Introduction: Seeing the Invisible

Welcome to one of the most exciting "turning points" in physics! For centuries, scientists argued about what light actually was. Was it a particle? A wave? Something else? In this chapter, we explore how Maxwell and Hertz proved that light is an electromagnetic wave, how Fizeau finally measured its incredible speed, and how we eventually used the wave nature of electrons to build microscopes so powerful they can see individual atoms.

Don't worry if the names or formulas seem a bit intimidating at first. We’ll break them down step-by-step, focusing exactly on what you need for your AQA exams.

1. The Nature of Electromagnetic Waves

In the mid-1800s, James Clerk Maxwell did something incredible: he unified electricity and magnetism. He predicted that a changing electric field creates a changing magnetic field, and vice versa. These "coupled" fields travel through space as an Electromagnetic (EM) Wave.

Maxwell’s Formula for Speed

Maxwell derived a formula to calculate the speed of these waves in a vacuum. He used two constants that were already known from experiments with electricity and magnetism:

  1. \(\epsilon_0\) (Permittivity of free space): Relates to electric fields.
  2. \(\mu_0\) (Permeability of free space): Relates to magnetic fields.

His formula was:

\(c = \frac{1}{\sqrt{\mu_0 \epsilon_0}}\)

When Maxwell plugged in the values for \(\mu_0\) and \(\epsilon_0\), the answer was approximately \(3 \times 10^8\) \(m s^{-1}\). This was exactly the speed of light measured by astronomers! This was a "Eureka" moment: it proved that light is an electromagnetic wave.

Hertz’s Confirmation

Maxwell had the theory, but Heinrich Hertz provided the proof. In 1887, Hertz used a spark-gap transmitter to produce radio waves. He showed that these waves had the same properties as light:

  • They could be reflected by metal sheets.
  • They could be refracted by insulators.
  • They could be polarised (Hertz used a wire grid to show this).
  • They travelled at the speed \(c\).

Quick Review: Maxwell predicted the speed of EM waves using electricity constants. Hertz proved the theory by showing radio waves act just like light waves.

2. Fizeau’s Speed of Light Experiment

Before Maxwell, people knew light was fast, but it was hard to measure on Earth. Hippolyte Fizeau came up with a brilliant mechanical way to do it without needing a telescope.

The Setup

Fizeau sent a beam of light through the gaps in a rotating cog wheel. The light travelled to a mirror about 8 km away, reflected, and came back toward the wheel.

How it Worked

  • If the wheel was stationary, the light went through a gap and returned through the same gap.
  • As the wheel spun faster, the light returning from the mirror might hit a tooth instead of a gap, making the light "disappear" to the observer.
  • At a specific frequency of rotation \(f\), the light would pass through one gap and return just in time to pass through the next gap.

To find the speed \(c\), Fizeau used the distance (\(2 \times D\), for the trip there and back) and the time it took for the wheel to rotate by one tooth.

Common Mistake: Remember that the light travels to the mirror and back, so the distance used in calculations is \(2D\).

3. Electron Microscopes

Why do we use electrons to look at things instead of just using better glass lenses and light? The answer lies in resolving power. To see a tiny object, the wavelength of the "probe" (light or electrons) must be similar to or smaller than the size of the object. Visible light has a wavelength of hundreds of nanometres, which is too big to see individual atoms.

As you learned in the Wave-particle duality chapter, moving electrons have a de Broglie wavelength (\(\lambda\)):

\(\lambda = \frac{h}{mv}\)

By accelerating electrons to high speeds, we can give them a wavelength much smaller than light, allowing us to see details 1,000 times smaller!

The Transmission Electron Microscope (TEM)

In a TEM, a beam of electrons is fired through an incredibly thin sample.

  • Anode Voltage: Electrons are accelerated by a high potential difference \(V\). The kinetic energy gained is \(eV = \frac{1}{2}mv^2\).
  • Magnetic Lenses: Since electrons are charged, they can be focused using magnetic fields (coils of wire). These act like the glass lenses in an optical microscope.
  • The Image: The electrons that pass through the sample are focused onto a fluorescent screen or detector.

Resolving Power: The higher the anode voltage, the faster the electrons, the shorter the de Broglie wavelength, and the better the resolution. However, resolution is limited by magnetic aberrations (the magnetic lenses aren't perfect) and the thickness of the sample.

The Scanning Tunnelling Microscope (STM)

The STM is different—it doesn't use "lenses" in the traditional sense. It uses a physical probe with a tip so sharp it ends in a single atom.

  • Quantum Tunnelling: The tip is brought very close to the surface of a conductor. Even though there is a tiny gap, electrons can "tunnel" across it due to their wave-like nature.
  • Tunnelling Current: A small voltage is applied, and a current flows. This current is extremely sensitive to the size of the gap. If the gap increases by the width of an atom, the current drops massively.
  • Scanning: The tip moves across the surface. By keeping the current constant (moving the tip up and down to follow the "bumps" of atoms), a map of the surface atoms can be created.

Did you know? The STM can only be used on conducting or semiconducting materials, because a current needs to flow!

Summary of Key Concepts

1. Maxwell’s Prediction: EM waves travel at \(c = \frac{1}{\sqrt{\mu_0 \epsilon_0}}\).

2. Hertz: Proved radio waves are part of the EM spectrum by reflecting and polarising them.

3. Fizeau: Measured \(c\) using a rotating cog wheel and a distant mirror.

4. Resolving Power: Better resolution requires shorter wavelengths. Electrons have much shorter wavelengths than light.

5. TEM: Uses magnetic lenses to focus electrons passing through a thin sample.

6. STM: Uses quantum tunnelling current between a sharp tip and a surface to "see" individual atoms.

Quick Equation Check: To find the wavelength in a TEM, first find the velocity using \(eV = \frac{1}{2}mv^2\), then plug it into \(\lambda = \frac{h}{mv}\).

Don't worry if the math for electron acceleration feels repetitive—it's one of the most common calculation marks in this section of the exam! Practice rearranging \(eV = \frac{1}{2}mv^2\) for \(v\) until it becomes second nature.