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The spectrum

Waves, sound and light · level 6, lesson 1 of 6

A question to start

Isaac Newton passed sunlight through a glass prism and saw it spread into a band of colours. What makes one colour different from another?

The idea

Light is a wave, and each colour is light of a different wavelength. The band of colours from a prism is the visible spectrum. Its wavelengths are tiny, so we measure them in nanometres (nm): \(1 \text{ nm} = 10^{-9}\) m.

Colour Wavelength, about
Red 620 to 750 nm
Orange 590 to 620 nm
Yellow 570 to 590 nm
Green 495 to 570 nm
Blue 450 to 495 nm
Violet 380 to 450 nm

A prism splits white light because glass slows short wavelengths a little more than long ones. Violet bends most, red least. This spreading is called dispersion.

white lightredviolet

The frequency of each colour follows from \(c = f\lambda\).

Worked examples

1. Red light at 700 nm. \(f = c/\lambda = 3.00\times10^8/700\times10^{-9} = 4.3\times10^{14}\) Hz.

2. Violet at 400 nm. \(f = 3.00\times10^8/400\times10^{-9} = 7.5\times10^{14}\) Hz.

3. Mixing back. Pass the spread colours through a second prism, turned the other way, and they mix back into white light.

Try it

  1. Which colour has the longest wavelength?
  2. Find the frequency of green light at 530 nm.
  3. Why does a prism split white light into colours?
  4. Light has a frequency of \(6.0\times10^{14}\) Hz. Find its wavelength and colour.
Answers
  1. Red.
  2. \(3.00\times10^8/530\times10^{-9} = 5.7\times10^{14}\) Hz.
  3. Glass slows each wavelength by a slightly different amount, so each colour bends by a different angle.
  4. \(\lambda = 3.00\times10^8/6.0\times10^{14} = 500\) nm: blue-green.

Common mistake

"The prism adds the colours." The colours were already in the white light. The prism only separates them.

Where it leads