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A LevelPhysicsCambridge (CIE)Revision Notes25. Astronomy & CosmologyHubble’s Law & the Big Bang TheoryDoppler Redshift

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First teaching 2023

First exams 2025

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Doppler Redshift (Cambridge (CIE) A Level Physics)

Revision Note

Ashika

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Ashika

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Redshift of EM radiation

  • The Doppler effect is defined as:

    The apparent change in wavelength or frequency of the radiation from a source due to its relative motion away from or toward the observer

  • On Earth, the Doppler effect of sound can be easily observed when sound waves move past an observer at a notable speed

  • In space, the Doppler effect of light can observed when spectra of distant stars and galaxies are observed, this is known as:

    • redshift if the object is moving away from the Earth, or

    • blueshift if the object is moving towards the Earth

  • Redshift is defined as:

    The fractional increase in wavelength (or decrease in frequency) due to the source and observer receding from each other

  • For non-relativistic galaxies, Doppler redshift can be calculated using:

fraction numerator increment lambda over denominator lambda end fraction space equals space fraction numerator space increment f over denominator f end fraction space equals fraction numerator space v over denominator c end fraction

  • Where:

    • Δλ = shift in wavelength (m)

    • λ = wavelength emitted from the source (m)

    • Δf = shift in frequency (Hz)

    • f = frequency emitted from the source (Hz)

    • v = speed of recession (m s-1)

    • c = speed of light in a vacuum (m s-1)

Worked Example

The spectra below show dark absorption lines against a continuous visible spectrum.

Redshift, downloadable AS & A Level Physics revision notes

A particle line in the spectrum of light from a source in the laboratory has a frequency of 4.570 × 1014 Hz.

The same line in the spectrum of light from a distant galaxy has a frequency of 4.547 × 1014 Hz.

What speed is the distance galaxy moving in relation to the Earth, and is it moving towards or away from the Earth?

Answer:

Step 1: Write down the known quantities

  • Emitted frequency, f = 4.570 × 1014 Hz

  • Shift in frequency, Δf = (4.547 – 4.570) × 1014 = –2.3 × 1012 Hz

  • Speed of light, c = 3.0 × 108 m s–1

Step 2: Write down the Doppler redshift equation

fraction numerator increment f over denominator f end fraction space equals v over c

Step 3: Rearrange for speed v, and calculate

v space equals fraction numerator c increment f over denominator f end fraction space equals fraction numerator open parentheses 3.0 space cross times space 10 to the power of 8 close parentheses space cross times space open parentheses 2.3 space cross times space 10 to the power of 12 close parentheses space over denominator 4.570 space cross times space 10 to the power of 14 end fraction space equals space 1.5 space cross times space 10 to the power of 6 space straight m space straight s to the power of negative 1 end exponent

Step 4: Write a concluding sentence

  • The observed frequency is less than the emitted frequency (the light from a laboratory source), therefore, the source is receding, or moving away, from the Earth at 1.5 × 106 m s–1

Examiner Tips and Tricks

In your exam, be sure to emphasise that redshift means the wavelength of spectral lines increases towards the red end of the spectrum, do not say that the spectral lines become red, as this is incorrect.

An expanding universe

  • After the discovery of Doppler redshift, astronomers began to realise that almost all the galaxies in the universe are receding

  • This led to the idea that the space between the Earth and the galaxies must be expanding

  • This expansion stretches out the light waves as they travel through space, shifting them towards the red end of the spectrum

  • The more red-shifted the light from a galaxy is, the faster the galaxy is moving away from Earth

Expanding universe balloon analogy

Expanding Universe Balloon, downloadable AS & A Level Physics revision notes

A balloon inflating is similar to the stretching of the space between galaxies

  • The expansion of the universe can be compared to dots on an inflating balloon

    • As the balloon is inflated, the dots all move away from each other

    • In the same way the rubber stretches when the balloon is inflated, space itself stretches between galaxies

    • Just like the dots, the galaxies move away from each other, however, they themselves do not move

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    Ashika

    Author: Ashika

    Expertise: Physics Project Lead

    Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.