The Doppler effect for light is the change in the observed wavelength and frequency of light when a source and observer move relative to each other. If a star or galaxy moves away, its light is stretched to longer wavelengths and looks redshifted. If it moves toward us, its light is compressed to shorter wavelengths and looks blueshifted.
This effect lets astronomers measure motion across enormous distances using only the light that reaches a telescope.
For light, the shift is detected by comparing known spectral lines from atoms with the same lines in light from space. A redshift means the lines move toward the red, longer-wavelength end of the spectrum, while a blueshift moves them toward the blue, shorter-wavelength end. For speeds much smaller than the speed of light, the fractional wavelength shift is approximately equal to the radial speed divided by the speed of light.
For very fast objects, the relativistic Doppler formula must be used because space and time effects become important.
Understanding Physics: The Doppler Effect for Light
Atoms provide the reference marks needed for this measurement. Electrons in an atom can move only between certain energy levels. When they change level, they absorb or emit light at very specific wavelengths.
This produces a pattern of dark or bright lines in a spectrum. Hydrogen, sodium, calcium, and other elements each have their own pattern. In a laboratory, scientists measure these patterns at rest.
In light from a distant object, they find the same pattern shifted by the same fraction. A whole pattern moving together is strong evidence of motion. A single line is less reliable because it could belong to a different element.
Only motion along the line of sight produces the ordinary Doppler shift. This component is called radial motion. A star can be moving very fast across the sky while producing little shift if its path is mostly sideways from Earth.
Its sideways motion must be measured in other ways, such as tracking its changing position against background stars over many years. Spectroscopy therefore gives one part of an object's motion, not always its full speed through space. This is an important limit when reading astronomy data.
For extremely high speeds, light behaves differently from sound because the speed of light has the same value for every observer in empty space. Relativity must then be included. A rapidly moving source has its time processes observed more slowly, which affects the light it emits.
The relativistic calculation combines this time effect with the change caused by motion toward or away from the observer. At lower speeds, the simpler estimate works well.
Students should first keep frequency and wavelength clear. When wavelength becomes longer, frequency becomes lower because the speed of light stays fixed in a vacuum.
Not every redshift comes from an object flying away through space. Light can be stretched while the universe expands during its journey. This cosmological redshift is one major piece of evidence that distant galaxies are generally receding as space expands.
Light can receive a gravitational redshift when it climbs away from a very strong gravitational field. Astronomers must decide which effect matters in each observation. Doppler shifts are useful closer to home too.
They reveal orbiting planets by the tiny back and forth motion they cause in their stars. They measure rotation in galaxies because one side can be shifted toward blue while the other shifts toward red. The key skill is comparing a measured spectrum with a trusted rest spectrum, then considering every physical cause of the displacement.
Key Facts
- Redshift means observed wavelength is longer: λobserved > λrest.
- Blueshift means observed wavelength is shorter: λobserved < λrest.
- Doppler shift in wavelength: z = (λobserved - λrest) / λrest.
- For low speeds compared with light: z ≈ v / c, where v is radial velocity.
- Speed of light in vacuum: c = 3.00 x 10^8 m/s.
- Light frequency and wavelength are related by c = fλ.
Vocabulary
- Doppler effect
- The change in observed frequency or wavelength caused by relative motion between a wave source and an observer.
- Redshift
- A shift of light toward longer wavelengths, usually caused by a source moving away from the observer or by cosmic expansion.
- Blueshift
- A shift of light toward shorter wavelengths, usually caused by a source moving toward the observer.
- Spectral line
- A bright or dark line at a specific wavelength that identifies an element or molecule in a light source.
- Radial velocity
- The part of an object's velocity directed along the line between the object and the observer.
Common Mistakes to Avoid
- Calling all red light redshift, which is wrong because redshift means a change from the original wavelength, not simply that the light is red.
- Forgetting that only radial motion causes a Doppler shift, which is wrong because motion sideways across the sky does not significantly compress or stretch the light waves along the line of sight.
- Using z ≈ v / c for objects moving near the speed of light, which is wrong because relativistic effects become important at high speeds.
- Confusing wavelength and frequency shifts, which is wrong because redshift increases wavelength but decreases frequency, while blueshift decreases wavelength but increases frequency.
Practice Questions
- 1 A hydrogen spectral line has a rest wavelength of 656.3 nm but is observed at 660.0 nm from a galaxy. Calculate the redshift z and estimate the galaxy's radial velocity using v ≈ zc.
- 2 A star is moving toward Earth at 90,000 m/s. Using z ≈ v / c with negative velocity for motion toward the observer, estimate the observed wavelength of a spectral line whose rest wavelength is 500.0 nm.
- 3 Two galaxies have identical spectral lines, but Galaxy A shows a larger redshift than Galaxy B. Explain what this tells you about their radial motion relative to Earth and why the spectral lines are useful evidence.