Scattering of light and the Tyndall effect

A beam of sunlight in a dark room

Sunlight comes through a small hole in the curtain of a dark room. You can see the beam as a bright line, and it shows dust that floats in the air. In the clean air of the room, the beam would be invisible. You see the beam because the dust scatters some of the light to your eyes.

What is scattering?

Scattering is the sending of light in many directions when it meets small particles. A particle takes in some of the light, and then it sends it out again in all directions. The light is not lost, and it does not bend in one direction. It is spread.

The Tyndall effect

The scattering of light by particles in a colloid or in a suspension, which makes the path of the beam visible, is called the Tyndall effect. It is named after the scientist John Tyndall.

You can see it in these cases:

• A beam of sunlight through the smoke of a fire or through the mist of a forest.
• The beam of a torch through a glass of water with a few drops of milk.
• The beam of the headlights of a car in the fog.
• Sunlight that passes between the leaves of a thick forest. The tiny droplets of water in the air scatter the light, and the beams are visible.

A true solution, such as clear salt water, does not show it, because the particles in a solution are too small. A mixture such as milk in water is a colloid, and it does.

The size of the particles decides the colour

The colour of the scattered light depends on the size of the particles.

• Very fine particles scatter mainly blue light (short wavelength).
• Larger particles scatter longer wavelengths too, so the scattered light is a mixture of colours.
• Very large particles scatter all wavelengths nearly equally, and the scattered light looks white.

This explains why a cloud, which is a collection of large water droplets, is white. It also explains why the air, which has very small molecules, scatters blue.

How much more is blue scattered?

Very small particles scatter light of wavelength $\lambda$ in the proportion $\dfrac{1}{\lambda^4}$. The wavelength is raised to the power $4$, so a small change of wavelength changes the scattering a lot.

You should find that violet at $400\ \text{nm}$ is scattered more than nine times as much as red, and blue about six times. Yellow and green sit in between.

A worked example

Blue light has a wavelength of about $450\ \text{nm}$ and red light about $700\ \text{nm}$. How many times more is blue scattered?

1. The ratio of wavelengths. $\dfrac{700\ \text{nm}}{450\ \text{nm}} = 1.556$.
2. The fourth power. $1.556^4 = 5.9$.
3. So very small particles scatter blue light about six times as much as red light.

Practise with new numbers

Try it in Python

The program finds how many times more each colour is scattered than red light.

Remember these

• Scattering is the spreading of light in many directions by small particles.
• The Tyndall effect: the scattering of light by the particles in a colloid makes the path of a beam visible.
• Very small particles scatter blue the most: the scattering is proportional to $1/\lambda^4$. Very large particles scatter all colours and look white.

Check yourself

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

1. A torch beam goes through a glass of water with a few drops of milk. What do you see from the side, and why?

2. What decides the colour of the scattered light?

3. Does a clear solution of salt in water show the Tyndall effect?

4. How many times more is violet light ($400\ \text{nm}$) scattered than red light ($700\ \text{nm}$)?