Know that the light emitted from distant galaxies appears redshifted in comparison with light emitted on the Earth

Enrichment – Optional Topic: Red‑shift of Light from Distant Galaxies

Note: This material is not part of the core Cambridge IGCSE 0625 specification (sections 6.1‑6.2). It is provided for students who wish to explore modern astronomy beyond the exam requirements.

Learning Objective

  • Explain why the light from distant galaxies is observed at longer (red) wavelengths than the same light measured on Earth.

  • Use the basic IGCSE concepts of wavelength, frequency, the Doppler effect and Hubble’s law to describe the phenomenon.

Context within the IGCSE Space‑Physics Unit

  • The core unit covers the Earth‑Moon‑Sun system, planetary motions and the basic Doppler effect for sound and light.

  • Red‑shift extends these ideas to the largest scales, showing how the same wave‑motion principles help astronomers investigate the expanding Universe.

Key Concepts

  • Electromagnetic (EM) waves: characterised by wavelength λ (m) and frequency f (Hz) with c = λf.


    Use c = 3.00 × 10⁵ km s⁻¹ (or 3.00 × 10⁸ m s⁻¹) for calculations.

  • Red‑shift (z): an increase in wavelength, i.e. a shift toward the red end of the visible spectrum.

  • Doppler effect for light: a source moving away stretches the emitted waves, increasing λ.

  • Cosmological expansion: on very large scales the space between galaxies expands, stretching any light travelling through it.

Mathematical Description

The red‑shift z is defined as the fractional change in wavelength:

\$z \;=\; \frac{\lambda{\text{obs}}-\lambda{\text{rest}}}{\lambda_{\text{rest}}}\$

For velocities much smaller than the speed of light (v ≪ c) the Doppler approximation gives a simple linear relation:

\$v \;\approx\; c\,z\$

Why Light from Distant Galaxies Is Red‑shifted

  • 1. Kinematic Doppler shift – For relatively nearby galaxies the recession can be treated as a motion through space; the emitted light is stretched in the same way as sound from a receding source.

  • 2. Expansion of space – On cosmological scales the metric that measures distances itself expands. Light travelling through this stretching space has its wavelength increased in exactly the same proportion.

  • 3. Cosmological red‑shift – For very distant galaxies the dominant cause is the expansion of space, not a simple motion through space. This allows the inferred recession speed (from Hubble’s law) to exceed c, which would be impossible for an object moving through space but is permitted for space‑expansion.

Observational Evidence – Hubble’s Law

Edwin Hubble’s spectroscopic measurements in the 1920s showed a systematic increase of red‑shift with distance, leading to the empirical relation:

\$v \;=\; H_{0}\,d\$

  • v – recessional velocity (km s⁻¹)

  • d – distance to the galaxy (Mpc)

  • H₀ – Hubble’s constant (≈ 70 km s⁻¹ Mpc⁻¹, current best estimate)

Sample Data

GalaxyRest λrest (nm)Observed λobs (nm)Red‑shift zRecessional v (km s⁻¹)
A500.0525.00.05015 000
B500.0560.00.12036 000
C500.0600.00.20060 000

Implications of Red‑shift

  • Provides direct evidence that the Universe is expanding.

  • Allows distances to far‑away galaxies to be estimated via Hubble’s law.

  • Helps constrain the age and size of the Universe.

  • Supports the Big‑Bang model of cosmology.

Practice Questions

  1. A spectral line has a rest wavelength of λrest = 656.3 nm (H‑α). In a distant galaxy it appears at λobs = 720.0 nm.

    • Calculate the red‑shift z.

    • Using c = 3.00 × 10⁵ km s⁻¹, find the recessional velocity v (assume the small‑z approximation).

    Solution

    z = (720.0 – 656.3)/656.3 ≈ 0.097.

    v ≈ c z ≈ 3.00 × 10⁵ km s⁻¹ × 0.097 ≈ 2.9 × 10⁴ km s⁻¹.

  2. Explain why the red‑shift of a galaxy is not simply due to the galaxy moving through space at a constant speed, but is instead a consequence of the expansion of space itself.

    Key points

    • In an expanding Universe the distance between any two points (including galaxies) increases because the fabric of space stretches.

    • The stretching acts on the light wave during its travel, lengthening its wavelength regardless of any local motion of the galaxy.

    • For very distant galaxies the recession speed inferred from Hubble’s law can exceed c, which would be impossible for an object moving through space but is allowed for space‑expansion.

  3. Given Hubble’s constant H₀ = 70 km s⁻¹ Mpc⁻¹, estimate the distance to a galaxy with a measured red‑shift z = 0.05.

    • Find the recessional velocity using the small‑z approximation.

    • Apply Hubble’s law.

    Solution

    v ≈ c z = 3.00 × 10⁵ km s⁻¹ × 0.05 = 1.5 × 10⁴ km s⁻¹.

    d = v / H₀ = 1.5 × 10⁴ km s⁻¹ / 70 km s⁻¹ Mpc⁻¹ ≈ 214 Mpc.

Quick Revision Box

  • Red‑shift: \(z = (\lambda{\text{obs}}-\lambda{\text{rest}})/\lambda_{\text{rest}}\)

  • Small‑z approximation: \(v \approx c\,z\) (use \(c = 3.00 × 10⁵ km s⁻¹\))

  • Hubble’s law: \(v = H{0}\,d\) (\(H{0}\approx70 km s⁻¹ Mpc⁻¹\))

  • Red‑shift origins:

    • Nearby galaxies – kinematic Doppler shift.

    • Distant galaxies – stretching of space (cosmological red‑shift), allowing apparent speeds > c.

Suggested diagram (two‑panel): left – a moving light source showing a Doppler‑shifted line; right – an expanding‑space illustration with a light wave stretched as it travels between galaxies.