Exploring the Mystery of Color Mixing with Red, Yellow & Blue

[fargoth]

im reading some of feynman's lecture notes, and i stumbled upon a statement which i do not understand...

he says that we can use ANY three different colors to produce any other color.
lets say we want to see the color X, and we use yellow blue and red (Y,B,R)
then X = yY + bB + rR.
where y,b and are are the color coefficients.
inorder to produce some colors (in my example let's say we want to get green) we would need to use a negative color coefficient.
i.e. the r should be negative while y and b have some positive value to produce green.

mathematically i can see it is so, but i couldn't understand how you practically make it... i'll give you the original quote:

By mixing these three colors in various proportions, we get quite an array of different clors, ranging over quite a spectrum. But as a matter of fact, after a lot of trial and error, we find that nothig ever looks like green.
The question is, can we make green? The answer is yes. How? by projecting some red onto the green then we can make a match with a certain mixture of yellow and blue! so we have matched them, except we had to cheat by putting the red on the other side.
But since we have some mathematical sophistication, we can appreciate that what we really showed was not that X could always be made of, say, red, blue and yellow, but by putting the red on the other side we found that red plus X could be made out of blue and yellow.
So if we allow that the coefficients in the equation can be both positive and negative, and if we interpret negative amounts to mean that we have to add those to the other side, then any color could be matched by any three, and there is no such thing as "the" fundamental primaries.

now, what does he mean when he says "to add them to the other side"?
does he mean that if i use three flashlights with red, yellow and blue colors, we have to use the red flashlight from one side of a sheet and the other two from the other side?
doesn't sound right to me...
can someone explain what he means?
how can i produce green in the lab using red, yellow and blue flashlights?

 

[Mk]

I don't think you can. Those are the primary colors of art, not physics. RGB (televisions and monitors) and CMYK (printing) are better to try this.

 

[fargoth]

i think i understand what he means.

i think he is referring to the test which was carried out to build the chromaticity diagram - in which one eye would see a sample color and the other one a color created from RGB, but not all colors could be created from RGB, and when such a sample was presented to people they were asked to add some RGB colors to the sample until they found the right match - and these colors you add to the sample are "negative amounts of color".

found a source that may have said it better:

The human retina has three kinds of color sensors (cones) with peak sensitivities
near 440nm (blue), 545nm (yellow-green), and 580nm (orange) in the visual part of the spectrum.
The blue sensor is much less responsive than the other two (Foley Fig.13.18).
(There are also "rods" that are more sensitive, but are essentially black&white sensors).
This leads to the tri-stimulus theory of color perception: which postulates that colors can be synthesized
from weighted sums of some primary colors, typically in the red, green, and blue range.
However this is not possible with only positive weighting factors;
some blue-green components of the spectrum require a negatively weighted red component (Foley Fig.13.20).
This means that the desired color sample has to be de-saturated with some red light,
so it can then be matched by positive blue and green components.

anyway, if we'd use another shade of green at ~515nm and change the R to ~640 B to ~440 and G to ~560 we'd get much better color accuracy...
but i guess most people are sattisfied with the variaty we get from only these three colors... (and monitors produce much more shades then printers, so graphic artists have no use for these accurate monitors).
and another problem is that we're limited by what colors of phosphor (or LED's, or gas-discharge) are available.

although i can't see any difficulty in making LCD monitors use the better wavelength's and even add a fourth one...
The typical CRT display can cover less than half of the visible domain of colors.

http://www.cs.berkeley.edu/~sequin/CS184/IMGS/CromaticityDiag.JPG