Light Travels as Waves (How Rainbows Form)
Discover what light really is and how sunlight, raindrops and your own eyes team up to paint a rainbow.
A puzzle after rain
Earlier in this course we saw that light travels in straight lines and makes shadows. Now for a puzzle. After a rain shower, when the Sun is low and behind you, a giant arch of colours can appear in the sky. Red is on the outside, then orange, yellow, green and blue, with violet on the inside. But sunlight looks white, and raindrops look clear. So where do all those colours come from? To answer that, we first need to find out what light really is.
What is a wave?
Drop a pebble into a still pond. Rings spread out. The water itself mostly bobs up and down in place, but the pattern travels outward, carrying energy. That travelling pattern is called a wave. The high points are called crests, and the low points are called troughs. The distance from one crest to the next crest is called the wavelength. Think of a stadium crowd doing a wave. Each person just stands up and sits down, but the wave races all the way around the stadium.
Proof light is a wave
How do we know light behaves like a wave? In the early eighteen hundreds, a scientist named Thomas Young shone light through two thin slits side by side. On the wall behind, he did not see just two bright lines. He saw many bright and dark stripes. Water waves do the same thing. Where two crests meet, they add up into a bigger wave. Where a crest meets a trough, they cancel out. This adding and cancelling is called interference, and it is something waves do.
Colour is wavelength
Light waves are incredibly tiny. Their wavelength is measured in nanometres, and one nanometre is one billionth of a metre. A human hair is roughly eighty thousand nanometres wide. Our eyes notice different wavelengths as different colours. Red light has the longest waves we can see, about seven hundred nanometres. Violet light has the shortest, about four hundred nanometres. Orange, yellow, green and blue sit in between. This whole band of colours that our eyes can see is called the visible spectrum.
Speed and frequency
Light is the fastest thing there is. In empty space it travels about three hundred thousand kilometres every second, so sunlight reaches Earth in about eight minutes. Because the waves are so short and so fast, hundreds of trillions of crests pass a point every second. How many waves pass each second is called the frequency. Speed equals frequency times wavelength. On screen, c is the speed of light, f is frequency, and the Greek letter lambda is wavelength. Short violet waves have the highest frequency.
What is waving?
A water wave needs water, and a sound wave needs air. But light crosses the empty space between the Sun and Earth, where there is almost nothing at all. So what is waving? Light is a wave of electric and magnetic fields, invisible pushes and pulls like the force you feel between two magnets. As the electric part changes, it makes the magnetic part change, and that makes the electric part change again, so the wave keeps itself going. Scientists call light an electromagnetic wave.
White light is a mix
Back to our puzzle. In the sixteen sixties, Isaac Newton let a thin beam of sunlight pass through a triangle of glass called a prism. Out came a band of colours, from red to violet. Some people thought the glass was adding the colours. Newton tested this cleverly. He sent one single colour through a second prism, and it stayed the same colour. He also mixed all the colours back together and got white again. So white light is a mixture of all the colours.
Why light bends
Put a pencil in a glass of water and it looks broken at the surface. Why? Light slows down when it goes from air into water or glass. In water it moves only about three quarters as fast as in air. Imagine pushing a shopping cart at a slant from a smooth floor onto thick carpet. One front wheel reaches the carpet first and slows down, so the cart swings round and changes direction. Light turns in a similar way. This bending at a boundary is called refraction.
Colours bend differently
Here is 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, and red bends the least. When white light refracts, its colours fan out and separate, like runners who start together but run at slightly different speeds. This spreading of white light into its colours is called dispersion. It is why a prism makes a spectrum, and it is half the secret of the rainbow.
Inside a raindrop
A falling raindrop is a tiny, nearly round ball of water. Follow one ray of sunlight. First, it bends as it enters the drop, and its colours begin to separate. Second, it reaches the back of the drop, and some of it bounces back. This bouncing is called reflection. Third, it bends again as it leaves, spreading the colours even more. Light that takes this path comes out brightest at one special angle, slightly different for each colour. Next we will see why that angle matters.
Why the Sun is behind
Stand with the Sun behind you. The shadow of your head points to a spot called the antisolar point. Raindrops about forty two degrees away from that spot send red light to your eyes. Drops about forty degrees away send violet, and drops in between fill in the other colours. Each drop sends you just one colour. All the drops at the same angle form a circle around your shadow, so a rainbow is really part of a circle. From an aircraft you can sometimes see the whole ring.
Double rainbows
Sometimes you see a second, fainter rainbow outside the first. Here the light bounces twice inside each drop before it leaves. Each bounce loses some light, so this bow is dimmer, and the extra bounce flips the order of colours. Red is on the inside and violet is on the outside. It appears about fifty one degrees from your shadow. The sky between the two bows looks darker, because few drops send light toward you from there. This darker strip is called Alexander's dark band.
Common mistake
Many people think a rainbow is a real object hanging in one place, so you could walk to its end. But a rainbow is not a thing. It is light reaching your eyes at special angles. When you move, a different set of drops makes your rainbow, so it moves with you, and the person beside you sees their own rainbow. Another mistake is thinking there are exactly seven colours. The colours blend smoothly. Newton chose seven names, partly to match the seven notes of a musical scale.
Limits and your turn
The wave picture explains rainbows beautifully, but it is not the whole truth. In the early nineteen hundreds, scientists found that light also arrives in tiny packets of energy called photons, which act a bit like particles. Light somehow behaves like both, and even experts find this strange. Faint extra stripes just inside some rainbows come from wave interference too. Now it is your turn. Explain to a friend how bending, bouncing and spreading inside raindrops makes a rainbow, and why the Sun must be behind you.