Doppler effect — redshift

What just happened?

The hydrogen absorption lines known from the lab (Hα, Hβ, …) sit at different positions in a star's spectrum than at rest. When the star recedes, the whole pattern of lines moves toward red; when it approaches — toward blue. This is the Doppler effect for light.

The formula for the Doppler shift:

— the relative change in wavelength equals the ratio of the radial velocity to the speed of light. $\Delta\lambda$ — change in wavelength, $\lambda$ — rest wavelength, $v$ — radial velocity, $c = 3\cdot10^5\,\mathrm{km/s}$.

The sign decides everything:

The direction of the shift depends solely on the sign of the radial velocity — not on the brightness or type of the star. By measuring $\Delta\lambda$ of a single line, we compute the velocity: $v = c\,\Delta\lambda/\lambda$. This is how we learn the motion of stars and galaxies whose movement we cannot "see" directly.

How does this differ from the Doppler effect for sound?

Sound needs a medium (air), and its shift depends separately on the motion of the source and of the observer relative to the medium. Light travels through a vacuum — only the relative radial velocity matters, and no medium is needed. For small $v \ll c$ both cases are described by the same simple formula $\Delta\lambda/\lambda = v/c$.

Why you need this for the exam:

Galaxy redshift is a cornerstone of cosmology — it ties in with Hubble's law ($v = H_0 d$): the farther a galaxy is, the faster it recedes and the larger its redshift. The trick: from the line shift compute $v$, and from Hubble's law — the distance.

Remember: redshift = receding, blueshift = approaching. The sign of the shift follows the sign of the radial velocity: Δλ/λ = v/c.