Point a telescope at almost any galaxy and its spectral-line barcode is slid towards the red. Not some galaxies — almost all of them. That one stubborn observation, plus a little Doppler physics, leads to one of the biggest conclusions in science: the universe is expanding.
📘 What you need to know
Redshift = the object is moving away from Earth: wavelength increases, frequency decreases
Blueshift = the object is moving towards Earth: wavelength decreases, frequency increases
Formally, redshift is the fractional increase in wavelength (or decrease in frequency) due to the source and observer receding from each other
Sign convention: observed frequency f0greater than the reference f → positive velocity → moving towards Earth; f0less than f → negative velocity → moving away
Almost all galaxies are redshifted → they are receding → the space between galaxies is expanding, stretching the light travelling through it
The greater the distance to a galaxy, the greater its redshift — so the furthest galaxies are receding the fastest
Red and Blue Shifts in the Sky
Everything from the last two pages now goes to work on the night sky. Compare the spectrum of a distant galaxy with a reference spectrum from a close, well-understood source — the Sun, or a lamp in the laboratory:
If the galaxy’s spectral lines sit at longer wavelengths than the reference, its light is redshifted — the galaxy is moving away from Earth (wavelength up, frequency down)
If the lines sit at shorter wavelengths, the light is blueshifted — the galaxy is moving towards Earth (wavelength down, frequency up)
The exam definition of redshift is worth learning word for word:
Redshift is the fractional increase in wavelength (or decrease in frequency) due to the source and observer receding from each other.
“Fractional” is doing real work there — redshift is the ratio Δλ/λ, so it’s a pure number with no units.
Positive and Negative Velocities
When you calculate a speed from Δf = f0 − f, the sign that pops out isn’t clutter — it’s the answer to “towards or away?”:
f0 > f
Δf positive
velocity positive
blueshift
moving TOWARDS Earth
f0 < f
Δf negative
velocity negative
redshift
moving AWAY — receding
An Expanding Universe
When astronomers surveyed the sky after discovering Doppler redshift, the result was startling: almost every galaxy is redshifted — almost everything is receding from us. The explanation isn’t that galaxies happen to be fleeing Earth; it’s that the space between the galaxies is expanding, and the expansion stretches the light waves as they travel through it, shifting them towards the red end of the spectrum.
The classic picture is dots on an inflating balloon:
Dots on an inflating balloon: as the rubber stretches, every dot moves away from every other dot — yet no dot moves across the rubber. In the same way, space itself stretches between galaxies; the galaxies themselves do not move through space.
The analogy carries three exam-ready points:
As the balloon inflates, the dots all move away from each other — there’s no special centre
The stretching rubber is like space itself stretching between galaxies
Just like the dots, the galaxies move apart, but they themselves do not move — the space between them grows
The Further, the Faster
One more observation seals the argument. Comparing spectra from galaxies at different distances shows that the greater the distance to a galaxy, the greater its redshift — and since a bigger redshift means a bigger recession speed, the furthest galaxies are receding the fastest. Exactly what you’d expect if all of space is expanding uniformly.
Redshift against distance for many galaxies: the points follow a straight line through the origin. Double the distance, double the redshift — the signature of uniformly expanding space.
🧭 Making the “expanding universe” argument in an exam
Observation 1: the spectral lines of almost all galaxies are shifted towards the red end — nearly every galaxy is receding
Observation 2: the greater the distance to a galaxy, the greater its redshift — the furthest galaxies recede fastest
Conclusion: the space between the galaxies must be expanding, stretching light waves in transit towards the red
Polish: add the balloon analogy — like dots on inflating rubber, galaxies separate without moving through space, and no galaxy is the centre
Quick recap: redshift (λ up, f down) = receding; blueshift = approaching. Nearly all galaxies are redshifted, and the further they are, the bigger the shift — evidence that space itself is expanding.
WE 1
A spectral line from a source in the laboratory has a frequency of 6.170 × 10¹⁴ Hz. The same line in the light from a distant galaxy is measured at 6.130 × 10¹⁴ Hz. Calculate the velocity of the galaxy relative to the Earth and state whether it is moving towards or away from the Earth.
Find the frequency shift (observed minus reference)Δf = f₀ − f = (6.130 − 6.170) × 10¹⁴ = −4.0 × 10¹² HzApply the Doppler equationv = cΔf/f = (3.0 × 10⁸ × −4.0 × 10¹²) ÷ (6.170 × 10¹⁴)v ≈ −1.9 × 10⁶ m s⁻¹Interpret the sign
The velocity is negative (the observed frequency is less than the reference), so the light is redshifted
the galaxy is receding at 1.9 × 10⁶ m s⁻¹
WE 2
State two observations about the light from distant galaxies and explain how they lead to the conclusion that the universe is expanding.
Observation 1
The spectral lines of almost all galaxies are redshifted compared with laboratory references — so almost all galaxies are moving away from Earth
Observation 2
The greater the distance to a galaxy, the greater its redshift — so more distant galaxies are receding faster
Conclusion
Both observations follow if the space between galaxies is expanding, stretching the light waves as they travel — like dots on an inflating balloon, every galaxy separates from every other without moving through space
the universe is expanding
💡 Top tips
Track the minus signs — they carry the physics: negative velocity (f₀ < f) means receding, positive means approaching
Redshift is a fraction (Δλ/λ), so it has no units — and the speed of light is in the data booklet
When using the balloon analogy, say “space itself expands” and “the galaxies do not move through space” — those are the phrases mark schemes reward
The redshift–distance graph is a straight line through the origin — worth sketching in a written answer about the expanding universe
⚠ Common mistakes
Explaining redshift as galaxies “flying through space away from Earth” — the modern picture is space between galaxies expanding
Concluding that Earth must be at the centre of the universe — on the balloon, every dot sees all the others receding; there is no centre
Mixing up the sign convention — a higher observed frequency means positive velocity and motion towards Earth
Confusing the redshift (the unitless fraction Δλ/λ) with the raw shift Δλ itself
And that completes the Doppler Effect — from squashed wavefronts, through Δλ/λ ≈ v/c, to the expanding universe. These same ideas come straight back whenever spectra, stars, or moving sources appear in an exam question.
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