C.5 · IB Physics
Doppler effect for light and redshift
Hydrogen absorbs the same visible wavelengths everywhere in the Universe. Compare the laboratory spectrum with that of a moving source: a receding source is redshifted, an approaching one blueshifted. Match the spectra of three mystery objects.
Predict first
Start from the default velocity of +15 000 km s⁻¹. If you double it to +30 000 km s⁻¹, what happens to the redshift z?
For v ≪ c, z = Δλ ÷ λ₀ = v ÷ c, so z is proportional to v. Doubling v doubles z (0.05 to 0.10).
Check it in the model: Move the Velocity of source v slider from +15 000 to +30 000 km s⁻¹ and compare the Redshift z readout.
z = Δλ ÷ λ₀ , λ(obs) = λ₀ (1 + z)
Δf ÷ f₀ = −z ÷ (1 + z) ≈ −v ÷ c
c = 3.00 × 10⁸ m s⁻¹
- Redshift z = Δλ ÷ λ₀
- Hα observed (λ₀ = 656.3 nm)
- Shift Δλ of Hα
- Frequency change of Hα
- Speed v ÷ c
- z from relativistic Doppler
- Hα: slider minus object
Try this
- Start at v = +15 000 km s⁻¹ and note the shift of Hα. Double v to +30 000 km s⁻¹. Compare the shifts of Hα and Hδ in the graph: which line moves further, and what stays the same?
- Choose Galaxy A and move the speed slider until the “Hα: slider minus object” readout is close to zero. What is the galaxy’s speed, and is it moving away or towards us?
- Set v = −20 000 km s⁻¹ (approaching). What happens to the observed wavelength and the frequency of Hα, and what sign does the shift Δλ have?
Common error: thinking every line moves by the same number of nanometres; the shift is a fixed fraction z of each wavelength, so the 656 nm line moves further than the 410 nm line, and “redshift” only means shifted towards longer wavelengths.