Doppler Redshift | CIE A Level Physics Revision Notes 2025

Redshift of EM Radiation

Recall 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 moves 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:

$\frac{∆ λ}{λ} = \frac{∆ f}{f} = \frac{v}{c}$

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?

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

$\frac{∆ f}{f} = \frac{v}{c}$

Step 3: Rearrange for speed v, and calculate

$v = \frac{c ∆ f}{f} = \frac{(3.0 \times 10^{8}) \times (2.3 \times 10^{12})}{4.570 \times 10^{14}} = 1.5 \times 10^{6} m s^{- 1}$

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

Exam Tip

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 lead 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 as the rubber stretches when the balloon is inflated, space itself is stretching out between galaxies
- Just like the dots, the galaxies move away from each other, however, they themselves do not move

Doppler Redshift (CIE A Level Physics)

Revision Note

Redshift of EM Radiation

Worked example

Exam Tip

An Expanding Universe

Expanding universe balloon analogy

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Author: Ashika