White light and the spectrum
Sunlight looks white, but it is a mix of colours. A prism bends each colour by a different amount, so the colours spread out into a spectrum: red, orange, yellow, green, blue, indigo, violet. Each colour has its own wavelength: red is longest (about 700 nm), violet is shortest (about 400 nm).
Energy carried by light
Light comes in tiny packets called photons. A photon's energy depends only on its colour (frequency): E = h × f, where h is Planck's constant. Light travels at c = f × λ (c = 3 × 108 m/s). So a short wavelength means a high frequency and more energy.
A handy shortcut: E (in eV) = 1240 ÷ λ (in nm). Red light at 700 nm: 1240 ÷ 700 = 1.77 eV. Violet at 400 nm: 1240 ÷ 400 = 3.1 eV. Brighter light means more photons, not more energy per photon.
Additive mixing: making colour with light
When coloured lights overlap, the colours add. The three primary colours of light are red, green and blue (RGB).
- Red + green = yellow
- Green + blue = cyan
- Red + blue = magenta
- Red + green + blue = white
Screens use this. Each pixel has tiny red, green and blue dots, and each dot can be set from 0 to 255. That gives 256 × 256 × 256 = 16,777,216 colours.
Subtractive mixing: paints, inks and filters
Paint does not make light. It takes away (absorbs) some colours from the white light that falls on it. The primaries of subtractive mixing are cyan, magenta and yellow (CMY). Cyan soaks up red, magenta soaks up green, yellow soaks up blue.
- Cyan + yellow = green (only green is left)
- Magenta + yellow = red
- Cyan + magenta = blue
- All three = near black
Printers add a black ink (K) to get a true black. This is CMYK.
Paint: pigments, solvents and recipes
Paint has three parts. Pigment is the coloured powder that gives the colour and does not dissolve. A binder (like oil or acrylic) holds the pigment on the wall. A solvent (water or thinner) makes it thin enough to spread, then dries away.
A paint recipe is a list of parts. For example, 2 parts blue + 1 part yellow gives a green; adding white makes it lighter. Shop paints are mixed by machine from a base and several coloured pigments in exact amounts, so the same shade can be made again.
Why objects have colour
An object's colour is the light it reflects. A red apple reflects red and absorbs the rest. A white shirt reflects all colours. A black shirt absorbs nearly all, so it feels hotter in the sun. Under a green light a red apple looks nearly black, because there is no red light for it to reflect.
How the eye sees colour
The retina at the back of the eye has rods (work in dim light, no colour) and cones (work in bright light, give colour). There are three kinds of cones: red-ish, green-ish and blue-ish. The brain compares how strongly each kind responds and tells you the colour. If one kind is missing or weak, the person has colour blindness (common: red-green).
This is why three light colours are enough for screens: they stimulate the three cones in different amounts.
Colour map and gamut
Scientists draw every colour a human eye can see on one flat curved chart, the chromaticity diagram. A screen's red, green and blue dots are three points on it; every colour the screen can make lies inside the triangle joining them. That triangle is the screen's gamut. A bigger triangle means the screen can show more vivid colours. No screen with three dots can show every visible colour.
Try it
In the 3D: go to the last step. Make yellow with only red and green. Then switch to paint mode and see what the same sliders do.
At home: look at a phone screen through a drop of water. You may see the tiny red, green and blue dots. In a dark room, shine a red torch on a green leaf; what colour does it look?
Key formulas and definitions
- E = h × f (photon energy)
- c = f × λ (c = 3 × 10⁸ m/s)
- E (eV) ≈ 1240 ÷ λ (nm)
- Additive (light): R + G + B = white
- Subtractive (paint): C + M + Y = near black
Worked examples
1. What colour do you get when red and green lights overlap? And paint cyan and yellow?
Red light + green light = yellow (light adds). Cyan paint + yellow paint = green (cyan takes away red, yellow takes away blue, so only green is left).
2. Find the frequency of green light of wavelength 500 nm.
f = c ÷ λ = 3 × 10⁸ ÷ (500 × 10⁻⁹) = 6 × 10¹⁴ Hz.
3. Find the energy in eV of a photon of wavelength 620 nm.
E = 1240 ÷ 620 = 2.0 eV.
4. Which photon has more energy, red (700 nm) or blue (450 nm)? By how much?
Red: 1240 ÷ 700 = 1.77 eV. Blue: 1240 ÷ 450 = 2.76 eV. Blue has about 1.6 times more energy (2.76 ÷ 1.77).
5. A pixel is set to (R, G, B) = (255, 255, 0). What colour is it?
Full red + full green + no blue = yellow.
6. A red rose is lit by pure blue light. What colour does it look?
Almost black. A red rose reflects red only. There is no red in blue light, so almost nothing is reflected.
Common mistakes
- Mixing up the two rules: lights add (RGB), paints subtract (CMY). Red + green = yellow only for light.
- Thinking primary colours of paint are red, yellow and blue only. Printers and physics use cyan, magenta and yellow.
- Saying brighter light has higher energy per photon. Brightness is the number of photons; colour sets the energy of each.
- Saying a red object "makes" red light. It only reflects the red that is already in the light that falls on it.