Study information

Waves and Optics - 2023 entry

MODULE TITLE CREDIT VALUE Waves and Optics 15 PHY1023 Dr Pablo Loren-Aguilar (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11
 Number of Students Taking Module (anticipated) 150
DESCRIPTION - summary of the module content

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.

AIMS - intentions of the module

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) (see assessment section below for how ILOs will be assessed)
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:
11. make a Fourier-series expansion of a simple periodic function;
12. 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:
13. undertake guided self-study successfully;
14. develop appropriate time-management strategies and meet deadlines for completion of work.

SYLLABUS PLAN - summary of the structure and academic content of the module
I. Introduction
Brief historical survey.
II. 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
III. 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
IV. 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
V. 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
VI. 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
VII. 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
VIII. 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
IX. Other Examples of Waves
1. Longitudinal waves in a solid
2. Sound waves in a gas
X. Optics
1. Geometrical optics
2. Imaging and ray tracing; thin-lenses; total internal reflection
3. Interference and diffraction
4. Young's experiment; diffraction limited resolution; diffraction-grating spectrometer; thin films and anti-reflection coatings; Fabry-Perot interferometer; Michelson interferometer
5. Dispersion by prisms and diffraction gratings
6. Polarization
7. Electromagnetic interpretation; Generation by polarizers, reflection and scattering; Birefringence
8. Optical cavities and laser action
LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
 Scheduled Learning & Teaching Activities Guided Independent Study 34 116
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
 Category Hours of study time Description Scheduled learning & teaching activities 22 hours 22×1-hour lectures Guided independent study 30 hours 5×6-hour self-study packages Guided independent study 14 hours 7×2-hour problems sets Scheduled learning & teaching activities 9 hours Problems class support Scheduled learning & teaching activities 3 hours Tutorial support Guided independent study 72 hours Reading, private study and revision

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Exercises set by tutor (0%) 3×1-hour sets (typical) (Scheduled by tutor) 1-14 Discussion in tutorials
Guided self-study (0%) 5×6-hour packages (Fortnightly) 1-14 Discussion in tutorials

SUMMATIVE ASSESSMENT (% of credit)
 Coursework Written Exams 10 90
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
7 × Problems Sets 10% 2 hours per set (Weekly) 1-14 Marked in problems class, then discussed in tutorials
Mid-term Test 1 15% 30 minutes (Week 4) 1-14 Marked, then discussed in tutorials
Mid-term Test 2 15% 30 minutes (Week 8) 1-14 Marked, then discussed in tutorials
Final Examination 60% 120 minutes (May/June assessment period) 1-14
Mark via MyExeter, collective feedback via ELE and solutions.

DETAILS OF RE-ASSESSMENT (where 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

RE-ASSESSMENT NOTES
An original assessment that is based on both examination and coursework, tests, etc., is considered as a single element for the purpose of referral; i.e., the referred mark is based on the referred examination only, discounting all previous marks. In the event that the mark for a referred assessment is lower than that of the original assessment, the original higher mark will be retained.

Physics Modules with PHY Codes
Referred examinations will only be available in PHY3064, PHYM004 and those other modules for which the original assessment includes an examination component - this information is given in individual module descriptors.
RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener
ELE: