The big idea: Split the light from a distant galaxy through a spectrometer and the familiar spectral lines sit further toward the red end than the same lines measured in a lab — the galaxy is racing away from us. This wavelength change from a moving light source is the Doppler effect for light.
Moving away → wavelength looks longer (toward the red end) → a redshift.
Moving toward you → wavelength looks shorter (toward the blue end) → a blueshift.
New words — redshift and blueshift: Wavelength (λ) is the length of one wave; red light has a long wavelength, blue light a short one.
Redshift = the wavelength is stretched longer (source receding).
Blueshift = the wavelength is squashed shorter (source approaching).
Redshift — source RECEDING
- Moving away from you
- Wavelength stretched longer
- Shifted toward the red end
- Δλ is positive (λ goes up)
Blueshift — source APPROACHING
- Moving toward you
- Wavelength squashed shorter
- Shifted toward the blue end
- Δλ is negative (λ goes down)
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Spot it: Red = Receding (away, longer λ). Blue = approaching (toward, shorter λ).
The bigger the shift, the faster the source is moving.
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For a source moving much slower than light, the fraction the wavelength shifts by equals the fraction the frequency shifts by, and both equal v ÷ c. This is given in the data booklet.
- change in wavelength, observed − lab (m) — written Δλ
- the source's true (laboratory) wavelength (m)
- change in frequency, observed − lab (Hz) — written Δf
- the source's true (laboratory) frequency (Hz)
- speed of the source toward or away from us (m s⁻¹)
- the speed of light, 3.0 × 10⁸ m s⁻¹
How to read it: Δλ/λ is the fraction by which the wavelength has shifted (e.g. 0.001 = 0.1%).
That fraction equals v/c — the source's speed as a fraction of the speed of light.
So a tiny shift means a small speed; a big shift means a big speed.
Rearranged: Δλ = (v/c) × λ. Cover the one you want — two side by side → multiply; one above the other → divide. To find v: v = (Δλ ÷ λ) × c.
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A spectral line that is 600.0 nm in the laboratory is seen at 600.3 nm in the light from a star. Find the star's speed, and state whether it is moving toward or away from us.
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How this is tested — light Doppler is almost always astronomical:
Paper 2 — explain
- Why a line from the approaching edge of a rotating star/Sun is at a shorter wavelength (blueshift), and the receding edge at a longer one.
Paper 2 — calculate
- Use Δλ/λ = v/c to find the speed of a star, a galaxy, or a rotating star's edge from the measured shift.
The classic trap: Δλ is the change (observed − lab), not the whole wavelength — divide the small change by the original λ.
A rotating star has BOTH shifts at once: One edge of a spinning star turns toward us (that edge is blueshifted, shorter λ); the other edge turns away (redshifted, longer λ). The edge speed v is the star's rotation speed at its surface.
A line that is 656.00 nm in the laboratory is observed at 655.87 nm in light from one edge of a rotating star. Explain whether that edge is approaching or receding, and calculate the speed of that edge.
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