|MadSci Network: Physics
What a great question (and one of my favorites)! You're recognition of the difference between the perceived "color wheel" and the linear spectrum of visible light is reminiscent of the work of Ernst Mach, who determined that our perceptions were so filtered by our sensory organs that scientific observations must be completely empirical to have merit; otherwise they are measurements of our senses rather than phenomena. There are actually several aspects of purple that require both physics and neuroscience to explain, depending upon in which end of the purple spectrum you are interested. As the common mnemonic for the colors of the rainbow, ROYGBIV, suggests, after Blue come Indigo and Violet, such that if Blue is set at a wavelength around 480 nm, then Indigo and Violet would be about 440 nm and 390 nm, respectively. So if violet (390 nm) and red (650 nm) mark the outer boundaries of the visible spectrum, then where are the "intermediate" colors like magenta? Well, they don't exist - at least not as discreet wavelengths of light!
To understand this phenomenon we must turn, as Mach would have, to the source of color perception, the retina. Colors are distinguished on the retina by three different sets of cone cells, each of which detect broad peaks of light centered around 420 nm ("blue" or short- wavelenght cones), 534 nm ("green" or middle- wavelength cones), and 564 nm ("red" or long- wavelength cones). The retina assigns a "color" to a specific wavelength of visible light according to which cones it stimulates at to what extent. However, this means that any form of light that stimulates the correct cones at the correct levels will give the same perception as light of a single wavelength (for examples of this click on, yellow or blue). Color cathode ray tubes, like televisions and computer screens, (as well as color printers and most color magazines) take advantage of this fact. If you look closely at your color monitor, especially if you have a magnifying glass, you can see that each pixel on the screen is actually three spots of light - one red, one green, and one blue (hence: "RGB") - each of which emit a narrow peak of light that roughly corresponds to one of the retina's cones. By directly stimulating each cone to the right degree, the three dots can give us the perception of every color in the visible spectrum - and then some.
Back to the retina. Since the retina is only able to directly detect the activities of the receptors, it approximates the color of something by summing the inputs of the receptors. So, in the same way that it uses yellows and oranges to represent the simultaneous stimulation of the long- and middle- wavelength cones in the absence of stimulation of the short- wavelength cones, the colors "between" violet and red are invented by the retina to explain different degrees of simultaneous stimulation of the short- and long- wavelength cones in the absence of stimulation of the middle- wavelength cones. The obvious question, then, is why would the retina be designed to invent a color where there isn't one? Well, there are actually a few very good reasons for this. From a neurological standpoint, it's simpler: since each colored pixel is interpreted by a retinal ganglion cells, that cell cannot send multiple outputs like "blue and red" to the brain - this would require more cells and many more connections - so it sends the single signal "blue+red". Since it is a single signal, it is interpreted by the brain as a single color, "purple". From a spectral standpoint, this is important for perceiving the "far-blues" like indigo and violet. If you look at the above diagram, you'll notice that the red signal stays constant as the blue signal diminishes below 420 nm; "violet" has a lower short- to long- wavelength stimulation ration than blue; that is: the long- wavelength (red) cones play a part in distinguishing violet from indigo from blue. In a way, purple, magenta, and fuchsia are the extension of the preceived spectrum; assuming the long- wavelength inputs remained constant and the short- wavelength inputs continued to diminish through the ultraviolet spectrum.
I suppose, part of the problem with thinking about purple may stem from thinking of colors as defining discreet wavelengths of electromagnetic radiation. If, instead, we think of colors as our retinas see them - as mixes of the three primary colors - the purples have more meaning: purple is the absence of green.
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