5.4 Colour and frequency — Practise

Work through these on your own. Most of the questions want an explanation, so answer in full sentences and name the wavelengths involved.

Both the questions and the answers below come from a set that is checked by computer every time the book is built.

Red light has a wavelength of 750 nm. Calculate its frequency.
Violet light has a wavelength of 400 nm. Calculate its frequency.
Compare red light and violet light. State which has the longer wavelength and which has the higher frequency.
White light passes through a prism and spreads into a spectrum. Explain why the colours separate.
White light shines on a red filter. Describe the light that passes through the filter, and explain what happens to the other colours.
A red football is taken into a room lit only by green light. State and explain the colour the ball appears.
A white wall is lit by red light. State and explain the colour the wall appears.
Explain why a black object looks black when it is lit by white light.
The light from a lamp has a frequency of 5.0e14 Hz. Calculate its wavelength in nanometres, and state the colour of the light.
Explain why a rough white wall looks white, even though the light is reflected in many directions.
A light source has a wavelength of 500 nm. Say which relationship you will use, then calculate the frequency.
Place the colours of the visible spectrum in order from the longest wavelength to the shortest.

Answers and concise solutions

1. Frequency of the red light

Answer: $f = \dfrac{c}{\lambda} = \dfrac{3.0 \times 10^8}{7.5 \times 10^{-7}} = 4.0 \times 10^{14}\,\text{Hz}$ .

2. Frequency of the violet light

Answer: $f = \dfrac{c}{\lambda} = \dfrac{3.0 \times 10^8}{4.0 \times 10^{-7}} = 7.5 \times 10^{14}\,\text{Hz}$ .

3. A comparison of red and violet light

Red light has the longer wavelength.
Violet light has the higher frequency.

4. Why the colours separate

The white light spreads out into the colours of the visible spectrum.
Each colour has a different frequency, so each colour is refracted by a different amount. Violet is refracted most and red least.

5. The light that passes through the filter

Red light passes through the filter.
The filter absorbs the other colours, so green and blue light are removed.

6. The colour of the ball in green light

The ball appears black.
A red object reflects red light and absorbs the other colours. There is no red light in the room, so the ball reflects almost nothing.

7. The colour of the wall in red light

The wall appears red.
A white surface reflects every colour. It reflects the red light that reaches it, so the wall looks red.

8. Why a black object looks black

A black surface absorbs all the wavelengths of visible light.
Almost no light is reflected from the surface to the eye, so the object looks black.

9. Wavelength of the light

Answer: $\lambda = \dfrac{c}{f} = \dfrac{3.0 \times 10^8}{5.0 \times 10^{14}} = 6.0 \times 10^{-7}\,\text{m} = 600\,\text{nm}$ . This is orange-red light.

10. Why the rough wall looks white

The rough surface reflects light in many directions. This is diffuse reflection.
Each part of the wall still reflects all the colours it receives, so the wall looks white from every direction.

11. Frequency of the light

Answer: Use $f = \dfrac{c}{\lambda}$ , so $f = \dfrac{3.0 \times 10^8}{5.0 \times 10^{-7}} = 6.0 \times 10^{14}\,\text{Hz}$ .

12. The colours in order of wavelength

Red, orange, yellow, green, blue, violet.
Red has the longest wavelength and the lowest frequency. Violet has the shortest wavelength and the highest frequency.