PH10053: Vibrations, waves & optics [WL]
[Page last updated: 05 August 2021]
Academic Year:  2021/2 
Owning Department/School:  Department of Physics 
Credits:  6 [equivalent to 12 CATS credits] 
Notional Study Hours:  120 
Level:  Certificate (FHEQ level 4) 
Period: 

Assessment Summary:  EX 85%, PR 15% 
Assessment Detail: 

Supplementary Assessment: 

Requisites: 
Before or while taking this module you must take PH10007 OR take MA10230
You must have Alevel Physics (or equivalent) and Alevel Mathematics (or equivalent) to take this unit 
Description:  Aims: The aims of this unit are to introduce students to the fundamental concepts and mathematical treatment of waves, to explore various phenomena arising from the superposition of two or more waves, and to outline some of the general principles governing the propagation of light. Learning Outcomes: After taking this unit the student should be able to: * analyse oscillating systems under different driving regimes; * apply the wavefunction for a onedimensional travelling wave to problems involving mechanical, acoustic, water and electromagnetic waves; * state the principle of superposition and use it to solve problems involving the superposition of more than one wave; * define and derive the impedance of a mechanical wave and apply it to reflection and transmission at interfaces; * construct ray diagrams for use in solving simple geometrical optics problems; * outline the mathematical analysis of multiplebeam interference; * derive mathematical expressions for simple diffraction patterns and relate the limits imposed by diffraction to the performance of optical instruments; * demonstrate the correct use of common laboratory equipment, maintain a scientific logbook, perform basic error analysis and produce a scientific report. Skills: Written Communication T/F A, Numeracy T/F A, Data Acquisition, Handling, and Analysis T/F A, Information Technology T/F A, Problem Solving T/F A, Working as part of a group T/F, Practical laboratory skills T/F A. Content: Simple harmonic motion (3 hours): Oscillations, including damped and forced oscillations. Resonance, Qfactors. Coupled oscillations and introduction to normal modes. Wave motion as the limit of coupled oscillations. The wave equation (1D). Introduction to waves (8 hours): Transverse and longitudinal waves. Plane, circular and spherical waves. Waves on strings; sound, water, particle and light waves. Mathematical representation of 1D plane waves; wavefunction, amplitude, frequency, wavelength, wavenumber, speed, energy, intensity and impedance. The Doppler effect. Superposition; standing waves, beats, interference. Phase and group velocity; dispersive and nondispersive media. Complex exponential notation. Mechanical impedance. Reflection and transmission at boundaries. The propagation of light (3 hours): Optical path length. Huygen's and Fermat's principles, Snell's Law. Reflection and refraction. Lenses; the focal plane. Geometric optics for thin lenses. Aberrations. Principles of the telescope and microscope. Interference and diffraction (8 hours): Coherence. Young's slits experiment. The Michelson interferometer. The FabryPerot etalon. Interference between N equally spaced sources. Fraunhofer diffraction as farfield case. Derivation of Fraunhofer pattern for single slit. Discussion of circular aperture, diffraction limits on optical systems, definition of resolution, Rayleigh criterion. The diffraction grating. Resolving power of the telescope and grating. Laboratory: Performance of experiments designed to develop practical skills and support lecture material. 
Programme availability: 
PH10053 is Compulsory on the following programmes:Department of Physics

Notes:
