I think the recent post by John Denker raises some good points, but I would like to offer some alternatives and counter-examples to a few things he said.
* * * Regarding the word "subtractive" * * *
I am not ready to throw it out, although I have an alternative. The fact that multiple same-colored filters in series do not yield a linear "subtraction" (1) does not necessarily mean this can't be called a subtractive process... (2) and whether it is linear depends on how you quantify the action of the filter.
(1) A yellow filter blocks a range of wavelengths from the region we normally call blue. Therefore the yellow filter subtracts blue. If we have two identical pale yellow filters (where the word pale is used to imply one filter alone does not subtract all the blue light that might be present) then putting the second filter in series with the first does "subtract" more blue light. The more filters we use, the more blue is subtracted until we reach the point that essentially "all" blue is subtracted.
(2) If the first filter subtracts 10% of the blue, and the second subtracts 10% of the 90% coming through the first, then the series combination subtracts 19% rather than 20%. More dramatically, if each subtracts 50% of the blue, then the two together in series transmit 25%, not 0%. Stated the other way, the two 50% filters in series remove 75%, not 100%. So yes, this is not linear.
But filters do not have to be quantified by their percent transmission, they can also be quantified by their "absorbance." A filter with 50% transmission has an absorbance of 0.301 (A = -log[transmission]). Two filters in series, each with absorbance of 0.301, have a combined absorbance of 0.602, so we see the process is indeed linear if the filters are quantified by their absorbance rather than by their percent transmission. I don't know of any law that says filters have to be quantified by percent transmission.
Therefore, my alternative wording would be that what we commonly refer to as "subtractive mixing" could be renamed as "absorptive mixing." But I do not believe this would improve the average "person on the street" understanding of color mixing.
Additionally, there is current usage (although it is quickly turning into historical usage) where CMY filters are clearly used in a linear subtractive manner. This usage is traditional color printing in the darkroom. I still have my two sets of Kodak "Color Printing Filters." Each set has three C, three M, and three Y filters. Taking the yellow as an example, they are labeled 5Y, 10Y, and 20Y. If the test print has an overall blue cast, I slip one of the yellow filters into my enlarger's filter tray, and I make a new test print. The 10Y will subtract twice as much blue as the 5Y, and the 20Y will subtract twice as much blue as the 10Y. If I combine the 5Y and 10Y then the result is 15Y (a result between the 10Y and the 20Y). If I choose two 10Y filters in series, the blue subtraction is the same as using one 20Y filter. It's clear the numbers on the filters are quantifying the filters by absorbance rather than transmission. Darkroom people have used this process for years.
* * * Regarding "yellow" dye turning to orange when concentrated * * *
Picking one particular dye like yellow food coloring does not prove the rule. One problem here is that the transition from high transmission to high absorbance is not a vertical line in the spectrum. At low concentrations the absorption in the green portion of the spectrum is minimal, but as the dye concentration increases, more and more green is absorbed, and the perceived color becomes more orange and eventually red. Not all yellow dyes/filters show this dramatic of a change to orange and then red (and eventually black).
The yellow theatrical gelatin filter I have is Roscolene number 608. It is a fairly dark yellow and has a sharper cut-off than yellow food dye. As you double it, quadruple it, even take eight layers of it, the students still say it is yellow. At eight layers I think it might be getting an orange tinge to it, but not much.
I have some dye-sublimation film from a printer, and I just took the yellow portions of that and made a stack of 20 yellow filters in series, and it still looks yellow to me.
A second problem was explained in a short paper I wrote some time ago about the spectrum of yellow food coloring and how it becomes orange then red in appearance at high concentrations. I think I made that paper available to one of the list-servers I am on, but it might not have been phys-l. In that paper I made this comment...
"Once we get as strong as about 2.0 μL/mL [yellow food coloring in water] we have just about subtracted everything [all the blue] we can subtract (i.e. the transmission is nearly zero) from about 380 to 460 nm. At this point it would be reasonable to say this dye is near the end of its usefulness as a filter for subtracting blue. Further additions of dye will not remove any more blue because there isn't any more blue to remove. Said a different way, if we choose to increase the color beyond 2 or 3 μL/mL we are moving outside the realm of subtractive color mixing."
The bracketed comments do not appear in the original paper. This full paper with the measured spectrums can be found at
John has often pointed out, and rightly so, that models, rules of thumb, etc. have limitations. They work where they work and they don't work where they don't work. I would say that when working with typical yellow food coloring, the subtractive model works with concentrations between zero and about 2 microliters dye per milliliter of water (and a 1-centimeter path length). Beyond this point the subtractive model quits working. So what? That's no reason to throw it out. We'd have to throw out lots of models and rules of thumb if we insisted they had to work all the time under all conditions. Long before the concentration of yellow food coloring is sufficient to make it appear orange or red (or black), its use as a subtractive filter is over. There's no blue light left to subtract. Adding more pigment/dye beyond the point there is no more of the color you want to subtract just wastes dye and moves us out of the realm of the subtractive mixing process.
* * * Regarding calling cyan "blue" * * *
Of course there is a range of what people call blue. The thing I find amazing is that no one calls cyan green. The cyan filters I have are clearly just as much green as blue. That is, if we define blue as roughly 400 nm to 460 nm, and green as roughly 500 nm to 560 nm, then the cyan filters that I have can be shown to transmit over 90% of the light from 400 to 560 nm, and therefore these are passing the same amount of green as blue. They are equally blue and green. That people call this blue rather than cyan or blue-green just indicates a learned response taught by parents, kindergarten and elementary-school teachers.
Michael D. Edmiston, Ph.D.
Professor of Chemistry and Physics
Bluffton University
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu