Lecture 5.2: The Duality of Light

Light is both a wave and a particle, a strange but fundamental truth of our universe.

Today’s Essential Questions

• What is an electromagnetic wave?
• What is a photon?
• How is the energy of a photon related to the frequency of the light?

Connecting to Our Last Investigation

Your research showed that electromagnetic (EM) waves are created by accelerating charges. This wave model is incredibly powerful, but it can’t explain every observation. There are puzzles that force us to think about light in a completely new way. Today, we’ll introduce a second model: the photon.

What is an Electromagnetic Wave?

An EM wave is a transverse wave composed of oscillating electric and magnetic fields. These fields are perpendicular to each other and to the direction of wave propagation.

Unlike mechanical waves (like sound or slinkys), EM waves do not require a medium. They can travel through the vacuum of space. This is how we see stars and how our microwaves heat food.

The Universal Speed Limit

All electromagnetic waves—from radio waves to visible light to gamma rays—travel at the same speed in a vacuum: the speed of light (c).

This is the ultimate speed limit of the universe.

A Problem for the Wave Model

In the late 1800s, scientists observed the photoelectric effect: when you shine light on a metal, it can eject electrons. But there was a puzzle:

• A very bright red light (high amplitude, low frequency) could not eject any electrons.
• A very dim violet light (low amplitude, high frequency) could eject electrons immediately.

The wave model, which links energy to amplitude, could not explain this. Why would a low-energy wave (violet) work when a high-energy wave (red) failed?

Einstein’s Solution: The Photon

In 1905, Albert Einstein proposed a radical idea: Light energy is not a continuous wave, but is instead delivered in discrete packets, or quanta, called photons.

A photon is a massless particle of light that carries a specific amount of energy.

Energy and Frequency: The Master Equation

Einstein connected the particle model (photon energy) to the wave model (frequency) with a simple, powerful equation:

\(E = hf\) \(\text{Energy of a Photon} = (\text{Planck's Constant}) \times \text{Frequency}\)

where $h = 6.626 \times 10^{-34} \text{ J} \cdot \text{s}$

This equation solved the photoelectric puzzle: each individual violet photon has more energy than each red photon. It doesn’t matter how bright the red light is; none of its individual photons have enough energy to eject an electron.

Wave-Particle Duality

So what is light? Is it a wave or a particle? Modern physics says it is both.

• It travels through space like a wave.
• It interacts with matter like a particle.

This concept of wave-particle duality is a cornerstone of quantum mechanics. Light’s nature depends on how you observe it.

Thinking Lens: Patterns

The equation E = hf reveals a fundamental pattern connecting two different models of light.

Question: How does this simple mathematical pattern help us predict how light of different colors (frequencies) will interact with matter, something the pure wave model could not do?

Preparing for Our Next Task

The relationship between a photon’s energy and its frequency, E = hf, is the key to understanding the data you will analyze in the upcoming ‘Particle Model of Light’ lab. You will use this equation to explain why some frequencies of light are more effective than others at interacting with matter.

Summary: Answering Our Questions

• What is an electromagnetic wave? It is a transverse wave of oscillating electric and magnetic fields that can travel through a vacuum at the speed of light.

• What is a photon? A photon is a discrete particle, or quantum, of light that carries a specific amount of energy.

• How is a photon’s energy related to frequency? The energy is directly proportional to the frequency, as described by the equation E = hf.

Prompt: In 2-3 sentences, explain the concept of wave-particle duality and why it is a central idea in modern physics.