5.4 Colour and frequency — Practise with help

Work each problem first. Open a hint only if you are stuck, and the full working only to check.

Warm-up: remember

Answer these from memory. They use ideas from Section 5.1.

Which has the shorter wavelength, red light or blue light?
Write 400 nm in metres, using standard form.
Work out $\dfrac{3.0 \times 10^8}{6.0 \times 10^{-7}}$ .

Answers

Blue light has the shorter wavelength.
$4.0 \times 10^{-7}\,\text{m}$ .
$5.0 \times 10^{14}\,\text{Hz}$ .

If question 1 went wrong, remember the order of the visible spectrum. If question 3 went wrong, take care with the powers of ten when you divide.

Practise with help

1. A red shirt is seen in green light. Explain the colour the shirt appears, and why.

Hint

Ask which colours a red object reflects, and whether green light contains any of them.

Next step

Say what happens to the green light when it reaches a surface that reflects only red.

Full working

The shirt appears black. A red object reflects red light and absorbs the other colours. Green light contains no red, so the shirt reflects almost nothing to the eye. With no light reflected, the shirt looks black.

This answer is a model answer for you to compare with your own wording.

2. White light shines on a red filter. Describe the light that passes through, and explain what happens to the other colours.

Hint

A filter absorbs some wavelengths and transmits others. Think about which wavelength a red filter lets through.

Next step

Name the colour that passes through. Then say where the energy of the absorbed colours goes.

Full working

Red light passes through the filter. The other colours, such as green and blue, are absorbed by the filter. The absorbed energy is transferred to the thermal store of the filter.

3. Violet light has a wavelength of 400 nm. Calculate its frequency.

Hint

Use the wave equation as $f = \dfrac{c}{\lambda}$ . Convert the wavelength to metres first.

Next step

$400\,\text{nm} = 4.0 \times 10^{-7}\,\text{m}$ . Put this into $f = \dfrac{3.0 \times 10^8}{\lambda}$ .

Full working

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

4. Explain why white light spreads into a spectrum when it passes through a prism.

Hint

White light is a mixture of colours. Each colour has its own frequency.

Next step

Link the frequency of each colour to the amount it is refracted.

Full working

White light contains all the visible wavelengths. Each colour has a different frequency, so each colour is refracted by a different amount when it enters the glass. Violet is refracted the most and red the least. The colours therefore spread out into a band, which is the spectrum.

This answer is a model answer for you to compare with your own wording.

5. A white wall is lit by red light. Explain the colour the wall appears.

Hint

A white surface reflects every colour that reaches it.

Next step

Say which colours reach the wall, then say which of them are reflected to the eye.

Full working

The wall appears red. A white surface reflects all the visible wavelengths. Only red light reaches the wall, so only red light is reflected to the eye. The wall therefore looks red.