## PH10005: Vibrations, waves & optics

[Page last updated: 05 August 2021]

Owning Department/School: Department of Physics
Credits: 6 [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Certificate (FHEQ level 4)
Period:
Semester 1
Assessment Summary: EX 100%
Assessment Detail:
• Composite Examination (EX 100%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites: Before or while taking this module you must take PH10007 OR take MA10230
You must have A-level Physics (or equivalent) and A-level 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 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-AFB10 : BSc(Hons) Physics with Astrophysics (Year 1)
• USPH-AAB10 : BSc(Hons) Physics with Astrophysics with Study year abroad (Year 1)
• USPH-AKB10 : BSc(Hons) Physics with Astrophysics with Year long work placement (Year 1)
• USPH-AFM02 : MPhys(Hons) Physics (Year 1)
• USPH-AFM04 : MPhys(Hons) Physics with Research placement (Year 1)
• USPH-AAM12 : MPhys(Hons) Physics with Study year abroad (Year 1)
• USPH-AKM03 : MPhys(Hons) Physics with Professional Placement (Year 1)
• USPH-AKM04 : MPhys(Hons) Physics with Professional and Research Placements (Year 1)
• USPH-AFM10 : MPhys(Hons) Physics with Astrophysics (Year 1)
• USPH-AFM11 : MPhys(Hons) Physics with Astrophysics with Research placement (Year 1)
• USPH-AAM14 : MPhys(Hons) Physics with Astrophysics with Study year abroad (Year 1)
• USPH-AKM10 : MPhys(Hons) Physics with Astrophysics with Professional Placement (Year 1)
• USPH-AKM11 : MPhys(Hons) Physics with Astrophysics with Professional and Research Placements (Year 1)
• USPH-AAM15 : MPhys(Hons) Physics with Astrophysics with Study year abroad and Research Placement (Year 1)
• USPH-AAM13 : MPhys(Hons) Physics with Study year abroad and Research Placement (Year 1)
Programmes in Natural Sciences
• UXXX-AFB01 : BSc(Hons) Natural Sciences (Biology with Physics stream) (Year 1)
• UXXX-AAB02 : BSc(Hons) Natural Sciences (Biology with Physics stream) with Study year abroad (Year 1)
• UXXX-AKB02 : BSc(Hons) Natural Sciences (Biology with Physics stream) with Year long work placement (Year 1)
• UXXX-AFB01 : BSc(Hons) Natural Sciences (Chemistry with Physics stream) (Year 1)
• UXXX-AAB02 : BSc(Hons) Natural Sciences (Chemistry with Physics stream) with Study year abroad (Year 1)
• UXXX-AKB02 : BSc(Hons) Natural Sciences (Chemistry with Physics stream) with Year long work placement (Year 1)
• UXXX-AFB01 : BSc(Hons) Natural Sciences (Environmental Science with Physics stream) (Year 1)
• UXXX-AAB02 : BSc(Hons) Natural Sciences (Environmental Science with Physics stream) with Study year abroad (Year 1)
• UXXX-AKB02 : BSc(Hons) Natural Sciences (Environmental Science with Physics stream) with Year long work placement (Year 1)
• UXXX-AFB01 : BSc(Hons) Natural Sciences (Physics with Biology stream) (Year 1)
• UXXX-AAB02 : BSc(Hons) Natural Sciences (Physics with Biology stream) with Study year abroad (Year 1)
• UXXX-AKB02 : BSc(Hons) Natural Sciences (Physics with Biology stream) with Year long work placement (Year 1)
• UXXX-AFB01 : BSc(Hons) Natural Sciences (Physics with Chemistry stream) (Year 1)
• UXXX-AAB02 : BSc(Hons) Natural Sciences (Physics with Chemistry stream) with Study year abroad (Year 1)
• UXXX-AKB02 : BSc(Hons) Natural Sciences (Physics with Chemistry stream) with Year long work placement (Year 1)
• UXXX-AFB01 : BSc(Hons) Natural Sciences (Physics with Environmental Science stream) (Year 1)
• UXXX-AAB02 : BSc(Hons) Natural Sciences (Physics with Environmental Science stream) with Study year abroad (Year 1)
• UXXX-AKB02 : BSc(Hons) Natural Sciences (Physics with Environmental Science stream) with Year long work placement (Year 1)
• UXXX-AFM01 : MSci(Hons) Natural Sciences (Biology with Physics stream) (Year 1)
• UXXX-AAM02 : MSci(Hons) Natural Sciences (Biology with Physics stream) with Study year abroad (Year 1)
• UXXX-AKM02 : MSci(Hons) Natural Sciences (Biology with Physics stream) with Professional Placement (Year 1)
• UXXX-AFM01 : MSci(Hons) Natural Sciences (Chemistry with Physics stream) (Year 1)
• UXXX-AAM02 : MSci(Hons) Natural Sciences (Chemistry with Physics stream) with Study year abroad (Year 1)
• UXXX-AKM02 : MSci(Hons) Natural Sciences (Chemistry with Physics stream) with Professional Placement (Year 1)
• UXXX-AFM01 : MSci(Hons) Natural Sciences (Physics with Biology stream) (Year 1)
• UXXX-AAM02 : MSci(Hons) Natural Sciences (Physics with Biology stream) with Study year abroad (Year 1)
• UXXX-AKM02 : MSci(Hons) Natural Sciences (Physics with Biology stream) with Professional Placement (Year 1)
• UXXX-AFM01 : MSci(Hons) Natural Sciences (Physics with Chemistry stream) (Year 1)
• UXXX-AAM02 : MSci(Hons) Natural Sciences (Physics with Chemistry stream) with Study year abroad (Year 1)
• UXXX-AKM02 : MSci(Hons) Natural Sciences (Physics with Chemistry stream) with Professional Placement (Year 1)

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

Department of Mathematical Sciences
• USMA-AFB15 : BSc(Hons) Mathematical Sciences (Year 2)
• USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 2)
• USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 2)
• USMA-AFB13 : BSc(Hons) Mathematics (Year 2)
• USMA-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 2)
• USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 2)
• USMA-AFM14 : MMath(Hons) Mathematics (Year 2)
• USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 2)
• USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 2)

 Notes: This unit catalogue is applicable for the 2021/22 academic year only. Students continuing their studies into 2022/23 and beyond should not assume that this unit will be available in future years in the format displayed here for 2021/22. Programmes and units are subject to change 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. Find out more about these and other important University terms and conditions here.