# Maxwell, Electromagnetic Waves and Spectra

> How Maxwell showed light is an electromagnetic wave, how the speed of light was measured, and what spectra tell us about stars.

From HSC Physics on WhizzNotes, free study notes for NSW students: https://whizznotes.com/physics/electromagnetic-waves/. Updated 2 November 2026.
Year 11 and Year 12 boxes go deeper than the Year 10 text around them.

### Story time: A number that gave the game away
In the 1860s, James Clerk Maxwell was writing equations for electricity and magnetism. Nothing to do with light, he thought. His maths said that a wiggling electric field should make a wiggling magnetic field, which should make another electric field, and so on, rippling out through space as a wave.

So he calculated how fast this wave should travel. He used two numbers measured in labs with magnets and charged plates. The answer came out at about 300 000 kilometres per second.

That was the speed of light, already measured by others. Maxwell wrote that light itself must be one of these waves. A whole branch of physics, light and optics, suddenly joined up with electricity and magnetism.

**In short:** Maxwell showed that electricity and magnetism are linked and predicted electromagnetic waves travelling at the speed of light, so light itself is an electromagnetic wave. The spectra of light from stars show their temperature, what they are made of and how they move.

## Maxwell's big idea

Before Maxwell, electricity, magnetism and light were thought of as separate topics. Maxwell **unified** electricity and magnetism with four equations. From them he predicted:

1. A changing electric field makes a magnetic field, and a changing magnetic field makes an electric field.
2. Together these can travel through empty space as an **electromagnetic (EM) wave**, with the two fields at **right angles** to each other and to the direction of travel.
3. These waves are made by **accelerating (oscillating) charges**.
4. They all travel at the same speed in a vacuum:

$$c = \frac{1}{\sqrt{\mu_0\varepsilon_0}} = 3.00 \times 10^8 \text{ m/s}$$

where $\mu_0$ and $\varepsilon_0$ are constants measured from magnetism and electricity.

5. Light is one of these waves, and there should be others with wavelengths we cannot see.

## Hertz proves it

In 1887, Heinrich Hertz used a spark gap to make charges oscillate rapidly. A small loop of wire across the room sparked too, so invisible waves had crossed the gap. He showed they **reflected, refracted, interfered and could be polarised**, just like light, and he measured their speed: the speed of light. These were the first **radio waves**, and they confirmed Maxwell's prediction.

## The electromagnetic spectrum

All EM waves travel at $c$ in a vacuum and obey the wave equation:

$$c = f\lambda$$

From longest wavelength (lowest frequency, lowest energy) to shortest: **radio, microwaves, infrared, visible, ultraviolet, X-rays, gamma rays**.

## Measuring the speed of light

| Who | Method |
|---|---|
| **Fizeau** (1849) | Shone light through the gaps of a fast-spinning toothed wheel to a mirror 8 km away and back. At the right speed, the returning light hit a tooth and was blocked. The time for one gap to be replaced by a tooth equals the round trip time. |
| **Foucault** (1850) | Used a rotating mirror. The mirror turned slightly while the light travelled to a distant mirror and back, so the returning beam was shifted. He also found light is **slower in water** than in air. |

### Worked example: Fizeau's wheel
A wheel with 100 teeth (and 100 gaps) sits 5.0 km from a mirror. Light is first blocked when the wheel turns at 150 revolutions per second.

- Round trip: $2 \times 5000 = 10\,000$ m.
- Moving from the middle of a gap to the middle of the next tooth is $\frac{1}{200}$ of a turn, which takes $\frac{1}{200 \times 150} = 3.3 \times 10^{-5}$ s.
- Speed: $c = 10\,000 \div 3.3 \times 10^{-5} = 3.0 \times 10^8$ m/s.

## Three kinds of spectra

A **spectroscope** spreads light into its colours using a prism or a diffraction grating.

| Spectrum | Looks like | Made by |
|---|---|---|
| **Continuous** | All colours, no gaps | Hot dense objects: a glowing filament, a star's surface |
| **Emission** (line) | Bright coloured lines on a dark background | Hot thin gas, such as a gas discharge tube |
| **Absorption** | Continuous spectrum with dark lines | Cooler gas in front of a hot source, such as a star's outer layers |

Each element makes its own pattern of lines, like a barcode. The dark lines in an absorption spectrum are at **exactly the same wavelengths** as the bright lines in that element's emission spectrum.

## What starlight tells us

By looking carefully at a star's spectrum, astronomers can find its:

- **Surface temperature**: from the colour and the peak wavelength (see Light: the Quantum Model).
- **Chemical composition**: from the absorption lines, matched to elements.
- **Translational velocity** (moving towards or away from us): all the lines are shifted. Shifted to longer wavelengths (**redshift**) means moving away. Shifted to shorter wavelengths (**blueshift**) means moving towards us.
- **Rotational velocity**: one side of a spinning star comes towards us and the other moves away, so each line is spread out (**broadened**). Faster spin, broader lines.
- **Density**: denser stars, with higher pressure in their atmospheres, have broader lines.

**Mind map**

```text
Electromagnetic Waves
  Maxwell
    Unified electricity and magnetism
    Predicted EM waves
    c = 1 / √(μ₀ε₀)
    Light is an EM wave
  Hertz
    Made radio waves
    Same speed as light
  Speed of light
    Fizeau: toothed wheel
    Foucault: rotating mirror
    c = fλ
  Spectra
    Continuous
    Emission lines
    Absorption lines
  Starlight
    Temperature
    Composition
    Red and blue shift
    Line broadening
```

### Year 11: Waves you already know
In Year 11 you learned $v = f\lambda$ for all waves. For EM waves in a vacuum, $v = c$. A radio station at 100 MHz broadcasts with $\lambda = \dfrac{3.00 \times 10^8}{1.00 \times 10^8} = 3.00$ m.

EM waves are **transverse**: the fields vibrate at right angles to the direction of travel. Unlike sound, they need **no medium**, which is why sunlight crosses empty space.

### Year 12: Calculating a star's speed from a redshift
For speeds much less than $c$, the shift in a spectral line gives the star's speed along our line of sight:

$$\frac{\Delta\lambda}{\lambda} \approx \frac{v}{c}$$

Hydrogen's red line is at 656.3 nm in a lab. In a star it is measured at 658.5 nm. The shift is $\Delta\lambda = 2.2$ nm, so $v = 3.00 \times 10^8 \times \dfrac{2.2}{656.3} = 1.0 \times 10^6$ m/s, moving **away** (redshift).

**Maxwell's limits.** Maxwell's waves were thought to need a medium, the "aether", to travel through. The Michelson and Morley experiment (1887) failed to find it. This puzzle was solved by Einstein's special relativity (see Light and Special Relativity).

**More on Fizeau.** At exactly twice the blocking speed, the light that left through one gap returns through the **next** gap, so the observer sees it again. The blocking speed for a wheel with $N$ teeth at distance $d$ comes from: time for half a tooth spacing $= \dfrac{1}{2Nf}$ equals the round trip $\dfrac{2d}{c}$, so $f = \dfrac{c}{4Nd}$.

**Foucault and the models.** Light being slower in water than in air supported the **wave** model and contradicted Newton's particle model, which needed light to speed up in water.

**What an AC wire gives off.** The charges oscillate at the AC frequency (50 Hz or radio frequencies for an antenna), so the wire gives off low-frequency radio waves.

**What absorption lines prove.** Matching lines show which elements are present. The absence of an element's lines suggests it is absent or very rare in the star's outer layers, but is not absolute proof.

**Using the constants.** $c = \dfrac{1}{\sqrt{\mu_0\varepsilon_0}} = \dfrac{1}{\sqrt{4\pi \times 10^{-7} \times 8.854 \times 10^{-12}}} \approx 3.00 \times 10^8$ m/s. In a material, $v = \dfrac{1}{\sqrt{\mu\varepsilon}}$ is slower, because $\mu\varepsilon$ is bigger than in a vacuum.

**Rotation from broadening.** A line spread from $\lambda - \Delta\lambda$ to $\lambda + \Delta\lambda$ gives the edge speed $v = c\dfrac{\Delta\lambda}{\lambda}$, using the half-width. A star that is moving away **and** spinning has lines that are both shifted to the red and broadened.

**Timing light.** If one path is 6.0 m longer and its pulse arrives 20 ns later, $c = \dfrac{6.0}{20 \times 10^{-9}} = 3.0 \times 10^8$ m/s.

**Safety with discharge tubes.** They run on high voltage (do not touch the terminals with the power on) and some give off ultraviolet (do not stare at them for long; use UV-blocking glasses).

**Michelson and Morley.** They found no difference in the speed of light in two directions at right angles, which suggested there is no aether and that light's speed is the same in every direction.

## Quick summary

- Maxwell unified electricity and magnetism and predicted EM waves travelling at $c = \dfrac{1}{\sqrt{\mu_0\varepsilon_0}}$. Light is an EM wave.
- EM waves are made by oscillating charges. Their electric and magnetic fields are at right angles.
- Hertz made radio waves and confirmed Maxwell's prediction.
- Fizeau and Foucault measured the speed of light. $c = f\lambda$.
- Continuous, emission and absorption spectra come from hot dense objects, hot thin gases and cool gas in front of a hot source.
- Star spectra reveal temperature, composition, motion towards or away, rotation and density.

## Quiz

Try these questions from the chapter quiz.

1. Who first predicted that light is an electromagnetic wave?
   - A. Newton
   - B. Hertz
   - C. Maxwell
   - D. Einstein
   - Answer: C. Maxwell. Maxwell's equations predicted EM waves moving at the speed of light.

2. Who first produced and detected radio waves, confirming the prediction?
   - A. Maxwell
   - B. Hertz
   - C. Fizeau
   - D. Planck
   - Answer: B. Hertz. Hertz used a spark gap and showed the waves behaved like light.

3. Electromagnetic waves are produced by:
   - A. Charges at rest
   - B. Oscillating (accelerating) charges
   - C. Steady magnetic fields
   - D. Sound vibrations
   - Answer: B. Oscillating (accelerating) charges. An oscillating charge makes changing electric and magnetic fields that travel outwards.

The whole chapter quiz is on the page, for signed-in students: https://whizznotes.com/physics/electromagnetic-waves/#quiz