Doppler Effect for Light

The Doppler effect for light is a change in the observed wavelength and frequency of light caused by relative motion between a light source and an observer.

For light:

source moving away → longer observed wavelength → redshift

source moving toward observer → shorter observed wavelength → blueshift

Astronomers use these wavelength shifts to measure the motion of stars and galaxies. Redshift also provides some of the most important observational evidence that the universe is expanding.

---

Light as an Electromagnetic Wave

Light is an electromagnetic wave.

Unlike sound, light does not require a material medium and can travel through a vacuum.

In a vacuum, all electromagnetic waves travel at:

c ≈ 3.00 × 10⁸ m/s

The relationship between speed, frequency, and wavelength is:

c = fλ

where:

c = speed of light

f = frequency

λ = wavelength

Therefore, frequency and wavelength are inversely related.

longer wavelength → lower frequency

shorter wavelength → higher frequency

---

Relative Motion and Light

Suppose a star and an observer are moving relative to one another.

If their separation is increasing, the observed light is shifted toward:

longer wavelengths

If their separation is decreasing, the observed light is shifted toward:

shorter wavelengths

These shifts are called:

redshift and blueshift

---

Redshift

Redshift occurs when observed light is shifted toward longer wavelengths.

For motion-related Doppler redshift, this occurs when a light source is:

moving away from the observer

The name comes from the visible spectrum, where red light has a longer wavelength than blue light.

Therefore:

receding source → wavelength increases → redshift

---

Blueshift

Blueshift occurs when observed light is shifted toward shorter wavelengths.

For Doppler motion, this occurs when the source moves:

toward the observer

Therefore:

approaching source → wavelength decreases → blueshift

Blue and violet light have shorter wavelengths than red light.

The term "blueshift" therefore describes a shift toward the shorter-wavelength end of the visible spectrum.

---

Redshift and Blueshift Compared

A useful memory rule is:

away → red

toward → blue

---

Does a Redshifted Star Actually Look Red?

Not necessarily.

Astronomers usually do not determine redshift simply by looking at the apparent colour of a star or galaxy.

Instead, they examine its:

spectrum

and look for recognizable spectral lines.

The positions of these lines can be measured extremely precisely.

---

Spectral Lines

Atoms and ions absorb or emit light at specific wavelengths.

These wavelengths produce recognizable patterns called:

spectral lines

Different elements have characteristic sets of spectral lines.

Examples include:

• hydrogen
• helium
• sodium
• calcium

These patterns act somewhat like fingerprints.

If astronomers know where a particular line should normally appear, they can compare it with where the line appears in light from a moving astronomical object.

---

Measuring Redshift

Suppose a particular spectral line has a laboratory wavelength:

λ_rest = 500 nm

Astronomers observe the same identifiable line from a galaxy at:

λ_observed = 510 nm

The observed wavelength is longer.

Therefore, the line has shifted toward the red end of the spectrum.

The galaxy has:

redshift

For motion-related redshift, this indicates recession.

---

Measuring Blueshift

Suppose the same spectral line normally occurs at:

500 nm

but astronomers observe it at:

495 nm

The observed wavelength is shorter.

Therefore:

blueshift

This indicates motion toward the observer when the shift is caused by relative motion.

---

Rest Wavelength

The wavelength measured when there is no relative Doppler motion between source and observer is called the:

rest wavelength

It is often written:

λ₀

Astronomers compare the observed wavelength with this known value.

If:

λ_observed > λ₀

there is redshift.

If:

λ_observed < λ₀

there is blueshift.

---

Change in Wavelength

The wavelength change can be calculated using:

Δλ = λ_observed − λ₀

If Δλ is positive:

redshift

If Δλ is negative:

blueshift

This provides a simple numerical way to identify the direction of the shift.

---

Redshift Parameter

Astronomers often describe redshift using the quantity:

z = (λ_observed − λ₀)/λ₀

or:

z = Δλ/λ₀

The quantity z has no units.

If:

z > 0

the light is redshifted.

If:

z < 0

the light is blueshifted.

---

Worked Example: Calculating Redshift

A spectral line has a rest wavelength:

λ₀ = 600 nm

It is observed at:

λ_observed = 606 nm

First calculate:

Δλ = 606 − 600

Δλ = 6 nm

Then:

z = 6/600

z = 0.010

The positive value indicates:

redshift

---

Doppler Speed for Small Velocities

When an object's speed is much smaller than the speed of light, a useful approximation is:

v/c ≈ Δλ/λ₀

or:

v ≈ cz

This approximation works well for relatively small Doppler shifts.

It should not be used blindly for objects moving at speeds approaching the speed of light or for interpreting large cosmological redshifts.

---

Worked Example: Estimating Stellar Speed

Suppose:

z = 0.001

Using:

v ≈ cz

and:

c = 3.00 × 10⁸ m/s

v ≈ (3.00 × 10⁸)(0.001)

v ≈ 3.00 × 10⁵ m/s

or:

300 km/s

Because z is positive, this motion-related shift indicates recession.

---

Stellar Motion

Astronomers can use Doppler shifts to determine the radial velocity of stars.

Radial velocity means motion:

toward or away from the observer

If spectral lines are blueshifted:

star moving toward us

If spectral lines are redshifted:

star moving away from us

The greater the shift, the greater the radial speed in the simple low-speed Doppler model.

---

Radial vs Sideways Motion

The Doppler effect primarily reveals motion along the line of sight.

Imagine a star moving directly sideways across the sky.

Its distance from Earth may not be changing significantly at that instant.

Therefore, it may have:

little or no radial Doppler shift

Astronomers use other measurements to study sideways motion.

Thus, Doppler measurements reveal:

radial velocity

not necessarily the object's total velocity through space.

---

Measuring Stellar Motion

A simplified astronomical procedure is:

1. Collect light from the star with a telescope.
2. Separate the light into a spectrum.
3. Identify known spectral lines.
4. Measure their observed wavelengths.
5. Compare them with laboratory rest wavelengths.
6. Determine whether the lines are redshifted or blueshifted.
7. Calculate the size of the shift.
8. Use the shift to estimate radial velocity.

This allows motion to be measured even though the star may be trillions of kilometres away.

---

Detecting Binary Stars

Many stars orbit another star.

As one star moves around the system, it may alternately move:

toward Earth

and:

away from Earth

Its spectral lines therefore shift periodically:

blueshift → redshift → blueshift → redshift

This repeating pattern can reveal orbital motion.

Some binary systems can be detected this way even when telescopes cannot visually separate the two stars.

---

Detecting Exoplanets

A similar technique can help detect planets around other stars.

A planet does not simply orbit a perfectly stationary star.

The planet and star both orbit their common centre of mass.

As a result, the star makes a small repeating motion.

At one part of its motion:

star moves slightly toward Earth → blueshift

At another:

star moves slightly away → redshift

---

The Radial Velocity Method

Astronomers measure the repeating shifts in the star's spectrum.

The pattern can provide information about:

• orbital period
• radial velocity of the star
• evidence for an orbiting planet
• a minimum estimate related to the planet's mass when combined with other information

This technique is called the:

radial velocity method

It has been extremely important in the discovery and study of exoplanets.

---

Redshift of Galaxies

When astronomers examine the spectra of many distant galaxies, they commonly find that their spectral features are shifted toward:

longer wavelengths

In other words, many distant galaxies show:

redshift

The systematic relationship between galaxy distance and redshift played a major role in establishing that the universe is expanding.

---

Hubble's Observations

In the early twentieth century, observations showed an important relationship between galaxy distance and recession.

In the nearby universe, the relationship is approximately:

v = H₀d

where:

v = recession velocity

H₀ = Hubble constant

d = distance

This is known as the:

Hubble–Lemaître law

It indicates that more distant galaxies generally recede faster.

---

What Does an Expanding Universe Mean?

The expansion of the universe should not simply be pictured as galaxies flying outward from one central explosion point into empty space.

On large scales, it is better described as:

space itself expanding

As the universe expands, distances between widely separated, gravitationally unbound galaxies increase.

This expansion also stretches the wavelengths of light travelling through space.

The resulting wavelength increase is called:

cosmological redshift

---

Cosmological Redshift

For nearby objects and relatively small velocities, Doppler language provides a useful introduction.

However, the redshift of very distant galaxies is more accurately described as:

cosmological redshift

As the universe expands while light travels through it, the wavelength of the light is stretched.

Therefore:

expansion of space → wavelength increases → cosmological redshift

This is related to, but not exactly the same physical situation as, the ordinary Doppler effect from a source moving through space.

---

A Useful Expansion Model

Imagine dots drawn on the surface of an expanding balloon.

As the balloon expands:

• distances between dots increase
• each dot sees other distant dots moving farther away
• there is no special central dot on the two-dimensional surface

This can help visualize cosmic expansion.

However, the balloon is only an analogy.

The universe is not necessarily expanding into a larger surrounding space in the way a balloon expands into a room.

---

Redshift and Distance

For relatively nearby galaxies following the Hubble flow:

greater distance → generally greater redshift

This does not mean every individual galaxy follows the relationship perfectly.

Galaxies also have local motions caused by gravity.

These are sometimes called:

peculiar velocities

For nearby galaxies, these local motions can noticeably affect the observed redshift or blueshift.

---

A Nearby Blueshifted Galaxy

Not every galaxy is redshifted.

Some nearby galaxies can move toward us because local gravitational motion is stronger than the expansion effect over that distance.

Such galaxies can show:

blueshift

This does not contradict the overall expansion of the universe.

The expansion relationship applies to the large-scale pattern.

---

Redshift as Evidence for Cosmic Expansion

Astronomers observe redshift in the spectra of large numbers of distant galaxies.

The general pattern is:

more distant galaxy → greater cosmological redshift

This supports the conclusion that the universe is expanding.

Redshift therefore provides important evidence for modern cosmological models.

It is not the only evidence, but it is one of the foundational observations.

---

Sound and Light: An Important Similarity

Both sound and light can show Doppler shifts.

For both:

approaching → higher observed frequency

receding → lower observed frequency

For sound:

higher frequency → higher pitch

lower frequency → lower pitch

For visible light:

higher frequency / shorter wavelength → blueshift

lower frequency / longer wavelength → redshift

---

Sound and Light: An Important Difference

Sound is a:

mechanical wave

It requires a medium such as:

• air
• water
• solids

Light is an:

electromagnetic wave

It does not require a material medium and can travel through a vacuum.

This makes the physics of their Doppler effects different in important ways.

---

Moving Sources and Sound

For sound in still air, the medium provides a reference frame.

A moving sound source changes the spacing of wavefronts in the air.

Ahead:

compressed

Behind:

stretched

A moving observer instead changes how rapidly they encounter those wavefronts.

Therefore, moving-source and moving-observer cases have different classical sound equations.

---

Light Does Not Need a Medium

There is no equivalent stationary "light medium" like air for sound.

The speed of light in a vacuum is:

c

for all inertial observers.

Therefore, the Doppler effect for light must be described consistently with:

special relativity

At low relative speeds, the results resemble the familiar approaching/receding pattern from sound.

At speeds approaching c, relativistic effects become essential.

---

Comparing Sound and Light

---

Frequency and Wavelength for Light

Because:

c = fλ

frequency and wavelength change in opposite directions.

For blueshift:

λ decreases

f increases

For redshift:

λ increases

f decreases

This is why redshift and blueshift can be described using either wavelength or frequency.

Astronomers commonly express the shift using wavelength.

---

Example: Predicting a Shift

A star is moving toward Earth.

No calculation is required.

Step 1:

Source is approaching.

Step 2:

Observed frequency increases.

Step 3:

Observed wavelength decreases.

Step 4:

The spectral lines move toward shorter wavelengths.

Therefore:

blueshift

---

Example: Receding Galaxy

A galaxy is receding.

Step 1:

Separation increases.

Step 2:

Observed wavelength becomes longer.

Step 3:

Spectral features move toward the red end of the spectrum.

Therefore:

redshift

For a distant galaxy participating in cosmic expansion, the more precise explanation is usually:

cosmological redshift

---

Worked Example: Identify the Motion

A hydrogen spectral line has a rest wavelength of:

656.3 nm

It is observed from a star at:

656.8 nm

Since:

656.8 nm > 656.3 nm

the wavelength has increased.

Therefore:

redshift

The star has a radial component of motion:

away from the observer

if the shift is interpreted as an ordinary motion-related Doppler shift.

---

Worked Example: Blueshift

A spectral line normally occurs at:

500.0 nm

It is observed at:

499.5 nm

Calculate:

Δλ = 499.5 − 500.0

Δλ = −0.5 nm

The negative change means the wavelength has decreased.

Therefore:

blueshift

The source is approaching along the line of sight.

---

Worked Example: Redshift Parameter

A galaxy has a spectral line with:

λ₀ = 400 nm

Observed wavelength:

λ_observed = 440 nm

Then:

z = (440 − 400)/400

z = 40/400

z = 0.10

The light is strongly redshifted.

For a shift this substantial, treating v = cz as an exact ordinary velocity relationship would not be appropriate.

---

Why Astronomers Use Spectra

A galaxy's overall colour can depend on many factors, including:

• types of stars present
• temperature
• dust
• star formation
• chemical composition

Therefore, simply saying:

"That galaxy looks red, so it must be moving away"

would be unreliable.

Spectral lines provide identifiable wavelength markers.

Astronomers measure how these markers have shifted.

---

Spectroscopy

Spectroscopy is the study of spectra.

A spectroscope or spectrometer separates incoming light according to wavelength.

Spectroscopy can provide information about:

• chemical composition
• temperature
• motion
• density
• magnetic fields
• other physical conditions

Doppler shifts are therefore part of a much larger set of information contained in light.

---

Redshift Is Not Always Caused by Motion

It is important not to assume that every redshift has exactly the same cause.

Three important types include:

Doppler redshift

Associated with relative motion.

Cosmological redshift

Associated with the expansion of the universe.

Gravitational redshift

Associated with light moving through gravitational fields.

At this level, Doppler and cosmological redshift are the most important to distinguish.

---

Doppler Effect and the Expanding Universe

A useful progression is:

individual star

Doppler shift can reveal radial motion.

nearby galaxy

Spectral shift can reveal motion relative to us, including local gravitational motion.

distant galaxy

Large-scale redshift is interpreted in the context of cosmic expansion.

This prevents the oversimplification that all astronomical redshift is simply an ordinary source moving through stationary space.

---

Why Redshift Is So Useful

Astronomers cannot usually travel to stars or galaxies and directly measure their motion.

Instead, they analyze the light that reaches Earth.

From tiny shifts in wavelength, they can investigate:

• stellar velocities
• binary stars
• exoplanets
• galaxy motion
• galaxy clusters
• expansion of the universe

The wave properties of light therefore allow scientists to measure motion across enormous distances.

---

A Complete Stellar Example

A star produces hydrogen absorption lines.

One known line has:

λ₀ = 500 nm

Astronomers measure it at:

λ_observed = 501 nm

Since:

501 > 500

the wavelength has increased.

Therefore:

redshift

Calculate:

Δλ = 501 − 500

Δλ = 1 nm

Then:

z = 1/500

z = 0.002

For a relatively small shift:

v ≈ cz

v ≈ (3.00 × 10⁸)(0.002)

v ≈ 6.00 × 10⁵ m/s

or:

600 km/s

The positive motion-related shift indicates recession along the line of sight.

---

A Complete Universe Example

Astronomers observe many distant galaxies.

They identify known spectral lines.

Most of these distant galaxies show:

redshift

Furthermore, galaxies at greater distances generally show greater cosmological redshift.

This reveals a large-scale pattern in which distances between widely separated galaxies increase with time.

The evidence supports:

an expanding universe

The wavelength of light travelling across expanding space is also stretched.

---

A Reliable Strategy for Redshift and Blueshift Questions

1. Identify the rest wavelength.
2. Identify the observed wavelength.
3. Compare them.
4. If observed wavelength is longer, identify redshift.
5. If observed wavelength is shorter, identify blueshift.
6. For ordinary Doppler motion, redshift indicates recession.
7. For ordinary Doppler motion, blueshift indicates approach.
8. Calculate Δλ if required.
9. Calculate z if required.
10. For small Doppler shifts, use v ≈ cz if appropriate.
11. Identify whether the question concerns a star, nearby galaxy, or cosmological expansion.
12. Do not assume every redshift is simply an ordinary Doppler shift.
13. Interpret the result in terms of radial motion or cosmic expansion as appropriate.

---

Common Mistakes

Thinking redshift means an object simply looks red

Astronomers usually measure shifts in spectral lines.

Thinking blueshift means a star must look blue

Blueshift refers to wavelengths shifting toward shorter values, not necessarily the overall visible colour.

Reversing redshift and blueshift

Away → redshift. Toward → blueshift.

Thinking wavelength and frequency both increase

Because c = fλ, increasing wavelength corresponds to decreasing frequency in vacuum.

Thinking Doppler measurements reveal all of an object's motion

They primarily reveal radial motion along the line of sight.

Thinking sound and light require the same medium

Sound requires a material medium. Light does not.

Thinking light behaves exactly like sound for moving sources

The qualitative approaching/receding pattern is similar, but the detailed physics of light requires relativity.

Using v = cz for every redshift

This is a useful low-redshift approximation, not a universal velocity equation.

Thinking all astronomical redshift has exactly the same cause

Doppler, cosmological, and gravitational redshifts are distinct phenomena.

Thinking galaxies are simply flying outward from one central point

Cosmic expansion is better understood as increasing distances caused by the expansion of space on large scales.

---

Key Terms

Doppler effect — change in observed frequency or wavelength associated with relative motion.

Electromagnetic wave — oscillating electric and magnetic fields capable of travelling through a vacuum.

Redshift — shift of observed light toward longer wavelengths.

Blueshift — shift of observed light toward shorter wavelengths.

Rest wavelength (λ₀) — wavelength measured without the relevant Doppler shift.

Observed wavelength — wavelength measured by the observer.

Spectral line — identifiable wavelength feature produced by emission or absorption.

Spectrum — distribution of electromagnetic radiation according to wavelength or frequency.

Spectroscopy — study and measurement of spectra.

Radial velocity — component of velocity toward or away from an observer.

Redshift parameter (z) — fractional change in wavelength, z = Δλ/λ₀.

Hubble–Lemaître law — approximate relationship between distance and recession rate for galaxies in the nearby expanding universe.

Hubble constant (H₀) — proportionality constant in the Hubble–Lemaître relationship.

Cosmological redshift — increase in observed wavelength associated with the expansion of the universe while light travels through space.

Gravitational redshift — wavelength increase associated with gravitational effects.

Binary star — system containing two stars orbiting a common centre of mass.

Exoplanet — planet orbiting a star outside our Solar System.

Radial velocity method — technique that detects periodic stellar spectral shifts caused by orbital motion associated with an orbiting companion.

---

Key Takeaways

• Light can undergo a Doppler shift.
• Light approaching an observer is shifted toward shorter wavelengths.
• Shorter-wavelength motion-related shifts are called blueshift.
• Light from a receding source is shifted toward longer wavelengths.
• Longer-wavelength motion-related shifts are called redshift.
• Blueshift corresponds to higher observed frequency.
• Redshift corresponds to lower observed frequency.
• Astronomers usually measure shifts in spectral lines rather than simply looking at an object's colour.
• Spectral lines provide known wavelength markers.
• Comparing observed and rest wavelengths reveals the direction of a shift.
• Redshift can indicate radial motion away from an observer.
• Blueshift can indicate radial motion toward an observer.
• Doppler measurements primarily reveal radial velocity rather than total space velocity.
• Repeating redshift and blueshift can reveal orbital motion.
• The radial velocity method can help detect exoplanets.
• Most sufficiently distant galaxies show cosmological redshift.
• Greater distance is generally associated with greater cosmological redshift on large scales.
• These observations support the conclusion that the universe is expanding.
• Cosmic expansion is better described as the expansion of space rather than galaxies exploding outward from a central point.
• Cosmological redshift is related to but physically distinct from the simple classical Doppler effect.
• Sound requires a material medium, while light does not.
• Both sound and light show higher observed frequency for approach and lower observed frequency for recession.
• Sound Doppler shifts can be heard as pitch changes.
• Light Doppler shifts are measured as changes in wavelength or frequency.
• Precise light Doppler physics at high relative speeds requires special relativity.
• Understanding redshift allows astronomers to investigate motion and the structure and evolution of the universe.

---

Check Your Understanding

1. Define redshift and blueshift.
2. A star is moving toward Earth. Predict whether its spectral lines will be redshifted or blueshifted.
3. A galaxy's spectral lines are shifted toward longer wavelengths. What type of shift has occurred?
4. Explain the relationship between wavelength and frequency for light using c = fλ.
5. A spectral line has a rest wavelength of 500 nm but is observed at 505 nm. Identify the shift and describe the motion it would indicate if caused by the ordinary Doppler effect.
6. A spectral line normally occurs at 650 nm but is observed at 648 nm. Is this redshift or blueshift? What does it indicate about radial motion?
7. Calculate the redshift parameter z for a line with λ₀ = 600 nm and λ_observed = 603 nm.
8. Explain how astronomers use spectral lines to determine whether a star is moving toward or away from Earth.
9. Why is simply looking at whether a galaxy appears red or blue not a reliable method for measuring Doppler shift?
10. Explain what radial velocity means and why Doppler measurements do not necessarily reveal an object's complete velocity through space.
11. Describe how repeating redshift and blueshift of a star can provide evidence for an orbiting planet.
12. Explain how observations of distant galaxy redshifts support the idea that the universe is expanding.
13. Distinguish between an ordinary Doppler redshift and cosmological redshift.
14. Compare the Doppler effect for sound and light. Include at least two similarities and two differences.
15. A student says, "Distant galaxies are redshifted because they are all flying through space away from one central point, exactly like the lower pitch of an ambulance driving away." Evaluate this statement. Explain what the analogy gets right, what it oversimplifies, and how cosmic expansion provides a more accurate description.