PHY1023 Waves and Optics 2017-18
Dr P. Vukusic

Delivery Weeks: T2:01-11
Level: 4 (NQF)
Credits: 15 NICATS / 7.5 ECTS
Enrolment: 150 students (approx)

### Description

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 PHY2021 Electromagnetism I, PHY2022 Quantum Mechanics I and PHY2024 Condensed Matter I.

### Module Aims

This module pre-dates the current template; refer to the description above and the following ILO sections.

### Intended Learning Outcomes (ILOs)

A student who has passed this module should be able to:

• Module Specific Skills and Knowledge:
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 and Knowledge:
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 and Key Transferable / Employment Skills and Knowledge:
1. undertake guided self-study successfully;
2. develop appropriate time-management strategies and meet deadlines for completion of work.

### Syllabus Plan

1. Introduction
Brief historical survey.
2. 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
3. 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
4. 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
5. 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
6. 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
7. 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
8. 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
9. Other Examples of Waves
1. Longitudinal waves in a solid
2. Sound waves in a gas
10. 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

### Learning and Teaching

#### Learning Activities and Teaching Methods

Description Study time KIS type
22×1-hour lectures 22 hours SLT
5×6-hour self-study packages 30 hours GIS
7×2-hour problems sets 14 hours GIS
Problems class support 9 hours SLT
Tutorial support 3 hours SLT
Reading, private study and revision 72 hours GIS

#### Assessment

Weight Form Size When ILOS assessed Feedback
0% Exercises set by tutor 3×1-hour sets (typical) Scheduled by tutor 1-14 Discussion in tutorials
0% Guided self-study 5×6-hour packages Fortnightly 1-14 Discussion in tutorials
10% 7 × Problems Sets 2 hours per set Weekly 1-14 Marked in problems class, then discussed in tutorials
15% Mid-term Test 1 30 minutes Weeks T2:04 1-14 Marked, then discussed in tutorials
15% Mid-term Test 2 30 minutes Weeks T2:08 1-14 Marked, then discussed in tutorials
60% Final Examination 120 minutes May/June assessment period 1-14 Mark via MyExeter, collective feedback via ELE and solutions.

### Resources

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).

Core text:

Supplementary texts:

ELE:

### Further Information

#### Prior Knowledge Requirements

Pre-requisite Modules Vector Mechanics (PHY1021) and Mathematics Skills (PHY1025) none

#### Re-assessment

Re-assessment is not available except when required by referral or deferral.

Original form of assessment Form of re-assessment ILOs re-assessed Time scale for re-assessment
Whole module Written examination (100%) 1-14 August/September assessment period

Notes: See Physics Assessment Conventions.

#### KIS Data Summary

Learning activities and teaching methods
SLT - scheduled learning & teaching activities 34 hrs
GIS - guided independent study 116 hrs
PLS - placement/study abroad 0 hrs
Total 150 hrs
Summative assessment
Coursework 10%
Written exams 90%
Practical exams 0%
Total 100%

#### Miscellaneous

 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. Availability unrestricted Distance learning NO Keywords Physics; Amplitudes; Diffraction; Dispersion; Examples; Impedance; Motion; Phase; Reflection; Systems; Waves. Created 01-Oct-10 Revised N/A