Here's a thought experiment. Consider these two scenarios:

1. Take two different lights, one with a yellow filter, one with a blue filter, and shine them both on a white surface.
2. Take one light, place both a yellow and a blue filter on it and shine it on a white surface.

What color do you see on the white surface in each example? Do you get the same color or different colors? If you're not sure, don't feel bad. This one even stumped Leonardo da Vinci.

In his book, The Science of Art, Optical themes in western art from Brunelleschi to Seurat, Martin Kemp describes an 'experiment' performed by Leonardo:

His notebooks show that he did precociously attempt to analyze the phenomenon of mixing coloured lights. In a typical experiment he showed a spherical object illuminated by blue and yellow lights which result in the white surface of the object appearing to be a “most beautiful green.” These results are, as we know, incorrect…

Leonardo could not have performed the experiment as described. As Kemp points out, it must have been more of a thought experiment. Incidentally, Wikipedia describes the motivation for publishing this kind of science in the article on scientific misconduct under the heading, Motivations—Laziness. I'm willing to forgive a little laziness from the guy who thought up helicopters in the 15th century.

Leonardo was wrong on this one, but why? We all learned either from Sesame Street or Zip-lock bag commercials that blue and yellow make green. Sometimes they do as Leonardo pointed out in his notebooks, this time correctly:

…if the rays of the sun pass through two panes of glass in close contact, of which one is blue and the other yellow, the rays, in penetrating them, do not become blue or yellow but a beautiful green.

Leonardo separately described both of our scenarios concluding that they each result in a beautiful green.

Since it's not difficult to recreate the scenarios, we can test the results. Beginning with scenario one—two lights, one filtered blue and one filtered yellow—we'll put the yellow filter on a wide spot and the blue on a narrower spot to make it easier to see the interaction. Here are the individual lights photographed separately:

Scenario one Two lights filtered separately:

Two lights one with a blue filter and one with a yellow filter.

Leonardo was indeed wrong here; there's not a hint of green.

Scenario two Both filters on a single light:

One light with both a blue filter and a yellow filter together.

Now yellow and blue do make green.

Why are they different? Additive vs. subtractive models
This is a very clear example of the difference between additive and subtractive color mixing. Just about all digital color involves additive color models. This is what the standard RGB model is—monitors and TVs create color by adding various proportions of red, green, and blue light together. Add a bit of all of them and you approach white. In Leonardo's world artificial light wasn't as pervasive as it is today and you generally weren't adding colored light together, you were mixing paint and mixing paint is a subtractive color process. Subtractive color begins with white light reflecting off or passing through a surface. Pigments selectively absorb parts of the spectrum from that light. The color you see is what was not absorbed. With paint, if you mix all the primaries together, you'll never get white but rather began to approach black. A gel in front of a light is also a subtractive process. The gel selectively absorbs a chunk of the spectrum from the white source. A blue gel in front of a light absorbs most of the non-blue light. A blue and yellow filter together on the same light filter out all the non-blue and the non-yellow light leaving only that little sliver of light that was able to pass through both filters. In this case green light is all that's left over.

The reason the results are different when you use two lights is because you are no longer subtracting wavelengths twice from the same source. You are subtracting light individually from each source, then adding the results together. The blue filter removes yellow light from the white source leaving a hole in that part of the spectrum. Adding yellow from the other light fills in this hole resulting in a relatively even spectrum again, which looks white. The opposite happens with the yellow filter—it removes blue from the spectrum which is replaced by the blue light. This is another way of saying that blue and yellow are complimentary in additive models so when you mix them they neutralize each other resulting in white or grey. Leonardo would have seen this had he actually performed his experiment.