Quick Summary
- Doppler shift — a moving wave source changes the wavelength/frequency an observer detects: squashed (shorter λ) in front, stretched (longer λ) behind.
- Redshift = light stretched to longer wavelength because the source (a galaxy) is receding from us. Blueshift = shorter wavelength, source approaching.
- The redshift equation links the fractional wavelength/frequency shift to the recession speed:
Δλ/λ = Δf/f = v/c.
- Hubble's Law:
v ≈ H₀d — the further away a galaxy is, the faster it's moving away from us. This is the key evidence for an expanding universe.
- The Hubble constant, H₀, is the gradient of a velocity-vs-distance graph for galaxies. Current best estimate ≈ 67.4 km s⁻¹ Mpc⁻¹.
- Dark matter is inferred because galaxies rotate faster at their edges than visible mass alone predicts — there must be extra, unseen mass spread through the galaxy.
Topic 1 — The Doppler Shift
Think about an ambulance siren. As it speeds towards you, the pitch sounds . As it speeds away, the pitch drops . Nothing about the siren itself has changed — the change is entirely due to the ambulance's motion relative to you, the observer. This is the Doppler effect, and it applies to any wave, including light.
Here's the mechanism: imagine the source emits wavefronts (crests) at regular time intervals while it's moving. If it's moving you, each successive wavefront is emitted from a position slightly closer to you than the last one — so the wavefronts "pile up" and arrive closer together. That means a shorter wavelength and higher frequency is observed. If the source moves , the opposite happens: wavefronts get stretched apart, giving a longer wavelength and lower frequency.
STATIONARY SOURCE MOVING SOURCE (→)
. . . . . . .
. () . . ()--v-->
. . . . . . .
wavefronts spread out squashed in front (short λ)
symmetrically — same λ stretched behind (long λ)
in every direction
🔑 Crucial point examiners love to test
The wavelength emitted by the source never changes — the source is doing exactly what it always does. It's only the wavelength received by the observer that appears different, because of the relative motion between source and observer.
Applying this to light: redshift & blueshift
The Doppler effect works for electromagnetic radiation too. If we compare the absorption line spectrum of a distant galaxy to the spectrum of a nearby, "stationary" reference source (like our Sun), we can see whether the galaxy's lines have shifted:
- Redshift — spectral lines shift towards the red (longer wavelength) end → the galaxy is moving away from Earth.
- Blueshift — spectral lines shift towards the blue (shorter wavelength) end → the galaxy is moving towards Earth.
the universe is expanding
⚠️ Common mistake
Practice Question 1.1