||Waves and Optics
||Prof. P. Vukusic
||15 NICATS / 7.5 ECTS
||150 students (approx)
The module first considers the characteristic parameters of a forced, damped harmonic oscillator, and relates them
to the characteristic parameters of wave propagation. Later stages discuss the propagation and
reflection of waves, using waves on a stretched string as the model system. Longitudinal waves in
solids, sound waves in gases, and waves in periodic structures (key to much of solid-state physics)
are also discussed, followed by an introduction to geometrical optics and optical systems.
The concepts of oscillation amd wave propagation permeate the whole of physics. This module
identifies and applies the underlying principles enabling the student to understand many apparently
unrelated systems. A wide range of physical phenomena are used as examples. The
concepts introduced in this module underpin, and will be developed in later modules, e.g. in
PHY2021 Electromagnetism I,
PHY2022 Quantum Mechanics I and
PHY2024 Condensed Matter I.
Intended Learning Outcomes (ILOs)
A student who has passed this module should be able to:
Module Specific Skills and Knowledge:
- set up the equations associated with simple-harmonic motion,
solve them for different physical conditions and recognise
situations where they are applicable;
- construct the relevant expressions for alternating current
and voltage (using complex-number representation) in an
electrical circuit and derive basic quantities, e.g.
- manipulate the wave equation and its solution, explain the concepts
of wave number, phase velocity, group velocity and dispersion; apply
these concepts to waves in periodic structures and to longitudinal
waves in solids and gases;
- solve problems involving simple systems of lenses and mirror, derive
relations such as the lens makers formula, describe the origin and use of
total internal reflection;
- describe Young's experiment using complex amplitudes and phasors;
- calculate the diffraction limited resolution of a simple imaging system;
- discuss thin-film interference fringes and anti-reflection coatings and
calculate the properties needed by an optimal anti-reflection coating.
- describe the diffraction grating, Fabry-Perot, and Michelson interferometers and their
use as spectrometers, and calculate their dispersion and resolving power;
- discuss the origin of polarisation, its generation and manipulation via dichroism and birefringence;
- describe important features of laser light such as coherence, monochromaticity and directionality;
Discipline Specific Skills and Knowledge:
- make a Fourier-series expansion of a simple periodic function;
- to take notes in lectures and then refine them
later thereby developing skills in the efficient summarising of material;
Personal and Key Transferable / Employment Skills and Knowledge:
- undertake guided self-study successfully;
- develop appropriate time-management strategies and meet deadlines for completion of work.
Brief historical survey.
The Physics of Simple and Damped Harmonic Motion (SHM)
- SHM - mass on a spring, equation of
- Phase angle, displacement, velocity, acceleration
- Energy of simple harmonic motion
- Damped SHM (mechanical system) -
oscillatory and logarithmic decrement (exponential
- Quality factor, Q - energy dissipation
- Critical-, under- and over-damped mechanical systems
- Steady-state solution for mass on a spring plus driving
- Mechanical impedance (complex impedance, amplitude, phase factor);
power supplied by the driving force, Q-value
Alternating Electrical Currents (Steady State)
- Alternating voltage, phasor diagram, amplitude, phase,
- Resistance, inductance and capacitance in an AC
circuit: current-voltage relationships
- Complex impedance in AC circuits;
power in AC circuits;
series and parallel resonance
Introduction to Waves
- The electromagnetic spectrum
- Definition and examples of wave motion; transverse and longitudinal
waves; polarization; plane and spherical waves
- Basic wave concepts: amplitude and phase; wave number k and angular
frequency ω; phase velocity
- The wave equation and its solutions
- The Doppler effect
- Example: transverse waves on a string
- Energy transfer in wave motion
Superposition of Waves
- Standing waves and normal modes
- Partial standing waves
- Fourier series
- Wave packets, dispersion and group velocity
- Example: dispersed wave on a string
Reflection and Transmission of Waves
- Characteristic impedance; reflection and transmission
coefficients of amplitude and energy
- Example: Reflection and transmission of transverse
waves on a string
- Impedance matching and the quarter-wave transformer
Waves on Periodic Structures
- Transverse waves on a one-dimensional periodic
structure: dispersion relation, low-pass
characteristic, first Brillouin zone
- Normal modes on a one-dimensional periodic structure
Other Examples of Waves
- Longitudinal waves in a solid
- Sound waves in a gas
- Geometrical optics
Imaging and ray tracing; thin-lenses; total internal reflection
- Interference and diffraction
Young's experiment; diffraction limited resolution;
thin films and anti-reflection coatings; Fabry-Perot interferometer;
- Dispersion by prisms and diffraction gratings
Electromagnetic interpretation; Generation by polarizers, reflection and scattering;
- Optical cavities and laser action
Learning and Teaching
Learning Activities and Teaching Methods
|5×6-hour self-study packages
|7×2-hour problems sets
|Problems class support
|Reading, private study and revision
||Exercises set by tutor
||3×1-hour sets (typical)
||Scheduled by tutor
||Discussion in tutorials
||Discussion in tutorials
||7 × Problems Sets
||2 hours per set
||Marked in problems class, then discussed in tutorials
||Mid-term Test 1
||Marked, then discussed in tutorials
||Mid-term Test 2
||Marked, then discussed in tutorials
||May/June assessment period
||Mark via MyExeter, collective feedback via ELE and solutions.
The following list is offered as an indication of the type & level of information that
students are expected to consult. Further guidance will be provided by the Module Instructor(s).
1963), Lectures on Physics, Vol. I, Addison-Wesley, ISBN 0-201-02116-1 (UL: 530 FEY/X)
2017), Optics (5th edition), Addison-Wesley, ISBN 978-0133977226 (UL: 535 HEC)
2005), The Physics of Vibrations and Waves (6th edition), Wiley, ISBN 0-470-01296-X (UL: 531.32 PAI)
2007), Introduction to Optics (3rd edition), Pearson Prentice-Hall, ISBN 978-0-131-97133-2 (UL: 535 PED)
Prior Knowledge Requirements
||Vector Mechanics (PHY1021) and Mathematics Skills (PHY1025)
Re-assessment is not available except when required by referral or deferral.
|Original form of assessment
||Form of re-assessment
||Time scale for re-assessment
||Written examination (100%)
||August/September assessment period
Notes: See Physics Assessment Conventions.
KIS Data Summary
|Learning activities and teaching methods|
|SLT - scheduled learning & teaching activities
|GIS - guided independent study
|PLS - placement/study abroad
|IoP Accreditation Checklist
- WV-01 Free, damped, forced and coupled oscillations to include resonance and normal modes.
- WV-02 Waves in linear media to the level of group velocity.
- WV-03 Waves on strings, sound waves and electromagnetic waves.
- WV-04 Doppler effect.
- EM-02 DC and AC circuit analysis to the level of complex impedance, transients and resonance.
- EM-05 Electromagnetic spectrum.
- OP-01 Geometrical optics to the level of simple optical systems.
- OP-02 Interference and diffraction at single and multiple apertures.
- OP-03 Dispersion by prisms and diffraction gratings.
- OP-04 Optical cavities and laser action.
||Physics; Amplitudes; Diffraction; Dispersion; Examples; Impedance; Motion; Phase; Reflection; Systems; Waves.