# PX263 Electromagnetic Theory and Optics

##### Weighting: 7.5 CATS

The module develops the ideas of first year electricity and magnetism into Maxwell's theory of electromagnetism. Maxwell's equations pulled the various laws of electricity and magnetism (Faraday's law, Ampere's law, Lenz's law, Gauss's law) into one unified and elegant theory. Establishing a complete theory of electromagnetism has proved to be one the greatest achievements of physics. It was the principal motivation for Einstein to develop special relativity, it has served as the model for subsequent theories of the forces of nature and it has been the basis for all of electronics (radios, telephones, computers, the lot...).

The module shows that Maxwell's equations in free space have time-dependent solutions, which turn out to be the familiar electromagnetic waves (light, radio waves, X-rays etc), and studies their behaviour at material boundaries (Fresnel Equations). The module also covers the basics of optical instruments and light sources.

Aims:

The module should study Maxwell's equations and their solutions.

Objectives:

By the end of the module you should:

• understand Maxwell's equations and quantities like the Poynting vector and refractive index
• be able to manipulate these equations in integral or differential form and derive the appropriate boundary conditions at boundaries between linear isotropic materials
• be familiar with plane-wave solutions to these equations in free space, dielectrics and ohmic conductors
• have an understanding of geometrical optics, polarisation of light, the behaviour of light in lenses and prisms, and the properties of different light sources (including lasers)

Syllabus:

Refresher on vector calculus
Ampere's law, Faraday/Lenz's law, Gauss's law in differential form. Need for the displacement current. Statement of Maxwell's equations.
Maxwell equations in vacuum and in matter. Magnetisation and polarization of materials. Relation of E and P, B and M.
Solutions to Maxwell equations in vacuum. Electromagnetic waves, Poynting vector, intrinsic impedance, polarisation.
Boundary conditions. Interfaces between dielectrics, separation into perpendicular and parallel components. Refractive index.
Ohm's law. Interface with a metal, skin effect.
Optics: reflection and refraction. Wavefronts at plane and spherical surfaces. Lenses. Basics of optical instruments, resolution.

Commitment: about 18 Lectures + problems classes

Assessment: 1 hour examination(85%) + assessed work (15%)