PHY1023 Waves and Optics
2011-2012
Code: PHY1023
Level: 1
Title: Waves and Optics
Instructors:
Dr P. Vukusic
CATS Credit Value: 15
ECTS Credit Value: 7.5
Pre-requisites: N/A
Co-requisites: N/A
Duration:
T2:01-11
Availability: unrestricted
Background Assumed: -
Total Student Study Time
150 hours, to include:
22×1-hour lectures;
44 hours directed self-study;
9 hours of problems class support;
3 hours of tutorial support;
72 hours private study.
Aims
The concepts of oscillation amd wave propagation permeates 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 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 introduced in this module underpin, and will be developed in later modules, e.g. in
electromagnetism (PHY2021), quantum mechanics
(PHY2022) and condensed matter
physics (PHY2024).
Intended Learning Outcomes
Students will be able to:
- Module Specific Skills:
- 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.
power dissipation;
- 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:
- 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 Transferable Skills:
- undertake guided self-study successfully;
- manage their time appropriately in order to meet the weekly-homework
assignment deadlines.
Learning / Teaching Methods
Lectures,
e-Learning resources (ELE PHY1023),
and problems classes.
Assessment and Assignments
Contribution | Assessment/Assignment | Size (duration/length) | When |
10% | Problem Sets | 7×2hrs | Weekly |
15% | Mid-term Test 1 | 30 minutes | Week T2:04 |
15% | Mid-term Test 2 | 30 minutes | Week T2:08 |
60% | Final examination | 120 minutes | Term 3 |
Formative | Guided self-study | 5×6-hour packages | Fortnightly |
Syllabus Plan and Content
- Introduction
Brief historical survey.
- The Physics of Simple and Damped Harmonic Motion (SHM)
- SHM - mass on a spring, equation of
motion
- Phase angle, displacement, velocity, acceleration
- Energy of simple harmonic motion
- Damped SHM (mechanical system) -
oscillatory and logarithmic decrement (exponential
notation)
- Quality factor, Q - energy dissipation
- Critical-, under- and over-damped mechanical systems
- Forced Oscillator
- Steady-state solution for mass on a spring plus driving
force
- Mechanical impedance (complex impedance, amplitude, phase factor);
amplitude resonance;
power supplied by the driving force, Q-value
- Alternating Electrical Currents (Steady State)
- Alternating voltage, phasor diagram, amplitude, phase,
period
- 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
- Optics
- Geometrical optics
Imaging and ray tracing; thin-lenses; total internal reflection
- Interference and diffraction
Young's experiment; diffraction limited resolution;
diffraction-grating spectrometer;
thin films and anti-reflection coatings; Fabry-Perot interferometer;
Michelson interferometer
- Dispersion by prisms and diffraction gratings
- Polarization
Electromagnetic interpretation; Generation by polarizers, reflection and scattering;
Birefringence
- Optical cavities and laser action
Core Text
Pedrotti F.L. and Pedrotti F.J.L.S. ,
Introduction to Optics,
Prentice-Hall (UL:
535 PED)
Young H.D. and Freedman R.A. (
2011),
University Physics (with Modern Physics) (
13th edition),
Addison-Wesley,
ISBN 978-1-292-02063-1 (UL:
530 YOU)
Supplementary Text(s)
Feynman R.P., Leighton R.B. and Sands M. (
1963),
Lectures on Physics, Vol.
I,
Addison-Wesley,
ISBN 0-201-02116-1 (UL:
530 FEY/X)
Hecht E. (
1987),
Optics (
2nd edition),
Addison-Wesley,
ISBN 0-201116111 (UL:
535 HEC)
Pain H.J. (
2005),
The Physics of Vibrations and Waves (
6th edition),
Wiley,
ISBN 0-470-01296-X (UL:
531.32 PAI)
IOP Accreditation Compliance 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.
Formative Mechanisms
Students monitor their own progress by attempting the problem sets
which will be discussed in classes. Students who need additional
guidance are encouraged to discuss the matter with the lecturer or their tutor.
Evaluation Mechanisms
The module will be evaluated using information gathered via the student representation mechanisms, the staff peer appraisal scheme, and measures of student attainment based on summative assessment.