I am interested to understand what is happening on a wave-form representation of visible light, and what the waveform looks like, when various colors are "added" or "subtracted". For instance, if you say the visible spectrum is a continuous spectrum of a simple sinusoidal (sine wave) waveform, but then shine a red light and a green light on a board, you get yellow light reflecting, but the 2 sinusoidal waveforms have different frequencies so you will get a non-simple sinusoidal waveform reflecting. But you assumed the color spectrum was a continuous variation in simple sine-wave frequency, so how is this possible?
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Light obeys something known as the superposition principle - that is, shining the red and green light together gives a combined waveform that is a simple sum of the two waveforms.
This is a caricature of what happens - the $\sin(x)$ can be taken as the 'red' light, the $\sin(2x)$ as the 'green' light, and the yellow plot is the sum of the two.
It turns out that there are infinitely many waveforms capable of being seen as 'yellow' due to the way that humans perceive light. You've probably heard that humans have red, green, and blue receptors - they are actually stimulated at all visible wavelengths, but have varying response strengths to different wavelengths:
To get the impression of 'yellow,' the brain thinks "I need a roughly equal 'red' and 'green' signal from the retina" – this can come from either monochromatic 575nm light, or a mixture of 545nm and 605nm light. These are two very different waveforms, but they are both seen as yellow light!
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$\begingroup$ As an aside, the little bump at the low end of red is why we can see color as a wheel, with indigo connecting to violet. $\endgroup$ Commented Jan 6, 2017 at 1:56
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When red and green light both shine on a board, they don't actually make yellow light! Our eyes only interpret that mixture the same way as yellow. To understand how this works, see this picture of absorption spectra of our cones.
Green light at 535 nm mostly activates the green cones, while red light at 575 nm mainly activates the red cones. Yellow light at 560 activates both the green and red cones. However, the same effect can be made by activating the red cone and green cones separately. Therefore, our eyes interpret these the same way.
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1$\begingroup$ So... you could look at a yellow light with wavelength 560, a simple sinewave, and the eyes would interpret it as yellow by how much each cone responds to it. Or you could shine red and green lights at the eye and depending on the relative brightness you get yellow. BUT - do the 'red' and 'green' lights have to be red and green? Is there only one combination of frequencies and amplitudes that combine to make the interpretation of yellow? Do the cones need to be excited at some exact frequency to do this? Very interesting, Thank you. $\endgroup$ Commented Jan 6, 2017 at 4:46
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$\begingroup$ As far as I understand it, the colors would have to be on opposite sides of yellow on this image, so pretty much your only choices are red and green. But you can use different versions of red and green, as long as yellow is in between them. $\endgroup$ Commented Jan 6, 2017 at 4:54