## PHAS1040 Vibrations, Waves and Optics

Module manager: Julian Pittard
Email: j.m.pittard@leeds.ac.uk

Taught: Semesters 1 & 2 (Sep to Jun) View Timetable

Year running 2024/25

### Pre-requisite qualifications

'A' Level Physics and Maths or equivalent

### Co-requisites

 PHAS1000 First Year Physics Assessment PHAS1010 Mechanics, Relativity and Astrophysics PHAS1020 Thermodynamics PHAS1030 Electronics, Solid State and Introduction to Quantum Physics PHAS1050 Coding and Experimental Physics

Module replaces

PHYS1210

This module is not approved as a discovery module

### Module summary

This module covers the fundamental underpinning theories of vibrations, waves, and optics. It also develops the required underlying mathematical techniques using complex numbers, solutions to second order differential equations and Fourier series.

### Objectives

Vibrations and waves are ubiquitous phenomena, occurring in widely different physical systems, from molecules to musical instruments to tectonic plates. Nevertheless, they can be described by a common mathematical approach, which this module provides.
In vibrations and waves, students will learn about oscillators, energy and resonance, different types of waves, energy/power transfer, reflection and transmission, impedance, superposition and interference, the wave-like behaviour of light, mirrors, lenses, nonlinear optics and lasers, the solution of 2nd order partial differential equations, complex numbers, fourier series and an introduction to Fourier transforms.

Learning outcomes
On successful completion of the module students will be able to demonstrate knowledge, understanding and application of the following:
In Vibrations and Waves:
1. Damped and Driven harmonic oscillators
2. Travelling waves, impedance and sound

In Optics:
3. Diffraction and Interference (including Fourier Series and Transforms)
4. Laws of Reflection and Refraction (Geometrical optics) (including total internal reflection and evanescent waves)
5. Polarisation, birefringence
6. Introduction to non-linear optics and lasers

In general:
7. Solutions to second order differential equations representing waves.
8. Application of complex numbers to the solution of the wave equation and problems in optics.
9. Fourier series and introductory Fourier transforms as applied to waves and optics.

Skills Learning Outcomes
On successful completion of the module students will be able to do the following:
1. Manage time and plan work to meet deadlines
2. Problem solving
3. Application of appropriate mathematics

### Syllabus

Details of the syllabus will be provided on the Minerva organisation (or equivalent) for the module

### Teaching methods

 Delivery type Number Length hours Student hours Lecture 50 1.00 50.00 Tutorial 6 1.00 6.00 Independent online learning hours 24.00 Private study hours 120.00 Total Contact hours 56.00 Total hours (100hr per 10 credits) 200.00

### Methods of assessment

Coursework
 Assessment type Notes % of formal assessment Assignment Coursework 100.00 Total percentage (Assessment Coursework) 100.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated