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:
1. set up the equations associated with simple-harmonic motion, solve them for different physical conditions and recognise situations where they are applicable;
2. 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;
3. 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;
4. 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;
5. describe Young's experiment using complex amplitudes and phasors;
6. calculate the diffraction limited resolution of a simple imaging system;
7. discuss thin-film interference fringes and anti-reflection coatings and calculate the properties needed by an optimal anti-reflection coating.
8. describe the diffraction grating, Fabry-Perot, and Michelson interferometers and their use as spectrometers, and calculate their dispersion and resolving power;
9. discuss the origin of polarisation, its generation and manipulation via dichroism and birefringence;
10. describe important features of laser light such as coherence, monochromaticity and directionality;
Discipline Specific Skills:
1. make a Fourier-series expansion of a simple periodic function;
2. to take notes in lectures and then refine them later thereby developing skills in the efficient summarising of material.
Personal Transferable Skills:
1. undertake guided self-study successfully;
2. 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)
1. SHM - mass on a spring, equation of motion
2. Phase angle, displacement, velocity, acceleration
3. Energy of simple harmonic motion
4. Damped SHM (mechanical system) - oscillatory and logarithmic decrement (exponential notation)
5. Quality factor, Q - energy dissipation
6. Critical-, under- and over-damped mechanical systems
Forced Oscillator
1. Steady-state solution for mass on a spring plus driving force
2. Mechanical impedance (complex impedance, amplitude, phase factor); amplitude resonance; power supplied by the driving force, Q-value
Alternating Electrical Currents (Steady State)
1. Alternating voltage, phasor diagram, amplitude, phase, period
2. Resistance, inductance and capacitance in an AC circuit: current-voltage relationships
3. Complex impedance in AC circuits; power in AC circuits; series and parallel resonance
Introduction to Waves
1. The electromagnetic spectrum
2. Definition and examples of wave motion; transverse and longitudinal waves; polarization; plane and spherical waves
3. Basic wave concepts: amplitude and phase; wave number k and angular frequency ω; phase velocity
4. The wave equation and its solutions
5. The Doppler effect
6. Example: transverse waves on a string
7. Energy transfer in wave motion
Superposition of Waves
1. Standing waves and normal modes
2. Partial standing waves
3. Fourier series
4. Wave packets, dispersion and group velocity
5. Example: dispersed wave on a string
Reflection and Transmission of Waves
1. Characteristic impedance; reflection and transmission coefficients of amplitude and energy
2. Example: Reflection and transmission of transverse waves on a string
3. Impedance matching and the quarter-wave transformer
Waves on Periodic Structures
1. Transverse waves on a one-dimensional periodic structure: dispersion relation, low-pass characteristic, first Brillouin zone
2. Normal modes on a one-dimensional periodic structure
Other Examples of Waves
1. Longitudinal waves in a solid
2. Sound waves in a gas
Optics
1. Geometrical optics
  Imaging and ray tracing; thin-lenses; total internal reflection
2. Interference and diffraction
  Young's experiment; diffraction limited resolution; diffraction-grating spectrometer; thin films and anti-reflection coatings; Fabry-Perot interferometer; Michelson interferometer
3. Dispersion by prisms and diffraction gratings
4. Polarization
  Electromagnetic interpretation; Generation by polarizers, reflection and scattering; Birefringence
5. 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) (13^th 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 (2^nd edition), Addison-Wesley, ISBN 0-201116111 (UL: 535 HEC)
Pain H.J. (2005), The Physics of Vibrations and Waves (6^th 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.