Reflection, Refraction, and Dispersion
At interfaces electromagnetic waves reflect and refract following the Fresnel equations, and in media their speed varies with frequency, causing dispersion.
Definition
The study of how electromagnetic waves split into reflected and transmitted parts at an interface, governed by continuity of the fields, and how the wave speed and refractive index depend on frequency, producing dispersion and the separation of phase and group velocities.
Scope
This topic covers the behaviour of electromagnetic waves at boundaries between media: the laws of reflection and refraction (Snell's law), the Fresnel equations for amplitudes and intensities, Brewster's angle and total internal reflection, and the frequency dependence of the refractive index (dispersion) with its associated phase and group velocities and absorption. It connects the macroscopic optics of interfaces to the electromagnetic boundary conditions.
Core questions
- How are the directions and amplitudes of reflected and refracted waves determined?
- What are Brewster's angle and total internal reflection?
- Why does the refractive index depend on frequency, and what is dispersion?
Key concepts
- Snell's law
- Fresnel equations
- Brewster's angle
- total internal reflection
- refractive index
- dispersion
- phase velocity
- group velocity
Key theories
- Fresnel equations and Snell's law
- Matching the fields across an interface gives Snell's law for the refraction angle and the Fresnel equations for the reflected and transmitted amplitudes, including polarization-dependent effects like Brewster's angle.
- Dispersion and the frequency-dependent index
- Because a medium's response depends on frequency, the refractive index and wave speed vary with frequency, separating phase and group velocity and producing dispersion and frequency-dependent absorption.
Clinical relevance
These principles govern lenses, prisms, anti-reflection coatings, optical fibers relying on total internal reflection, dispersion management in communications, and spectroscopic analysis used throughout science and medicine.
History
Snell's law of refraction was established in the seventeenth century, and Fresnel derived the amplitude relations from wave theory in the 1820s. Brewster identified the polarizing angle, and dispersion was explained electromagnetically once the frequency dependence of a medium's response was understood.
Key figures
- Augustin-Jean Fresnel
- Willebrord Snellius
- David Brewster
Related topics
Seminal works
- born1999
- jackson1998
Frequently asked questions
- Why does a prism split white light into colours?
- The refractive index of glass varies with frequency (dispersion), so different colours refract by different angles at the prism surfaces and emerge along separated paths.
- What is total internal reflection?
- When a wave travels from a denser to a less dense medium beyond a critical angle, no light is transmitted and all of it is reflected; this confines light in optical fibers.