Wavelength and Colour (How Rainbows Form)
Discover how sunlight, wavelengths and raindrops work together to paint a rainbow across the sky.
A Puzzle in the Sky
In the last chapter we learned that light travels as a wave. Now let us use that idea to solve a beautiful puzzle. Have you noticed that rainbows only appear when two things happen together? There must be rain or spray in the air, and the Sun must be shining from behind you. Try it with a garden hose on a sunny morning. Face away from the Sun, make a fine mist, and a little rainbow appears. But why? Where do the colours come from?
Light Is a Wave
Picture shaking one end of a long rope. Bumps travel along it: hill, valley, hill, valley. The distance from the top of one hill to the top of the next is called the wavelength. Light waves are not ropes. They are ripples in electric and magnetic fields, but they also have a wavelength. It is tiny. We measure it in nanometres, and one nanometre is a millionth of a millimetre. About two hundred waves of green light would fit across the thickness of one sheet of paper.
Each Wavelength Is a Colour
Here is the amazing part. Light with different wavelengths looks like different colours to us. The longest waves we can see, around seven hundred nanometres, look red. Shorter ones look orange, then yellow, green, blue, and finally violet, at around four hundred nanometres. This whole band of colours is called the visible spectrum. Scientists also talk about frequency, meaning how many wave crests pass by each second. Short waves have high frequency, like quick little steps compared with long strides.
Colour Lives in Your Eyes
But why does a seven hundred nanometre wave look red? The colour is not painted on the wave. At the back of your eye, in a layer called the retina, are cells called cone cells. Most people have three kinds. One kind responds most to long waves, one to medium waves, and one to short waves. Your brain compares their signals and creates the feeling we call colour. So colour is partly physics and partly you. Exactly how the brain makes the experience of red is still a mystery.
White Light Is a Mixture
Sunlight looks white, so where does the red come from? In about sixteen sixty six, Isaac Newton made a small hole in his window shutter and let a beam of sunlight shine through a triangle of glass called a prism. On the wall appeared a strip of colours. Then he did something clever. He used a second prism to bring the colours back together, and they made white light again. So white light is a mixture of all the visible wavelengths travelling together.
Light Bends: Refraction
Put a pencil in a glass of water and it looks broken at the surface. That happens because light travels more slowly in water than in air, at about three quarters of its speed in air. When a beam enters water at a slant, it changes direction. This bending is called refraction. Here is a simplified picture. Imagine a row of marchers walking from a smooth road onto sand at an angle. The marchers who reach the sand first slow down first, so the whole row swings round and turns.
Colours Bend Differently
Now the key step. In water and glass, the different colours do not slow down by exactly the same amount. Violet light slows a little more than red light, so violet bends a little more. When white light is refracted, the colours fan out and separate. This spreading is called dispersion. Why does violet slow more? Light shakes the tiny electrons inside the material, and shorter waves are affected more strongly. The full explanation needs advanced physics, so for now, that is our honest best picture.
Common mistake
A very common mistake is to think a prism or a raindrop adds colour to light, like a paintbrush. It does not. The colours were already inside the white sunlight. The prism only sorts them, the way a sieve sorts sand from pebbles. Another mistake is thinking a rainbow has exactly seven colours. Really, the colours blend smoothly with no sharp edges. Newton chose seven names, red, orange, yellow, green, blue, indigo and violet, partly because he liked the number seven.
Inside One Raindrop
Now let us follow sunlight into a single round raindrop. First, light enters the front of the drop and refracts, so the colours begin to separate. Second, the light hits the back of the drop, and some of it reflects, bouncing back like a ball off a wall. Third, the light leaves the front of the drop and refracts again, spreading the colours even more. The light comes out heading back towards the side where the Sun is. That is why the Sun must be behind you.
The Magic Angle
Here is the clever geometry. Imagine a line from the Sun, through your head, to the shadow of your head. Drops send out red light most strongly at about forty two degrees from that line, and violet at about forty degrees. All the drops at that angle form a circle around the line, so a rainbow is really part of a circle. The ground usually hides the lower part. If the Sun is higher than forty two degrees, the bow sinks below the horizon, so rainbows love mornings and evenings.
Red on Top, Violet Below
Why is red on the outside of the bow? Red leaves the drops at the bigger angle, so the red light reaching your eye comes from drops higher in the sky. Violet comes from drops a little lower. Each drop sends your eye mainly one colour at a time. And because the angle is measured from your own eyes, your friend standing beside you sees light from different drops. Everyone sees their own personal rainbow. That is also why you can never walk to the end of one.
Double Rainbows
Sometimes you see a second, fainter rainbow above the first. This one is made when light reflects twice inside each drop before coming out. At every reflection some light escapes, so less is left, and the second bow is dimmer. It sits at about fifty one degrees, and its colours are reversed, with red on the inside. Between the two bows the sky looks darker. This is called Alexander's dark band, because very few drops send light to your eye from those angles.
Colours We Cannot See
The rainbow does not really stop at red and violet. In the year eighteen hundred, the astronomer William Herschel spread sunlight with a prism and put thermometers just beyond the red end. They warmed up! Invisible light with longer waves was there. We call it infrared, meaning below red. Beyond violet is ultraviolet, meaning beyond violet, with shorter waves that cause sunburn. Our cone cells cannot detect these, but some animals can. Bees, for example, see ultraviolet patterns on flowers that we cannot see.
Now You Explain It
Let us put it together. White sunlight is a mixture of wavelengths, and our eyes and brain experience each wavelength as a colour. Raindrops bend light, bounce it off their backs, and bend it again. Violet bends a little more than red, so the colours fan out, and each colour reaches you from drops at its own angle. Now try teaching a friend. Can you explain why the Sun must be behind you, and why red is on top? If you can, you truly understand rainbows.