5.5FieldsStretch

The Doppler Effect, Redshift and Hubble’s Law

Look at the light from almost any distant galaxy and its spectral lines sit at slightly longer wavelengths than they should — as if every single galaxy in the universe is fleeing from us. That single observation, redshift, is the observational foundation of the entire Big Bang model of the universe.

40 min Video by MissLowePhysics Module 5.5 Astrophysics and cosmology

A-level Physics: Space - Redshift & Hubble’s LawWatch the full walkthrough before the notes below.

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What you'll be able to do

Explain the Doppler effect for light in terms of relative motion
Define redshift and use $z = \frac{Δ λ}{λ} \approx \frac{v}{c}$
State Hubble’s law and use $v = H_{0} d$
Explain how redshift and Hubble’s law provide evidence for an expanding universe

The Doppler effect for light

The $Doppler effect$ is the change in observed frequency (and wavelength) of a wave due to relative motion between source and observer. A source moving away stretches the observed wavelength — a $redshift$ for light, since wavelengths shift toward the red end of the visible spectrum; a source moving toward the observer compresses the wavelength, a $blueshift$ .

Quantifying redshift

Redshift, $z$ , measures the fractional change in wavelength, directly related to the source’s recession speed (for speeds much less than $c$ ).

z = \frac{Δ λ}{λ} \approx \frac{v}{c}

Redshift, and its relation to recession velocity (v ≪ c).

1Change in wavelength:

Δ λ = 486.6 - 486.1 = 0.5

nm.

2Redshift:

z = \frac{Δ λ}{λ} = \frac{0.5}{486.1}

3Recession velocity:

v = z c = 1.03 \times 1 0^{- 3} \times 3.00 \times 1 0^{8}

Answer

z \approx 1.03 \times 1 0^{- 3}

;

v \approx 3.09 \times 1 0^{5}

m s⁻¹

Tip — Always use the fractional change Δλ/λ, not the raw wavelength shift alone — redshift is inherently a ratio.

Hubble’s law

Edwin Hubble observed that almost every distant galaxy is redshifted (receding from us), and that more distant galaxies recede proportionally faster — $Hubble’s law$ .

v = H_{0} d

Hubble’s law; H₀ = Hubble constant.

1Rearrange

v = H_{0} d

d = \frac{v}{H _{0}}

d = \frac{2.1 \times 1 0 ^{6}}{2.2 \times 1 0 ^{- 18}}

Answer

d \approx 9.5 \times 1 0^{23}

Tip — Hubble’s constant itself provides a rough estimate of the age of the universe: since v=H₀d resembles distance = speed × time, 1/H₀ gives an approximate age.

Evidence for an expanding universe

Universal redshift, growing with distance, is best explained not as galaxies individually flying through space, but as $space itself expanding$ , stretching the wavelength of light as it travels. Crucially, this doesn’t place Earth at any special centre — an observer in any galaxy would see every other galaxy receding, exactly as Hubble’s law describes from any vantage point. This observation is one of the central pieces of evidence supporting the Big Bang model of the universe’s origin.

Equation recap

z = \frac{Δ λ}{λ} \approx \frac{v}{c}

Redshift.

v = H_{0} d

Hubble’s law.

Common mistakes to avoid

Believing redshift means galaxies are physically flying apart through fixed space.

The best interpretation is that SPACE ITSELF is expanding, stretching the wavelength of light in transit — not simply galaxies moving through a static space.

Assuming Earth must be at the centre of the expansion, since everything appears to recede from us.

Uniform expansion means every observer, in any galaxy, would see the same pattern of recession — there is no special centre.

Using the raw wavelength shift instead of the fractional shift (Δλ/λ) for redshift.

Redshift z is always a ratio, Δλ/λ, not simply Δλ on its own.

Key takeaways

The Doppler effect shifts light to longer wavelengths (redshift) for a receding source, shorter (blueshift) for an approaching one.
Redshift z = Δλ/λ ≈ v/c.
Hubble’s law: v = H₀d — recession velocity is proportional to distance.
Universal redshift, increasing with distance, is evidence for an expanding universe with no special centre, supporting the Big Bang model.

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The Doppler Effect, Redshift and Hubble’s Law

40 min Video by MissLowePhysics Module 5.5 Astrophysics and cosmology