Physics HL · Chapter 16: The Doppler Effect
16.2 The Doppler Effect for Light and Red-Shift
Apply low-speed approximate Doppler relations for light, connect sign interpretation to red/blue shift, and read astrophysical motion from spectral data.
Estimated time: 34 minutes
Approximate Light-Shift Relations for Small Speeds
When relative speed is small compared with c, light Doppler shifts can be handled with approximate fractional relations. These are accurate enough for many IB-style problems where spectral lines shift modestly relative to their emitted wavelengths.
rac{Delta f}{f}approx - rac{v}{c},qquad rac{Delta lambda}{lambda}approx rac{v}{c}
Positive radial speed (receding source) lowers frequency and increases wavelength.
These two expressions carry the same information because c = flambda. If wavelength increases by a small fraction, frequency decreases by roughly the same fraction. Keeping both forms available lets you match whichever quantity the question gives directly.
Blue-Shift and Red-Shift Language
If observed wavelength is shorter than emitted wavelength, the light is blue-shifted and the source has an approaching radial component. If observed wavelength is longer than emitted wavelength, the light is red-shifted and the source has a receding radial component.
Always state what is deduced precisely: Doppler shift gives information about radial velocity component, not total three-dimensional velocity. A source can have substantial sideways velocity and still show little shift if radial motion is small.
Astrophysical Use and Validity Limits
Measured red-shifts from many galaxies are interpreted as increasing source-observer separation and are a key observational pillar for expansion models. In this chapter we keep the low-speed approximation as the working tool. At larger fractions of c, full relativistic Doppler treatment is required.
Simulation: Red-Shift and Blue-Shift Spectrum Explorer
Set emitted wavelength and radial velocity, then observe shifted spectrum position and approximate fractional-shift calculations.
Doppler Effect Lab
Shift type
Red-shift (receding)
Fractional shift (v/c)
0.050035
Observed wavelength
689.14 nm
Observed frequency
4.35e+14 Hz
Visible-spectrum shift view
Test Yourself
Hydrogen light emitted at 656 nm is observed at 689 nm. Using the low-speed approximation, enter the source speed in km/s.
Hint: Use v/c ~ delta lambda / lambda with c = 3.00 x 10^8 m/s.