Introduction

The Nature of Light: A Historical Debate

The study of wave optics begins with a fundamental question: What is light? The corpuscular model was first put forward in 1637 by René Descartes, who used it to derive Snell's law of refraction. It was later developed further and popularised by Isaac Newton in his book Opticks — which is why the corpuscular model is so often (if not entirely accurately) credited to Newton alone. A rival model was proposed in 1678 by the Dutch physicist Christiaan Huygens: the wave model, which is the model this chapter develops.

• Corpuscular Model (Descartes, popularised by Newton): Light consists of tiny particles (corpuscles) that travel in straight lines.
• Wave Model (Huygens): Light is a wave that spreads out from a source.

The Crucial Prediction: Speed of Light in a Denser Medium

Both models could explain reflection and refraction (Snell's law), but they made opposite predictions about the speed of light in the second medium.

• Corpuscular Model Prediction: If a ray of light bends towards the normal upon entering a denser medium, the corpuscular model predicts that the speed of light in the second medium is greater than in the first.
• Wave Model Prediction: If a wavefront bends towards the normal upon entering a denser medium, the wave model predicts that the speed of light in the second medium is less than in the first.

Because light travels through vacuum, and it was believed a wave always needs a medium, the wave theory was not readily accepted at first — Newton's authority added to the resistance. The dispute was eventually settled by two independent lines of evidence.

The Triumph of the Wave Theory

1. Foucault's Experiment (1850): Foucault directly measured the speed of light in water and found it to be less than in air — confirming the wave model's prediction and contradicting the corpuscular model's.
2. Young's Interference Experiment (1801): Thomas Young's famous double-slit experiment showed that light could interfere with itself, producing bright and dark fringes — a signature property of waves, not particles. This firmly established light as a wave phenomenon. Over the following four decades, many more interference and diffraction experiments were carried out that could only be explained by a wave model, and by the mid-nineteenth century the wave theory was very well established.

Light as an Electromagnetic Wave

Even with interference and diffraction explained, one major difficulty remained: if light is a wave, what medium does it travel through to cross the vacuum of space? This was resolved by James Clerk Maxwell, whose equations of electricity and magnetism (around 1855) yielded a wave equation predicting the existence of electromagnetic waves. The speed these equations predicted for such waves in free space matched the measured speed of light almost exactly — leading Maxwell to conclude that light itself must be an electromagnetic wave.

• Key Idea: Light waves consist of changing electric fields ($\mathbf{E}$) and changing magnetic fields ($\mathbf{B}$), perpendicular to each other and to the direction of propagation.
• Self-Propagation: A changing electric field generates a changing magnetic field, which in turn generates a changing electric field — this mutual generation is what lets the wave propagate even through vacuum, with no material medium required.
• Later confirmation: Maxwell's prediction was itself confirmed experimentally around 1890, when Heinrich Hertz produced radio waves in the laboratory. J. C. Bose and G. Marconi went on to build practical applications using these Hertzian waves.

The Role of Wavelength and Geometrical Optics

The wavelength of visible light is extremely small — for example, yellow light has a wavelength of about $0.6\ \mu\text{m}$.

Because this wavelength is so small compared to the size of everyday mirrors, lenses, and obstacles, the wave nature of light is often negligible, and light appears to travel in straight lines. This approximation is the basis of geometrical optics, the subject of the previous chapter.

• Definition: In geometrical optics, a ray is defined as the path of energy propagation in the limit where the wavelength ($\lambda$) tends to zero ($\lambda \to 0$).

What We Will Study in This Chapter

This chapter develops the wave picture of light in full, covering:

• Huygens Principle: A geometrical construction used to derive the laws of reflection and refraction from first principles.
• Interference: The superposition of waves from coherent sources (Young's experiment).
• Diffraction: The bending of waves around obstacles, based on the Huygens–Fresnel principle.
• Polarisation: A phenomenon that confirms light waves are transverse electromagnetic waves.

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