# [Physics] Can two different RGB color triplets give the same color

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It is easy to understand that RGB color models cannot represent all colors. First the coding on a finite number of bits (16, 24…) cannot reproduce the infinite number of tones. Second, the RGB triangle does not encompass the whole gamut that a human eye can detect, as can be seen on this plot:

https://commons.wikimedia.org/wiki/File:Cie_Chart_with_sRGB_gamut_by_spigget.png

Here, I am asking the opposite question. For a given RGB device, can two different RGB values $(R_1, G_1, B_1)$ and $(R_2, G_2, B_2)$ lead to the perception of the same color?

Of course, this could work for $R_2 = R_1 + \epsilon$ with an infinitely small $\epsilon$, because of the limitations of our eyes. But can this also happen for very different values?

This is a question that depends greatly on the RGB implementation of your device. Humans are sensitive to colors because of the cones in their eyes, this is a general reference to explain what I mean:

Now if you had an LED screen, you have to realise that it is not a laser, so it can not possibly emit only a single frequency of light. But, they emit a fairly narrow range, I found a random independent test from somebody on the internet as shown below:

Now the important thing to note is, the Intensity is a function of the amount of current being fed through the LED. When you set an RGB value, if you set R to 255, you are basically saying that the intensity should be 100% of what the LED can produce. You can also imagine that this graph doesn't necessarily just increase or decrease by a constant as you reduce the power.

You can imagine that the net frequency response is what you would get by adding the intensity curves of the red, green and blue LED's. This is then normalised by multiplying by your relative sensitivity above.

Therefore, on different screens, a single RGB color could produce a wide range of different frequency responses. So unless you develop a standardised mapping to move from RGB to "human perception" (which is what other color spaces such as LAB attempt to do), you can't possibly develop the inverse mapping.

However, it is interesting to note that color spaces that do move from their initial to their final space can indeed produce the same output color given different input parameters.

I hope that helps :)