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Questions and Answers
Who is the Ussher Assistant Professor for the Science of Energy and Energy Systems for this course?
Who is the Ussher Assistant Professor for the Science of Energy and Energy Systems for this course?
Which of the following is NOT a primary focus of this course?
Which of the following is NOT a primary focus of this course?
Which textbook is listed as a primary resource for this course?
Which textbook is listed as a primary resource for this course?
Besides lectures, which of the following is a component of the contact hours for this course?
Besides lectures, which of the following is a component of the contact hours for this course?
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How many lectures are scheduled for this course?
How many lectures are scheduled for this course?
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What kind of problems are being used for CA (Continuous Assessment)?
What kind of problems are being used for CA (Continuous Assessment)?
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Which of the following lab experiments is related to interference and diffraction?
Which of the following lab experiments is related to interference and diffraction?
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Where can optional course content be found?
Where can optional course content be found?
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What does the expression $\oint \vec{E} \cdot d\vec{A} = \frac{Q_{encl}}{\epsilon_0}$ represent?
What does the expression $\oint \vec{E} \cdot d\vec{A} = \frac{Q_{encl}}{\epsilon_0}$ represent?
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The equation $\oint \vec{B} \cdot d\vec{A} = 0$ mathematically expresses what?
The equation $\oint \vec{B} \cdot d\vec{A} = 0$ mathematically expresses what?
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What physical phenomenon is described by the equation $\oint \vec{E} \cdot d\vec{l} = - \frac{d\Phi_B}{dt}$?
What physical phenomenon is described by the equation $\oint \vec{E} \cdot d\vec{l} = - \frac{d\Phi_B}{dt}$?
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In the context of Maxwell-Ampère's Law, what quantity is represented by the term $\epsilon_0 \frac{d\Phi_E}{dt}$?
In the context of Maxwell-Ampère's Law, what quantity is represented by the term $\epsilon_0 \frac{d\Phi_E}{dt}$?
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What is the significance of a wavefront moving in the +x direction with velocity $c$?
What is the significance of a wavefront moving in the +x direction with velocity $c$?
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Which phenomenon is NOT typically associated with the wave nature of light in physical optics?
Which phenomenon is NOT typically associated with the wave nature of light in physical optics?
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What distinguishes Fraunhofer diffraction from Fresnel diffraction?
What distinguishes Fraunhofer diffraction from Fresnel diffraction?
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Which optical element is most closely associated with manipulating the polarization state of light?
Which optical element is most closely associated with manipulating the polarization state of light?
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What is a key characteristic of coherent light sources compared to incoherent light sources?
What is a key characteristic of coherent light sources compared to incoherent light sources?
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Which mathematical tool is used to describe the polarization of light?
Which mathematical tool is used to describe the polarization of light?
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What phenomenon is exploited in thin film interference?
What phenomenon is exploited in thin film interference?
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In the context of diffraction, what does 'resolution' refer to?
In the context of diffraction, what does 'resolution' refer to?
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Which of the following is a characteristic of geometrical optics?
Which of the following is a characteristic of geometrical optics?
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According to the derivation, what is the relationship between $E$ and $B$?
According to the derivation, what is the relationship between $E$ and $B$?
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What physical constants are required to determine the speed of electromagnetic waves using the derived formula?
What physical constants are required to determine the speed of electromagnetic waves using the derived formula?
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Given the values $\mu_0 = 4\pi \times 10^{-7} \frac{Tm}{A}$ and $\epsilon_0 = 8.85 \times 10^{-12} \frac{F}{m}$, which calculation correctly determines the speed of light ($c$)?
Given the values $\mu_0 = 4\pi \times 10^{-7} \frac{Tm}{A}$ and $\epsilon_0 = 8.85 \times 10^{-12} \frac{F}{m}$, which calculation correctly determines the speed of light ($c$)?
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What is the significance of the Maxwell-Ampere correction to Ampere's Law?
What is the significance of the Maxwell-Ampere correction to Ampere's Law?
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If a cubical surface is placed in a uniform electric field E with two faces perpendicular to E, what can be said about the net electric flux through the cube?
If a cubical surface is placed in a uniform electric field E with two faces perpendicular to E, what can be said about the net electric flux through the cube?
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If a disturbance exists in the electromagnetic field, what can be determined using Maxwell's equations and the provided derivation?
If a disturbance exists in the electromagnetic field, what can be determined using Maxwell's equations and the provided derivation?
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Which of the following is NOT a direct consequence of Maxwell's equations?
Which of the following is NOT a direct consequence of Maxwell's equations?
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What would be observed if the Ampere-Maxwell law did not include the displacement current term?
What would be observed if the Ampere-Maxwell law did not include the displacement current term?
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What is the result of replacing $x'$ with $x - vt$ in the equation $\psi = e^{-ax'^2}$?
What is the result of replacing $x'$ with $x - vt$ in the equation $\psi = e^{-ax'^2}$?
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In the context of harmonic waves, why are sine and cosine functions considered important?
In the context of harmonic waves, why are sine and cosine functions considered important?
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What are the units of $k$ if $kx'$ is in radians and $x'$ is in meters?
What are the units of $k$ if $kx'$ is in radians and $x'$ is in meters?
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Given the equation $\psi(x, t) = A \sin[k(x - vt)]$, what does $A$ represent?
Given the equation $\psi(x, t) = A \sin[k(x - vt)]$, what does $A$ represent?
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If $\phi = k(x - vt)$, what does $\phi$ represent?
If $\phi = k(x - vt)$, what does $\phi$ represent?
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What physical phenomenon is described by the statement “the ‘disturbance’, $\psi$ is the same at any position $x$ and the position $x + \lambda$”?
What physical phenomenon is described by the statement “the ‘disturbance’, $\psi$ is the same at any position $x$ and the position $x + \lambda$”?
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What is the relationship between the second partial derivative of $\psi$ with respect to $x$ and the second partial derivative of $\psi$ with respect to $t$ according to the wave equation?
What is the relationship between the second partial derivative of $\psi$ with respect to $x$ and the second partial derivative of $\psi$ with respect to $t$ according to the wave equation?
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Given $\psi(x, t) = A \sin[k(x - vt)]$, what happens to $\psi(x, t)$ if $x$ is replaced by $x + \lambda$, where $\lambda$ is the wavelength?
Given $\psi(x, t) = A \sin[k(x - vt)]$, what happens to $\psi(x, t)$ if $x$ is replaced by $x + \lambda$, where $\lambda$ is the wavelength?
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What condition must be met for a sine wave to repeat every $\lambda$?
What condition must be met for a sine wave to repeat every $\lambda$?
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How is the period $T$ related to wavelength $\lambda$ and wave velocity $v$?
How is the period $T$ related to wavelength $\lambda$ and wave velocity $v$?
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What is the angular frequency $\omega$ in terms of frequency $f$?
What is the angular frequency $\omega$ in terms of frequency $f$?
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If a wave has a phase shift, what does this imply about the wave's 'disturbance' at the origin?
If a wave has a phase shift, what does this imply about the wave's 'disturbance' at the origin?
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Which of the following expressions represents a wave with a phase shift $\epsilon$?
Which of the following expressions represents a wave with a phase shift $\epsilon$?
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What is the relationship between wavenumber $k$ and wavelength $\lambda$?
What is the relationship between wavenumber $k$ and wavelength $\lambda$?
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Given $\psi = \sin(\phi - \frac{\pi}{4})$, how can this be interpreted?
Given $\psi = \sin(\phi - \frac{\pi}{4})$, how can this be interpreted?
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How is $\cos(\phi)$ related to a sine function?
How is $\cos(\phi)$ related to a sine function?
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Flashcards
Electromagnetic Waves
Electromagnetic Waves
Waves that propagate through space and include light, radio, and X-rays, composed of oscillating electric and magnetic fields.
Polarisation
Polarisation
The orientation of oscillations in a light wave, which can be linear, circular, or elliptical.
Interference
Interference
The phenomenon that occurs when two or more waves overlap, resulting in a new wave pattern.
Diffraction
Diffraction
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Maxwell’s Equations
Maxwell’s Equations
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Phasors
Phasors
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Vector Fields
Vector Fields
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Coherence
Coherence
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Electric Flux
Electric Flux
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Gauss’ Law
Gauss’ Law
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Faraday’s Law
Faraday’s Law
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Maxwell-Ampere’s Law
Maxwell-Ampere’s Law
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Wavefront Concept
Wavefront Concept
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Linear Polarization
Linear Polarization
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Coherence Length
Coherence Length
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Apertures
Apertures
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Fresnel Diffraction
Fresnel Diffraction
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Quantum Electrodynamics (QED)
Quantum Electrodynamics (QED)
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Electromagnetic Wave Speed
Electromagnetic Wave Speed
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μ0
μ0
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ε0
ε0
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Maxwell's Equations
Maxwell's Equations
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Faraday's Law
Faraday's Law
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Maxwell-Ampere Law
Maxwell-Ampere Law
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Electric Field Orientation
Electric Field Orientation
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Wavenumber (k)
Wavenumber (k)
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Wave Period (T)
Wave Period (T)
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Frequency (f)
Frequency (f)
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Angular Frequency (ω)
Angular Frequency (ω)
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Wave Function (ψ)
Wave Function (ψ)
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Phase Shift (ε)
Phase Shift (ε)
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Sine vs Cosine Waves
Sine vs Cosine Waves
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Disturbance
Disturbance
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Wave Equation
Wave Equation
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Harmonic Waves
Harmonic Waves
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k (wave number)
k (wave number)
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Traveling Wave
Traveling Wave
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Amplitude (A)
Amplitude (A)
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Phase ()
Phase ()
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Wavelength (\u03BB)
Wavelength (\u03BB)
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Velocity (v)
Velocity (v)
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Study Notes
Optics and Waves II: Module PYU22P20
- Lecturer: David McCloskey, Ussher Assistant Professor for the Science of Energy and Energy Systems, Trinity College Dublin
- Module code: PYU22P20
- Contact hours: 14 lectures, 1 revision lecture, 1 test, 2 small group tutorials
- Course objectives:
- Connect electricity, magnetism, and light
- Provide mathematical tools to describe light as a vector field
- Explore light's vectorial properties (polarization, interference, diffraction)
- Understand applications of electromagnetic waves in technology and daily life
Course Structure
- Textbooks:
- Optics by Hecht, Addison Wesley, University Physics Chapters 32, 33, 35, 36
- Thomas’ Calculus: Early Transcendental, 12th Edition, by George B. Thomas
- Div Grad Curl and all that, H.M. Schey
- Online content: Mastering Physics, Blackboard
- Assessment: Coursework assignments (Mastering Physics problems), end-of-year exam (2 questions, paper II)
- Related labs: Interference and diffraction, Michelson Interferometer, polarized light, Fourier analysis
Topics
- Electromagnetism and Scalar Waves: History, Maxwell's equations, wave equation, phasors, sources of light, coherence, and vector fields (divergence, curl)
- Properties of Light 1: Polarization: Linear, Circular, Elliptical polarization, degree of polarization, phase retarders, optical activity, Jones Calculus, Stokes parameters, polarizers
- Properties of Light 2: Interference: Superposition, coherence length, interferometers (Fabry-Perot), visibility, thin films, localized/non-localized multiple-beam interference
- Properties of Light 3: Diffraction: Near-field, far-field, diffraction limit, resolution, apertures, Fresnel and Fraunhofer diffraction, image formation, spatial filtering
- Maxwell's displacement current: Ampere's law and its correction to account for time-varying electric fields in the context of charging capacitors. Key to understanding how electric fields generate magnetic fields.
Electromagnetic Spectrum
- Charts cover wavelength, wavenumber, electron volts, and frequency ranges for various electromagnetic waves (radio, microwave, terahertz, infrared, visible, ultraviolet, x-ray, and gamma).
- Explanations of various bands and their applications including radio, microwave, terahertz, infrared, visible light, and their various applications.
Current Theories of Light
- Distinguish between geometrical optics and physical optics (classical electromagnetism).
- Highlight the importance of quantum optics.
Historical Development of Light Theories (brief summary)
- Early concepts (Euclid's law of reflection, Snell's law of refraction, Grimaldi's study of diffraction, light's finite speed by Ole Römer)
- Particle theories (Newtonian)
- Wave theories (Young's interference experiments, Maxwell's equations, Einstein-Plank)
Today's Objectives (examples)
- Understand course structure and content
- Review of Maxwell's equations in integral form
- Maxwell-Ampere correction
- Derive the speed of an electromagnetic disturbance
Scalar and Vector Fields
- Scalar field: A field that only has a magnitude at each point in space and time (e.g., temperature).
- Vector field: A field that has both magnitude and direction at each point in space and time (e.g., wind velocity).
- Definitions & representations used for both types of fields
Electric and Magnetic Fields
- Explain how charge particles and currents exert a force on each other through electric and magnetic fields.
- Introduce the Lorentz Force Law: F = q(E+v×B)
Light as a Wave
- Explains the experimental evidence for light having wave-like properties through interference and diffraction experiments.
- Review of the theoretical connections between electricity, magnetism and light, specifically how Maxwell's equations combine these disciplines.
- Maxwell's laws derived in terms of integral equations and the differential equation for electro-magnetic radiation which shows light has a finite wave speed c
- Explains the derivation for the speed of electro-magnetic radiation and how this applies to light.
Maxwell's Equations
- Integral form: Gauss's Law, Gauss's Law for Magnetism, Faraday's Law, Maxwell-Ampere's Law
- Differential form:
- ∇⋅E = ρ/ε₀
- ∇⋅B = 0
- ∇×E = -∂B/∂t
- ∇×B = μ₀J + μ₀ε₀∂E/∂t
- Important vector identities: curl(▽ × E), divergence(∇ · E), Laplacian(∇² E)
- Discussion of the significance of Maxwell's Equations for understanding electromagnetic phenomena.
- Derivation of waves from Maxwell's equations.
Example Questions
- Electromagnetic disturbances and light: Demonstrate that a disturbance in the electromagnetic field travels at the speed of light by using differential forms of Maxwell's equations.
Today You Have Learned (examples)
- Review of Maxwell's equations in integral and differential form.
- Derived the Maxwell-Ampere correction.
- Derived the speed of an electromagnetic disturbance.
Section 2: The Differential Form of Maxwell's Equations
- Introduce the differential form of Maxwell's equations.
- Introduce and define ∇. (divergence), ∇× (curl), and ∇² (Laplacian)
Waves
- Definition: A disturbance or oscillation that travels through space and time, carrying energy and momentum.
- Types (transverse, longitudinal, plane, spherical, cylindrical)
- Wavefunction y: A function of position and time that describes the disturbance
The Wave Equation
- Derivation: Derive the wave equation from the wave's definition using the chain rule and differentiation.
- General and Specific Solutions: Explain the general properties for a wave, and also give examples of solutions in the context of harmonic and travelling waves.
- Wavenumber (k): How many cycles of sinusoidal waveform take place per unit distance (m⁻¹).
- Angular frequency (ω): How many cycles of waveform take place per unit time (rad s⁻¹).
Phase and Phasors
- Phase: a phase shift to a wave means the location of a maximum of the wave.
- Phasors: Representing plane waves as complex (rotating) vectors on an Argand diagram.
Light Sources
- Coherent light sources: Light sources with a fixed phase relationship, useful in interference experiments (examples include lasers)
- Incoherent light sources: Light sources without fixed phase relationship (e.g., lightbulb, sunlight).
- Spatial Coherence: The extent over which light keeps the same phase
- Temporal Coherence: The extent over which light keeps the same energy distribution
Energy, Power, and Momentum in Light
- Energy Density: Energy per unit volume associated with electric (uE) and magnetic (uB) fields
- Poynting vector: The direction that energy and power flow in an electro-magnetic wave calculated from the electric and magnetic field magnitudes and wave speed.
- Irradiance (Intensity): Magnitude of the average Poynting vector and the magnitude of power flow per unit area.
- Momentum: Light carries momentum which is related to the energy density.
Devices Using Radiation
- Crooks Radiometer
- Solar Sails
- Optical tweezers
Example Questions (examples)
- Satellite stabilization: Applying radiation pressure to counteract space debris.
- Collisions: Calculate the potential momentum change and risk level.
- Particle Collection: Calculating the velocity of particles collected by a laser beam in space.
- Antennae: Estimating induced electric fields from radiating power sources and antennae.
- Electric field verification: Show the electric field E=E0e^(i(kx-wt) satisfies the wave equation.
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Description
Test your understanding of the Energy Systems course with questions about content, resources, and fundamental equations in the field. This quiz covers key concepts related to energy, circuits, and the principles of electricity and magnetism. Prepare to evaluate your knowledge on these essential topics.