see" it as brown.

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    Quote Originally Posted by Rhaedas View Post
    It's a good question raised, when a camera records red and yellow, presumably it's recording orange, so when it's re-emitted on a screen, is it now truly orange, or is it sent out as red and yellow again in the appropriate levels?
    Our current TVs have essentially three colors for each pixel, red, blue and yellow, and sometimes red, blue and green but I have never understood that. So, orange is projected by turning on the red and yellow. Green by turning on the blue and yellow.

    In a way it is similar to the difference between bytes and bits in computer coding. A byte is comprised of eight bits. Each pixel on an LCD, LED or Plasma display, has at least three components. (Panasonic used to say they had a black pixel in there but again, I never understood that either.)

  13. #13
    Natural Philosopher RJBeery's Avatar
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    Quote Originally Posted by OnlyMe
    When you mix two pigments, red and yellow, each pigment particle reflects either red or yellow absorbing other wavelengths. The eye and mind "see".., perceive the red and yellow as orange. However if you could put the reflected light through a prism you would get red and yellow not orange, while you can hava discrete emission of orange light that would not be separated by the prism into red and orange.
    Yes this is a good description. What I'm after though is why does the mind "see" or "perceive" orange? What is it about red and yellow that make orange? I'm thinking in analogous terms of harmonics in music. There must be a reason and I'm wondering if it's mathematical in nature.

    Also, no one has addressed why violet loops back to red in the color wheel if the EM spectrum continues on in both directions. If our evolution included infrared in our visible spectrum what would the color wheel look like?

  14. #14
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    Quote Originally Posted by RJBeery View Post
    Yes this is a good description. What I'm after though is why does the mind "see" or "perceive" orange? What is it about red and yellow that make orange? I'm thinking in analogous terms of harmonics in music. There must be a reason and I'm wondering if it's mathematical in nature.
    Some of the process could be that individual cones in the eye, as in rods and cones, average out the signal they send on to the optical cortex when they are being stimulated by two wavelengths of light. This is a guess....

    Also, no one has addressed why violet loops back to red in the color wheel if the EM spectrum continues on in both directions. If our evolution included infrared in our visible spectrum what would the color wheel look like?
    This really most likely reverts to the difference between pigments and emitted light, but I cannot answer how or why just that for pigments it seems to.

  15. #15
    Valued Senior Member Rhaedas's Avatar
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    Exploring wikipedia on the subject, red and violet don't match up at all on a spectrum-based wheel, but on the color wheel they are joined together with the group of red-violets, purples.

    A color circle based on spectral wavelengths appears with red at one end of the spectrum and violet at the other. A wedge-shaped gap represents colors that have no unique spectral frequency. These extra-spectral colors, the purples, form from additive mixture of colors from the ends of the spectrum.
    So the color wheel is just an abstraction of ours, and if we could see farther on either end, then we'd have similar concepts to deal with that.

    But there are other variations of color wheels that represent more actual colors.

  16. #16
    Natural Philosopher RJBeery's Avatar
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    Quote Originally Posted by OnlyMe
    This is a guess....but I cannot answer...
    Casual discussion is OK for sparking ideas but I was hoping for a definitive answer. Is this not covered in a photography or optics class?

  17. #17
    Natural Philosopher RJBeery's Avatar
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    Quote Originally Posted by Raedas
    So the color wheel is just an abstraction of ours, and if we could see farther on either end, then we'd have similar concepts to deal with that.
    I'm sorry but when I claim that mixing red and blue pigment makes purple, you're saying that this depends on whether or not we can see infrared? I'm not convinced the color wheel can be described as an arbitrary abstraction.

  18. #18
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    Quote Originally Posted by RJBeery View Post
    Casual discussion is OK for sparking ideas but I was hoping for a definitive answer. Is this not covered in a photography or optics class?
    I think part of the problem here is that your question involves both the physics of light and the way our mind assembles sensory information. We cannot explain how our minds work with physics, yet. Perception is not just a direct and exact reflection of the world. It involves even cultural components.

    Two examples I can think of...

    In one there is an optical illusion, the name of which escapes me at the moment, where individuals educated in the western world almost always see two parallel lines as converging, while without exception when the same is shown to San Bushmen they see the lines as parallel.

    The other has to do with how people from eastern cultures, China etc. And those from the western world see a picture, they describe it from completely different perspectives. Western orientation focuses on people things and detail where the eastern influence focuses more on the background scene. This difference is most likely something that is changing.

    The point is that some of what your question involves is a matter of perception that goes beyond any objective scientific explanation and begins to involve the psychology of perception.

    The world we see is not actually in front of us. It is a mental reconstruction of the sensory information as moderated by past experience. All of the separate parts that go into our mind's image of the world don't even occur at the same speed in our brains. And what we "see" is actually some 400 microseconds? delayed (I added the ? To microseconds because I really don't remember off hand if it was micro or nano seconds).

    The answer lies somewhere in between a purely scientific mathematical description and one that involves the psychology of perception itself.

  19. #19
    Valued Senior Member Rhaedas's Avatar
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    My points were going on your original question of wavelengths of light, and how when we use the spectrum colors on a wheel, they don't actually blend where they meet at the reds and violets, so yes, that's a model for us to use in seeing how colors can go together, but it's not truly how colors are related in the EM band. I was just saying that if we saw further, that wheel would be adjusted likewise, but would still be just a construct and not mean that red and violet (or wherever we end our visible ability) are related. This is also why we can have different types of color wheel, because it's a tool for relationships of colors, and that can change depending on what we're trying to find out, as well as what medium we're using, such as light vs displays vs pigments.

  20. #20
    i think it is like music . vibrating or excited . In the excitement the colors converge and Replace each other bouncing back and forth . I know I am uneducated so please play nice . I know all ready anyone that wants to slam Me . Working on it

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