Colour "Math" and Its Equations

In combining various amounts of red, green, and blue we can generate a variety of colours, as the picture below clearly shows. It turns out that we can express these colours in terms of some equations.

It turns out that a very simple treatment of this addition colour method describes fairly accurately how we see the world. We can see from the picture that there are a few basic equations:

Blue +Red =Magenta
Red + Green =Yellow
Green +Blue = Cyan
Blue +Red + Green =White

From this, we also have other equations that we can also derive other "colour equations".

For example, what would happen if added magenta and yellow together?

Magenta is made up of Blue and Red.
Yellow is made up of  Red and Green.

The net result is: (Blue + Red) + (Green + Red) = (Blue + Red + Green) + (Red) = White + Red

The colour we see should be a combination of White,
Red and their mixture which is Pink.

What would happen if you had white light, and you had a filter that could absorbed all the blue light?

White is made up of Blue +Red + Green
Take away "Blue" from both sides of the equation, and we get:
White - Blue = Red + Green = Yellow

The colour we see should look something like Yellow.

When two colours together make white, they are called complementary. Yellow and blue are considered complementary, since when they mix together, they will make white light. As  these "equations" show, we can think of colour as being made up as a sum of each of the three components:

A (Blue) + B (Red) + C (Green) = Total Colour

where A, B, and C describe that total amount of each colour that we see.

When using a computer, each colour uses a value between 0 and 255 inclusive for each of green, red, and blue. Each of these number assigns a certain "deepness" or saturation for that colour. A colour is defined as saturated when there is only that mixture of light and there is no white light possible.  For example, the curve of magenta on the left is considered saturated. There are "red" and "blue" wavelengths being absorbed, but there is no white in the colour, since there is no (or very little) green being absorbed to make white. On the right, there is absorbance curve for pink. Notice that there are considerable amounts of blue, green and red being absorbed; this mean that the resultant colour will have a layer of white. Since the remaining colour is red, the mixture of red and white is the familiar pink.

If we recall the image of the overlaid absorbances, it turns out that there doesn't appear to be a region were there is only one colour that absorbed. As such, we as humans can only see "near-saturated" colours. It turns out that even at the very fringes of the spectrum near the ultra-violet and infared red, each of the pigments still absorbs a tiny bit, which slightly washes out the colour that we see.

Now that we understand how we see colour, the next section will discuss how we see in general. In this next part, it takes a much more technical twist.

Introduction
Colour Vision
Colour Math
Approximations
Focal Lengths and Distances
GRIN Systems
Human Vision
Vision Problems
Corrections