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This is a very basic question in optics: why the mathematical language we use corresponds to what we actually see.

There are (at least) two ways to think of a decomposition of a visible light.

One way is experimental: when a beam of light passes through a glass prism it decomposes to many beams according to their color. These colors are perceived by human eyes.

The second way is theoretical: the light is thought of as electromagnetic wave satisfying the Maxwell equaitons in vacuum. Then one uses the Fourier transform with respect to the time variable to decompose a given solution as a combintaion of solutions of the form $\vec E(\vec x)e^{i\omega t}$.

If I understand correctly it is claimed in all stadard textbooks in optics that the above two decompositions correspond to each other in the sense that the frequancy $\omega$ determines the color of the light. Why? How do we know that the color is determined by the frequency of light and not by some other parameter? I could not find any clear explanation of this correspondence so far. A reference would be helpful.

Remark. There is a similarly sounding question What determines color -- wavelength or frequency? It is different from my question, and the answers there do not answer my question.

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The reason is physiological, not physical. In short, human retina react differently on different wavelengths, and that varying reaction of the retina causes varying perception of color in the brain.

The retina can distinguish between different wavelength becuse it has several types of light-detecting detectors: one that reacts most strongly with long-wavelength light (corresponding to red), one that reacts strongly on short-wavelengths (blue) and one that reacts strongly with medium wavelengths (corresponding to green). So for example, if only long-wavength detectors are activated, human brain interpets this as "red light". With long- and medium- detectors activated, it's "yrllow". With long- and short-, but not medium- detectors activated, it's "purple", and so on. Specific proportion of the strengths of activation of various detectors give all the hues perceptible to humans.

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  • $\begingroup$ In these terms my question is how do we know that human retina reacts on wave length and not on some other parameter. $\endgroup$ – MKO Sep 28 '20 at 9:26
  • $\begingroup$ @MKO what parameters do you think it might react to? $\endgroup$ – The Photon Sep 28 '20 at 14:19
  • $\begingroup$ I have no idea. $\endgroup$ – MKO Sep 28 '20 at 15:34
  • $\begingroup$ @MKO Different photoreceptive chemicals in retina need different energy to get into an excited state and initialize a proces of sending a signal to the brain. So the retina actualy reacts to the energy of the photons, but it is directly correlated to the wavelength (longer wavelength = lower energy, $E = \frac{\hbar c}{\lambda}$) $\endgroup$ – Adam Latosiński Sep 29 '20 at 8:49
  • $\begingroup$ Do you have a refrence for these claims? Thank you. $\endgroup$ – MKO Sep 29 '20 at 15:23

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