The Doppler Effect for Light: Redshift

Light is a wave: it too undergoes the Doppler effect. But here, we do not reason in terms of pitch, but of color, that is, wavelength λ. A source moving away has its light shifted toward long wavelengths — the red — and a source moving closer toward short ones — the blue.

   reference spectrum      |B|...|V|...|R|
   receding source         |B|...|V|...|R| ->   (lines shifted toward the red)
   approaching source   <-  |B|...|V|...|R|     (lines shifted toward the blue)

This shift is quantified by the redshift z, the relative change in wavelength. For speeds small compared with the speed of light c:

   z = Δλ / λ ≈ v / c        (v = recession speed, c = 3 x 10^8 m/s)

A shift toward the red (z > 0) signals recession; toward the blue (z < 0), approach. The astronomers' trick: atoms emit lines at known, fixed wavelengths. By spotting how far these characteristic lines are shifted in the spectrum of a star or a galaxy, we directly read its speed along the line of sight.

   line known at λ₀   ->  observed at λ = λ₀ + Δλ   ->  v = c · Δλ / λ₀

Thus, without ever going there, we measure the speed of objects billions of kilometers away. Light carries, encoded in the shift of its lines, information about its own motion.