Theme C — Wave Behaviour

C.5.3 Galactic Redshift — IB Physics HL Revision Notes & Topical Questions

5 min read 9 parts Lesson 36 of 37 1 quiz

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Lesson summary

C.5.3 Galactic Redshift — IB PHYSICS SL notes: Interpret the redshift of distant galaxies as evidence for the expansion of the universe and use z = Δλ/λ and Hubble's law.Redshift — the fractional increase in wavelength (or decrease in frequency) due to source and observer recedin…

Observation
Comparison method
Redshift definition
Frequency form
Positive velocity
Negative velocity

Part 1 of 7Redshift and blueshift

Redshift

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

Blueshift

Blueshift the wavelength decreases and the frequency increases when the object moves towards Earth

Observation

Observation both stars and galaxies can be red- or blueshifted to an observer on Earth

Comparison method

Comparison method compare the spectrum of a nearby object such as the Sun with that of a distant galaxy
The galaxy's lines are shifted towards the red end.

Redshift definition

Redshift definition z = Δλ/λ₀ = (λ − λ₀)/λ₀ ≈ v/c for small z
λ₀ is the emitted wavelength and λ the observed one.

Speed

Speed for z ≪ 1 the recession speed is v ≈ cz

Part 2 of 7Sign of the velocity

Frequency form

Δf/f ≈ v/c, with f the source frequency and f₀ the observed frequency

Positive velocity

Positive velocity the galaxy moves towards Earth, with the observed frequency higher than the source frequency

Negative velocity

Negative velocity the galaxy moves away from Earth, with the observed frequency lower than the source frequency

Habit

Habit keep the minus signs in the calculation because they give the direction

Part 3 of 7Evidence for an expanding universe

Observation

Observation almost all galaxies beyond our local group are receding

Interpretation

Interpretation the space between Earth and the galaxies is expanding
The expansion stretches light waves as they travel, shifting them towards the red.
This is the cosmological redshift.

Distance link

Distance link the greater the distance to a galaxy, the greater its redshift
A greater redshift means the galaxy is receding faster.
The furthest galaxies are redshifted most.

Balloon analogy

Balloon analogy dots on an inflating balloon all move away from each other as the rubber stretches
Galaxies do not move through space so much as being carried along by the stretching of space.

No centre

No centre an observer in any galaxy would see the same pattern, so Earth is not at the centre

Part 4 of 7Hubble's law

Statement

Statement in 1929 Hubble found that recession speed increases with distance

Equation

Equation v = H₀d
What the symbols mean: v = recession speed of the galaxy (km s⁻¹) · H₀ = Hubble constant (km s⁻¹ Mpc⁻¹) · d = distance (Mpc)
H₀ is the Hubble constant, about 70 km s⁻¹ Mpc⁻¹, which is about 2.3 × 10⁻¹⁸ s⁻¹.

Graph

Graph v against d is a straight line through the origin with gradient H₀

Combined form

Combined form for small z, cz = H₀d

Part 5 of 7Age of the universe

Hubble time

Hubble time tracing motion backwards at constant speeds gives t = d/v = 1/H₀
With H₀ = 2.3 × 10⁻¹⁸ s⁻¹ this is 4.3 × 10¹⁷ s, about 13.8 billion years.

Big Bang

Big Bang the model in which the universe began hot and dense and has expanded since

Limit

Limit the estimate is approximate because the rate of expansion has changed with time

Part 6 of 7Supporting evidence and limits

Supporting evidence and limits

Cosmic microwave background

Cosmic microwave background it is the redshifted afterglow of the hot early universe, now at about 2.7 K

Light elements

Light elements the observed proportions of light elements also support the model

Distance measurement

Distance measurement it is the main limit on H₀, since distances use standard candles such as certain supernovae and variable stars

Large redshifts

Large redshifts for z above 1, v = cz overestimates the speed and relativistic formulae are needed

Wavelength stretching

Wavelength stretching every wavelength is stretched by the same factor 1 + z, so the whole spectrum looks shifted and not rearranged

Part 7 of 7More from the specification

1The Doppler Effect for Sound

When a source emitting sound waves moves toward a stationary observer, wavefronts are compressed,
- (such as a vehicle siren)
producing a higher observed pitch and frequency.

2Doppler Shift in Electromagnetic Radiation

For light and radio waves emitted by moving celestial bodies, relative velocity v causes a fractional frequency shift given by Δf / f ≈ v / c.

3Cosmological Redshift and Galactic Recession

Absorption lines in spectra from distant galaxies are shifted towards longer wavelengths (redshift), showing that galaxies are moving away from our reference frame.

4Expanding Universe Evidence

Measuring the Doppler shift of distant galaxies provides empirical confirmation that the universe is expanding uniformly according to Hubble's law.

5Stationary

Not moving.

6Doppler effect

Change in observed wavelength and frequency due to the motion of a source.

7Doppler shift

Change of observed wavelength due to relative motion.

8Electromagnetic wave

Transverse wave that transfers energy from a source to an absorber

Key terms

Term	Meaning
Redshift z	Fractional increase in wavelength, Δλ/λ₀.
Hubble's law	Recession speed proportional to distance, v = H₀d.
Hubble constant	Gradient of the v–d graph, about 70 km s⁻¹ Mpc⁻¹.
Cosmological redshift	Stretching of light by the expansion of space.
Big Bang	Model of an expanding universe from a hot dense initial state.

Avoid these mistakes

Concluding that Earth is at the centre of the expansion.

Treating galaxies as moving through space rather than space expanding.

Using v = cz for large redshifts.

Mixing units of H_{0} between km s^{−1} Mpc^{−1} and s^{−1}.

Reading the age 1/H_{0} as exact.

Last updated: 15 October 2026