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Programme & Unit Catalogues

## PH10005: Vibrations, waves & optics

Owning Department/School: Department of Physics
Credits: 6
Level: Certificate (FHEQ level 4)
Period: Semester 2
Assessment Summary: EX 100%
Assessment Detail:
• Examination (EX 100%)
Supplementary Assessment: PH10005 - Mandatory Extra Work (where allowed by programme regulations)
Requisites: Before taking this unit you must take PH10007 or equivalent.
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 one-dimensional 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 multiple-beam interference;
* derive mathematical expressions for simple diffraction patterns and relate the limits imposed by diffraction to the performance of optical instruments.

Skills:
Numeracy T/F A, Problem Solving T/F A.

Content:
Simple harmonic motion (3 hours): Oscillations, including damped and forced oscillations. Resonance, Q-factors. 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 non-dispersive 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 Fabry-Perot etalon. Interference between N equally spaced sources. Fraunhofer diffraction as far-field 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.
Programme availability:

#### PH10005 is Compulsory on the following programmes:

Department of Physics
• USPH-AFB01 : BSc(Hons) Physics (Year 1)
• USPH-AAB02 : BSc(Hons) Physics with Study year abroad (Year 1)
• USPH-AKB02 : BSc(Hons) Physics with Year long work placement (Year 1)
• USPH-AFM02 : MPhys(Hons) Physics (Year 1)
• USPH-AKM04 : MPhys(Hons) Physics with Professional and Research Placements (Year 1)
• USPH-AKM04 : MPhys(Hons) Physics with Professional and Research Placements (Year 5)
• USPH-AKM03 : MPhys(Hons) Physics with Professional Placement (Year 1)
• USPH-AFM04 : MPhys(Hons) Physics with Research placement (Year 1)
• USPH-AAM03 : MPhys(Hons) Physics with Study year abroad (Year 1)
• USPH-AFB05 : BSc(Hons) Physics with Computing (Year 1)
• USPH-AAB06 : BSc(Hons) Physics with Computing with Study year abroad (Year 1)
• USPH-AKB06 : BSc(Hons) Physics with Computing with Year long work placement (Year 1)

#### PH10005 is Optional on the following programmes:

Programmes in Natural Sciences
• UXXX-AFB01 : BSc(Hons) Natural Sciences (Year 1)
• UXXX-AAB02 : BSc(Hons) Natural Sciences with Study year abroad (Year 1)
• UXXX-AKB02 : BSc(Hons) Natural Sciences with Year long work placement (Year 1)
• UXXX-AFM01 : MSci(Hons) Natural Sciences (Year 1)
• UXXX-AKM02 : MSci(Hons) Natural Sciences with Professional Placement (Year 1)
• UXXX-AAM02 : MSci(Hons) Natural Sciences with Study year abroad (Year 1)

Notes:
* This unit catalogue is applicable for the 2014/15 academic year only. Students continuing their studies into 2015/16 and beyond should not assume that this unit will be available in future years in the format displayed here for 2014/15.
* Programmes and units are subject to change at any time, in accordance with normal University procedures.
* Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.