How to Convert RGB Values to Wavelength and Vice Versa?

[neurocomp2003]

How would one convert RGB values to a wavelength value
OR
a wavelength value to RGB?

ie 180,180,60=?

 

[LeonhardEuler]

I think that may be impossible. A blend of different colors of light does not have a unique wavelength. For example, you can't talk about the wavelength of the color brown because it is a mixture of light at different wavelengths.

 

[neurocomp2003]

but doesn't the superposition mean that those different wavelengths...superimpose into one wave? with a wavelength because its a finite #?

 

[LeonhardEuler]

No, waves of different frequencies do not combine into a single, normal wave. For example you can add two cosine waves of different frequencies. Suppose the average frequency of the two waves is m and that one wave has frequency (m+x) and the other (m-x). Then the function describing the amplitude of the wave is A=cos[(m+x)t] + cos[(m-x)t]. Using Euler's formula, that becomes
A = Re: e^[i(m+x)t] + e^[i(m-x)t]
= Re: {e^(imt)}*{e^(ixt) + e^(-ixt)}
= Re: {cos(mt) +i sin(mt)}*{cos(xt) + i sin(xt) + cos(-xt) + i sin(-xt)}
= Re: {cos(mt) +i sin(mt)}*{2cos(xt)}
= 2cos(mt)cos(xt)
Which is not a simple cosine wave (It looks like a cosine wave on top of a cosine wave for x<<m)
The eye contains three different light sensitive pigments which have maximum sensitivities at wavelengths corresponding roughly to red, green and blue. It is the relative extent to which these pigments are activated that determines what color is percieved. Each of these pigments can pick out of a complicated waveform that component of the the wave at the frequency to which it is most sensitive. No pure light could activate pigments that peak at different frequencies equally. This means that some colors can not be produced by pure light.

 

[neurocomp2003]

"It is the relative extent to which these pigments are activated that determines what color is percieved."
if so does this mean that the bipolar cells of the eye don't receive on/off signals from the cones&rods but REAL valued signals?

 

[LeonhardEuler]

The frequency with which a neuron is activated determines the perceived strength of the signal. For example, to use random numbers, if a cell with one pigment is activated 10 times a second and a different one is activated fifteen times a second, the brain will interpret this as meaning the second color is more abundant.