6.2.3 The Universe – Redshift of Light from Distant Galaxies
Learning Objective
Understand that the light emitted from distant galaxies appears redshifted when observed from Earth, and be able to explain why this occurs.
Key Concepts
Electromagnetic waves are characterised by their wavelength (\$\lambda\$) and frequency (\$f\$).
Redshift means an increase in wavelength (shift towards the red end of the spectrum).
The Doppler effect applies to light as well as sound.
In an expanding universe, most galaxies are moving away from us, causing their light to be redshifted.
Mathematical Description of Redshift
The redshift \$z\$ is defined as the fractional change in wavelength:
\$\$
z = \frac{\lambda{\text{observed}} - \lambda{\text{rest}}}{\lambda_{\text{rest}}}
\$\$
For velocities that are small compared with the speed of light (\$v \ll c\$), the Doppler approximation gives:
\$\$
v \approx c\,z
\$\$
where \$c = 3.00 \times 10^{8}\ \text{m s}^{-1}\$ is the speed of light.
Why Light from Distant Galaxies Is Redshifted
Expansion of Space: The universe is expanding, stretching the space through which light travels. This stretching increases the wavelength of the light.
Doppler Effect: Galaxies moving away from the observer cause the emitted light waves to be stretched, analogous to the lowering of pitch for a receding sound source.
Cosmological Redshift: At very large distances, the redshift is dominated by the expansion of the universe rather than simple motion through space.
Observational Evidence
Edwin Hubble’s observations in the 1920s showed a systematic increase in redshift with distance, leading to Hubble’s Law:
\$\$
v = H_0 d
\$\$
where \$H_0\$ is Hubble’s constant and \$d\$ is the distance to the galaxy.
Suggested diagram: A spectrum showing the shift of an absorption line from its laboratory (rest) wavelength to a longer (red) wavelength when observed from a distant galaxy.
Sample Data Table
Galaxy
Rest wavelength \$\lambda_{\text{rest}}\$ (nm)
Observed wavelength \$\lambda_{\text{obs}}\$ (nm)
Redshift \$z\$
Recessional velocity \$v\$ (km s\(^{-1}\))
Galaxy A
500.0
525.0
0.050
15,000
Galaxy B
500.0
560.0
0.120
36,000
Galaxy C
500.0
600.0
0.200
60,000
Implications of Redshift
Provides evidence for the expanding universe.
Allows astronomers to estimate distances to far‑away galaxies using Hubble’s Law.
Helps determine the age and size of the universe.
Supports the Big Bang model of cosmology.
Practice Questions
A spectral line has a rest wavelength of \$656.3\ \text{nm}\$ (H‑α). In the spectrum of a distant galaxy it appears at \$720.0\ \text{nm}\$. Calculate the redshift \$z\$ and the recessional velocity \$v\$ of the galaxy. (Use \$c = 3.00 \times 10^{5}\ \text{km s}^{-1}\$.)
Explain why the redshift of a galaxy is not caused by the galaxy moving through space at a constant speed, but rather by the expansion of space itself.
Given Hubble’s constant \$H_0 = 70\ \text{km s}^{-1}\text{Mpc}^{-1}\$, estimate the distance to a galaxy that has a measured redshift \$z = 0.05\$.