PX2637.5 Electromagnetic Theory and Optics
Introductory description
The module develops the ideas of first year electricity and magnetism into Maxwell's theory of electromagnetism. Maxwell's equations pulled the various laws (Faraday's law, Ampere's law, Lenz's law, Gauss's law and the "law with no name") 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 timedependent solutions, which turn out to be the familiar electromagnetic waves (light, radio waves, Xrays etc), and studies their behaviour at material boundaries (Fresnel Equations). The module also covers the basics of optical instruments and light sources.
Module aims
The module should study Maxwell's equations and their solutions.
Outline syllabus
This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.
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.
Learning outcomes
By the end of the module, students should be able to:
 Write down and manipulate Maxwell's equations in integral or differential form and derive the boundary conditions at boundaries between linear isotropic materials
 Derive the planewave solutions to Maxwell's equations in free space, dielectrics and ohmic conductors
 Describe the interaction of light with optical materials and explain the basics of geometrical optics
Indicative reading list
Young and Freedman, University Physics 11th Edition
IS Grant and WR Phillips, Electromagnetism
E Hecht, Optics
View reading list on Talis Aspire
Subject specific skills
Knowledge of mathematics and physics. Skills in modelling, reasoning, thinking.
Transferable skills
Analytical, communication, problemsolving, selfstudy
Study time
Type  Required 

Lectures  18 sessions of 1 hour (24%) 
Other activity  7 hours (9%) 
Private study  50 hours (67%) 
Total  75 hours 
Private study description
Working through lecture notes, solving problems, wider reading, discussing with others taking the module, revising for exam, practising on past exam papers
Other activity description
7 problem classes
Costs
No further costs have been identified for this module.
You do not need to pass all assessment components to pass the module.
Assessment group D1
Weighting  Study time  

Coursework  15%  
Assessed work as specified by department 

2 hour online examination (Summer)  85%  
Answer 2 questions

Feedback on assessment
Personal tutor, group feedback
Courses
This module is Core for:
 Year 2 of UPXAFG33 Undergraduate Mathematics and Physics (BSc MMathPhys)
 Year 2 of UPXAGF13 Undergraduate Mathematics and Physics (BSc)
 Year 2 of UPXAFG31 Undergraduate Mathematics and Physics (MMathPhys)
 Year 2 of UPXAF304 Undergraduate Physics (BSc MPhys)
 Year 2 of UPXAF300 Undergraduate Physics (BSc)
 Year 2 of UPXAF303 Undergraduate Physics (MPhys)
 Year 2 of UPXAF3N1 Undergraduate Physics and Business Studies
 Year 2 of UPXAF3N2 Undergraduate Physics with Business Studies
This module is Option list B for:
 Year 2 of UMAAG105 Undergraduate Master of Mathematics (with Intercalated Year)
 Year 2 of UMAAG100 Undergraduate Mathematics (BSc)
 Year 2 of UMAAG103 Undergraduate Mathematics (MMath)
 Year 2 of UMAAG106 Undergraduate Mathematics (MMath) with Study in Europe
 Year 2 of UMAAG1NC Undergraduate Mathematics and Business Studies
 Year 2 of UMAAG1N2 Undergraduate Mathematics and Business Studies (with Intercalated Year)
 Year 2 of UMAAGL11 Undergraduate Mathematics and Economics
 Year 2 of UECAGL12 Undergraduate Mathematics and Economics (with Intercalated Year)
 Year 2 of UMAAG101 Undergraduate Mathematics with Intercalated Year