why overlapping two complementary colours would produce white light?

Answer 1

First of all, human vision perceives "white light", when equal intensities of Red, Green, and Blue light are mixed. Let x, y, z be the relative intensities of Red, Green, and Blue, so that all colors can be expressed as follows:

x R + y G + z B

If x = y = z = 1, we have white. So, let an arbitrary color be:

a R + b G + c B

Its complement color is in fact

(1-a) R + (1-b) G + (1-c) B

so that the sum of the two is white.

As an example, let a = 1, b = 0, and c = 0, so that we have the color Red. Then the complment color is where a = 0, b = 1, c = 1, which is a kind of a funny pale blue. The combined colors will be white.

Check link for the RGB color chart. Note that for any color, the complement color is the color directly opposite of and equal distance from the white center.

For sake of simplicity, the intensities of color are normalized so that x, y, z have a maximum value of 1.

Of course, this does not work if you mix paints or inks, because these are absorptive mediums, and the story is more complicated.

Answer 2

You see white light when you overlap 3 basic color frequencies (red, blue and green). The reason 2 complementary colors make white light is because when you break down all the colors within those 2 complementary ones you'll end up with your 3 basic frequencies. For example, green and purple would produce white light, but when you take apart purple you still have your blue and red frequencies overlapping the green, giving you all three frequencies, resulting in white light.
The physical reason this works has to do with the way the human eye works. The main theory on how the eye works has to do with how complementary colors pair up. The simplest explanation is that eyes have receptors that pick up the stronger of the 2 colors, creating what you see (opponent-color theory) for proof of this, google "after images" and try some (it's a bit of an optical trick). When the eye, and then the brain gets both "types" of light equally you see white (or when all colors are seen, I guess looking at a star would be a good example of that). On the contrary if there is a problem with how the receptors fire, it results in colorblindness (not being able to distinguish green from red hues, or more rarely blue from orange hues.)

Answer 3

The short answer is red and blue, but this is more complicated than it first appears. First, one has to consider: is one adding lights, or pigments? Pigments are subtractive, not additive. There is a thing called a "chromaticity diagram" which represents the response of the human eye to light of various wavelengths; it looks like a lopsided upside-down U. Red, orange, yellow, and green move up the figure from the lower right, with green at the top, and blues at the left. A pure color (one wavelength) is represented by a point on this curve. All points in the middle represent mixtures of color, with a point in the lower center representing white light (it's called Illuminant C, and is basically the color of sunlight). If you add two colors, the point representing the mixture is on the line connecting the points representing those colors, located so that the distance from the center point to the edges is in proportion to the brightness of the lights. Try "chromaticity diagram" in Wikipedia for more on this.