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# Electromagnetism, Waves & Optics - PHY00020C

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• Department: Physics
• Module co-ordinator: Prof. Christopher Ridgers
• Credit value: 20 credits
• Credit level: C
• Academic year of delivery: 2021-22

## Module will run

Occurrence Teaching cycle
A Spring Term 2021-22 to Summer Term 2021-22

## Module aims

The purpose of this module is to build on your existing knowledge of electric, magnetic andelectromagnetic phenomena, extending its scope slightly, but with the prime aim of ensuring that you have a firm grasp of fundamentals. The module is basic, and elementary in the proper sense of those words, i.e. it is concerned with the elements of the subject and lays emphasis on the application of basic laws in simple situations. Thinking in 3 dimensions is a skill which the module will encourage you to develop. Also much use will be made of calculus in presenting arguments and evaluating results.

Simple harmonic oscillation initiating propagation of waves through media is a fundamental method of energy transfer and is relevant to most physics modules. The sounds we hear, the light we see, the radio waves we use for communication, the microwaves we use for cooking, the X-rays used in hospitals, the vibration of heated atoms all underline the necessity to understand fully the processes involved and the mathematics used to interpret this oscillation. The module will examine the effects of damping of oscillations in the context of mechanical and electrical systems, and will explore mathematically and through application to common systems, the origin and characteristics of resonance. The topic of forced oscillations will also be presented in the context of real physical systems, and the underlying mathematics studied.

The wave equation is central to quantum mechanics and fundamental to electromagnetism. The ways in which waves interfere with one another will be studied and developed to characterise the nature of standing and travelling waves. Finally the topics of dispersion will be discussed in the context of propagation of waves. Throughout the module, examples taken from the telecommunications industry, and mechanical and electrical engineering, will relate content to the world of work.

The basic physics of geometrical optics will be introduced and applied to simple applications involving mirrors and lenses. The origins of spherical and chromatic aberration will be discussed and ways in which they can be avoided described. As the module progresses, more complex combinations of optical elements will be considered, with limited reference to applications. The module will also consider the absolute theoretical resolving power as determined by the Rayleigh criterion. The basic physics of physical optics will then be introduced. Topics will include diffraction and interference using the examples of Young’s double slit experiment and Newton’s rings. Polarization, phase and coherence will also be explained as will optical path difference and dispersion by prisms and diffraction gratings.

## Module learning outcomes

• discuss the basic concepts of electric field as a vector, forces on charges, scalar potential function, and potential energy
• determine the electric field from a distribution of charges, and/or a given potential gradient
• apply the Coulomb law to electric charges
• calculate the work done in a given electric field
• derive Gauss’ Law and apply it to symmetric distributions of charges
• apply the Biot-Savart law to calculate the magnetic fields generated by steady currents
• discuss what is meant by electric flux and magnetic flux
• explain electromagnetic induction, and apply Faraday/Lenz laws
• discuss the concepts of capacitance and self-inductance, and have an understanding of AC circuits containing reactive elements, including their role in resonant circuits
• describe the principles of simple harmonic motion, its relationship to uniform circular motion and derive the associated equations of motion
• demonstrate the ability to derive an expression for the energy associated with simple harmonic motion
• apply mathematical techniques to model, damped and forced oscillations and solve related expressions
• establish the conditions required for amplitude resonance
• evaluate the effect of changing the initial system conditions on the Q factor associated with amplitude resonance
• construct and solve expressions describing the motion associated with coupled oscillators
• relate mathematical solutions associated with coupled oscillators to the response of a physical system
• describe, with examples, the properties of different wave types and derive a mathematical description of a transverse mechanical wave
• derive expressions for the velocity and acceleration of particles in the wave medium
• derive the general wave equation for transverse mechanical waves
• calculate the speed of a transverse mechanical wave and the energy associated with the wave motion
• illustrate wave phenomena such as interference, reflection and standing waves via the principle of superposition
• evaluate the response of a mechanical system to a travelling wave reflecting from a boundary in the medium
• explain how beats are formed with reference to the supporting mathematics
• describe dispersion and how it originates via the process of interference
• derive an expression for the group velocity of a modulated wave
• derive an expression for the Doppler effect for sound and electromagnetic waves
• summarise the differences between Huygens wave nature and Newtons corpuscular theory of light and how Maxwells electromagnetic theory and Einsteins photoelectric effect provided a solution
• define spherical aberration and evaluate how this can be avoided using a parabolic mirror
• apply the rules of geometric optics to sketch ray diagrams relating to reflection from concave, convex and plane mirrors, and refraction through concave and convex lenses
• solve optics equations relating to object/image distance and lateral and angular magnification for a mirror, lens or combination of optical elements
• apply Snells Law to optical fibre design and the construction of Porro prisms
• apply the Lens-Makers equation to any shape of spherical lens in order to deduce image/object location and/or focal length/radius of curvature
• distinguish between long and short sightedness, calculate the strength of glasses required to correct these conditions
• devise an arrangement of lenses within a microscope or refracting telescope in order to yield specific angular magnification and image location
• relate the Rayleigh criterion to the maximum theoretical resolving power of a lens.
• describe what is meant by chromatic aberration and how achromats can be designed to reduce its effects
• demonstrate an understanding of the basic concepts of polarization, phase, coherence and optical path difference
• describe dispersion by prisms and diffraction gratings
• relate the Young’s double slit experiment to single slit diffraction and calculate the interference patterns produced

• recognise the relevance of the material in terms of mechanical and electrical industries
• develop capacity to conduct independent study through the use of formative assessment offered through the VLE
• evaluate the mechanical response of a system encountered outside a physics context, in terms of basic principles, and apply that knowledge to modify its response
• develop capacity to conduct independent study through the use of formative assessment offered through the VLE
• review and justify the commercial advantage of different forms of telecommunication system
• develop an awareness of how physics can be applied to a wide range of instruments and technologies, paying particular awareness to the limitations of materials, design and construction

## Module content

Syllabus

Electromagnetism

• Electric charge, Coulomb force law. Charge distributions, force vector at a point; superposition.
• Force and field; field vector E . (2)
• Electric flux and Gauss Law. Application in symmetric charge arrays; conductors. (2)
• Work and energy in the electric field - scalar potential function V. Field vector E as negative
• Potential energy U of a charge distribution. (1)
• Capacitance and capacitors. (1)
• Magnetic fields of steady currents, Biot Savart Law. (2)
• Magnetic flux, magnets, current loop. (1)
• Electromagnetic induction - Faraday/Lenz Laws, self-inductance. (2)
• Kirchoff Laws for current and voltage, linear DC networks, Transients in RC and RL circuits, time
• constants and waveforms. (1)

Waves and optics

• Impedance in AC circuits, complex impedance, j L, l/j C, power factor. (2)
• RLC circuits with sinusoidal excitation, resonance, Q values . (1)
• Unforced Simple Harmonic Motion (SHM)
• Undamped forced Linear Harmonic Oscillator
• Resonance applied to mechanical and electrical systems
• Coupled oscillators and normal modes
• Derivation of the wave equation
• Travelling waves along a string under tension and the creation of harmonics
• Principle of superposition and the role it plays in interference, reflection, and standing waves
• The Doppler effect
• Beats and dispersion
• Light as waves, rays and photons: a brief history of geometric optics
• Reflection from plane and curved surfaces
• Spherical and chromatic aberration, aspheric lenses and achromats
• Refraction of light through a thin lens and the Lens-maker’s equation
• The theoretical resolving power, Airy disc, Rayleigh’s criterion and focal ratio
• Spectacles and Porro prisms
• Diffraction
• Polarization, phase, coherence and optical path difference
• Dispersion by prisms and diffraction gratings
• Young’s double slit experiment and interference patterns
• Interference in thin films and Newton’s rings

## Assessment

Task Length % of module mark
Essay/coursework
Electromagnetism & Waves Assignments
N/A 20
Online Exam - 24 hrs (Centrally scheduled)
Electromagnetism, Waves & Optics Exam
8 hours 80

None

### Reassessment

Task Length % of module mark
Essay/coursework
Electromagnetism & Waves Assignments
N/A 20
Online Exam - 24 hrs (Centrally scheduled)
Electromagnetism, Waves & Optics Exam
8 hours 80

## Module feedback

Our policy on how you receive feedback for formative and summative purposes is contained in our Department Handbook.