5.4 Colour and frequency — Learn

Prerequisites: Section 5.1, especially the visible part of the spectrum and the wave equation; Section 5.2, especially absorption and reflection.

By the end of this section you can: describe the visible spectrum; explain the colour of an object in terms of the light it reflects and absorbs; and explain what a filter does.

1. The visible spectrum

Visible light is the small part of the electromagnetic spectrum that the human eye can detect. Its wavelengths run from about 400 nm to about 700 nm.

Within this range, each wavelength is seen as a different colour. In order of increasing wavelength the colours are:

violet, blue, green, yellow, orange, red.

Red light has the longest wavelength and the lowest frequency. Violet light has the shortest wavelength and the highest frequency. White light is a mixture of all the visible wavelengths.

Worked example 1. Red light has a wavelength of 750 nm. Calculate its frequency.

\begin{aligned} f &= \frac{c}{\lambda} \\ &= \frac{3.0 \times 10^8}{750 \times 10^{-9}} \\ &= \frac{3.0 \times 10^8}{7.5 \times 10^{-7}} \\ &= 4.0 \times 10^{14}\,\text{Hz} \end{aligned}

A violet wave of the same speed has a shorter wavelength, so its frequency is higher.

Try it: colour and frequency

The figure shows the visible spectrum as a band. The marker shows the colour of the wavelength you choose.

Predict first. Do not move the slider yet. Write down your answers.

Which light has the longer wavelength: red light or violet light?
As the wavelength gets longer, does the frequency get higher or lower?

Test. Move the wavelength slider from one end of the band to the other. Watch the colour name and the frequency. Stop when the readout says "green".

Explain. The speed of light in a vacuum is the same for every colour. Why does a longer wavelength mean a lower frequency? Write your answer in two or three sentences.

2. Dispersion

A prism can split white light into the colours of the spectrum. This is dispersion.

Each colour has a different frequency, so each colour is refracted by a different amount as it enters and leaves the glass. Violet is refracted the most and red the least. The colours therefore spread out into a band.

3. The colour of an object

An object does not have a colour of its own. The colour you see depends on two things:

which wavelengths the object reflects and absorbs;
which wavelengths are present in the light that reaches it.

A white object reflects all the visible wavelengths. A black object absorbs all of them. A red object reflects red light and absorbs the other colours.

This is why a red object looks black in green light. Green light contains no red, so the object has almost nothing to reflect.

4. Filters

A filter is a piece of transparent material that transmits some wavelengths and absorbs the rest.

A red filter transmits red light and absorbs the other colours.
A blue filter transmits blue light and absorbs the rest.

If white light passes through a red filter, red light comes out. The other colours have been absorbed.

Watch out. The colour of an object is not fixed. The same object can look a different colour under a different lamp, and it can look black if the light has no colour that the object reflects. Also keep the order straight: red has the longest wavelength of the visible colours, not the shortest.

5. Progress check

Return to the chapter problem. The visible-light image uses light with a wavelength of 600 nm. Work out its frequency, and decide whether this light is closer to the red end or the violet end of the spectrum. Explain how you decided.

You should now be able to

state the range of wavelengths of visible light;
list the colours of the visible spectrum in order of wavelength;
explain dispersion by a prism;
explain the colour of an object using absorption and reflection;
explain what a filter does;
explain why the same object can look a different colour in different light.