Dispersion of white light

Sunlight has many colours

Sunlight looks white. But if you let a narrow beam of sunlight go through a glass prism and fall on a wall, you see a band of colours, like a rainbow on the wall.

The splitting of white light into its colours is called dispersion. The band of colours is the spectrum.

The order of the colours

From the part that is bent the least to the part that is bent the most:

Red, Orange, Yellow, Green, Blue, Indigo, Violet.

We remember it with the word VIBGYOR (read from the violet end). Red is bent the least. Violet is bent the most.

Newton's experiments

The scientist Isaac Newton did two experiments.

1. He passed a beam of white light through a prism, and he got the spectrum.
2. He took a second prism and put it upside down next to the first one. The colours from the first prism went into it, and a beam of white light came out.

So the prism does not make the colours, and it does not change the light. White light is a mixture of the colours of the spectrum. The first prism separates them, and the second joins them again.

Newton also placed a small hole in a screen so that only one colour, say red, went through to a second prism. The second prism bent that colour, but it did not split it into more colours. This showed that the colours of the spectrum are pure.

Why does white light split?

The speed of light in a vacuum is the same for all colours. But in glass, each colour has its own speed.

• Red light goes faster in glass than violet light. So the refractive index of glass is smaller for red.
• Violet light goes slower in glass. So the refractive index is larger for violet, and the ray bends more.

For ordinary glass, the refractive index is about $1.51$ for red and $1.53$ for violet. The difference is small, but it is enough to spread the colours when the beam travels some distance after the prism.

Light of each colour has its own wavelength. Red light has the longest wavelength, about $700\ \text{nm}$, and violet light has the shortest wavelength, about $400\ \text{nm}$. The refractive index is larger for the shorter wavelength.

You should find that red is turned least and violet most, and that the fan is only a degree or two wide for real glass. That is why the screen must be some distance away to show a clear spectrum.

A worked example

A glass has $n = 1.513$ for red light and $n = 1.528$ for violet light. How fast does each colour travel in it?

1. Red. $v = \dfrac{3.00 \times 10^{8}\ \text{m/s}}{1.513} = 1.983 \times 10^{8}\ \text{m/s}$.
2. Violet. $v = \dfrac{3.00 \times 10^{8}\ \text{m/s}}{1.528} = 1.963 \times 10^{8}\ \text{m/s}$.
3. So red is faster by about $2 \times 10^{6}\ \text{m/s}$, about $1\%$. That small difference makes the whole spectrum.

Practise with new numbers

Try it in Python

The program finds the speed and the deviation of red, yellow and violet light in a prism.

Remember these

• White light is a mixture of seven colours: red, orange, yellow, green, blue, indigo and violet.
• Dispersion is the splitting of white light into its colours. It happens because the refractive index of glass is different for each colour.
• Red bends the least and violet bends the most. Red goes fastest in glass, and violet goes slowest.
• A second prism, upside down, joins the colours into white light.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. Which colour travels fastest in glass?

2. Newton sent pure red light into a second prism. Why did it not split again?

3. Do red and violet have the same speed in a vacuum? In glass?

4. Put the colours in order, from the least bent to the most bent.