Waves and Optics
A calculus-based course on oscillations, waves and light that pairs every derivation with runnable Python: the harmonic approximation near any stable equilibrium and phasors for adding sinusoids, simple harmonic motion with energy, phase portraits, physical and torsion pendulums, LC circuits and symplectic integration, damped and driven oscillators with critical damping, steady-state response, resonance curves, bandwidth and the quality factor, coupled oscillators, normal modes from mass and stiffness matrices and the dispersion relation of a chain of masses, the wave equation for strings with d'Alembert's solution, wave speeds in strings, gases and solids, power, impedance, reflection and transmission, standing waves on strings and in open and closed pipes, the harmonics of plucked strings, beats and equal temperament, Fourier series and transforms, the Gibbs phenomenon, Parseval's theorem, the bandwidth theorem, sampling and aliasing, and phase and group velocity in dispersive media, electromagnetic waves from Maxwell's equations with intensity, radiation pressure, Jones calculus, Malus's law, Fresnel's equations, Brewster's angle and wave plates, coherence and interference in Young's slits, thin films, anti-reflection coatings, Newton's rings and Michelson and Fabry–Pérot interferometers, single-slit, multi-slit and circular-aperture diffraction with grating resolving power, the Rayleigh criterion and Bragg's law, geometrical optics from Fermat's principle with total internal reflection, rainbows, thin lenses, mirrors, ray transfer matrices and aberrations, and a capstone on the eye, cameras, microscopes, telescopes, optical fibres and lasers and the limits that diffraction sets on them.
PHYS-230 Year 2 3 credits 12 lessons · 5 h 9 min ▶ Video lessons coming soon
Offered by HSM University · Physics
This is the Canadian version of this course. See the American version.
What you'll learn
- Explain why small oscillations about any smooth stable equilibrium are simple harmonic, and use phasors to add sinusoidal oscillations and waves.
- Solve the simple harmonic oscillator from initial conditions, analyse its energy and phase portrait, and integrate oscillators numerically with the velocity Verlet method.
- Classify damped oscillators, solve for the steady-state response of a driven oscillator, and use the quality factor to relate decay time, bandwidth and resonance.
- Find normal modes and frequencies of coupled oscillators from the mass and stiffness matrices, and derive the dispersion relation and continuum limit of a chain.
- Derive the wave equation for a string, apply d'Alembert's solution, compute wave speeds, power and impedance, and predict reflection and transmission at boundaries.
- Analyse standing waves on strings and in open and closed pipes, compute the harmonic content of plucked strings, and explain beats and equal temperament.
- Compute Fourier series and transforms, apply Parseval's theorem, the bandwidth theorem and the sampling theorem, and distinguish phase and group velocity in dispersive media.
- Derive electromagnetic waves from Maxwell's equations, compute intensity and radiation pressure, and use Jones calculus, Malus's law and Fresnel's equations for polarization.
- Apply coherence and two-beam interference to Young's slits, thin films, anti-reflection coatings, Newton's rings and Michelson and Fabry–Pérot interferometers.
- Derive single-slit, multi-slit and circular-aperture diffraction patterns, and use grating resolving power, the Rayleigh criterion and Bragg's law.
- Derive the laws of reflection and refraction from Fermat's principle, apply imaging equations for surfaces, lenses and mirrors, and use ray transfer matrices for lens systems.
- Design and evaluate optical instruments, including the eye, cameras, microscopes, telescopes and optical fibres, against their geometrical and diffraction limits.
Course content
12 lessons · 5 h 9 min total · final exam
- 1 Why waves and optics: oscillation, propagation and light 25 min · quiz
- 2 Simple harmonic motion and energy 24 min · quiz
- 3 Damped and driven oscillations and resonance 25 min · quiz
- 4 Coupled oscillators and normal modes 26 min · quiz
- 5 Mechanical waves and the wave equation 26 min · quiz
- 6 Superposition, standing waves and sound 26 min · quiz
- 7 Fourier analysis, dispersion and wave packets 26 min · quiz
- 8 Electromagnetic waves and polarization 26 min · quiz
- 9 Interference: thin films and interferometers 26 min · quiz
- 10 Diffraction: single slit, gratings and resolution 25 min · quiz
- 11 Geometrical optics: reflection, refraction, lenses and mirrors 26 min · quiz
- 12 Capstone: optical instruments from the eye to modern photonics 28 min · quiz
- E Final exam 20 questions
Requirements
Recommended background. You can start any course at any time.
Description
A calculus-based course on oscillations, waves and light that pairs every derivation with runnable Python: the harmonic approximation near any stable equilibrium and phasors for adding sinusoids, simple harmonic motion with energy, phase portraits, physical and torsion pendulums, LC circuits and symplectic integration, damped and driven oscillators with critical damping, steady-state response, resonance curves, bandwidth and the quality factor, coupled oscillators, normal modes from mass and stiffness matrices and the dispersion relation of a chain of masses, the wave equation for strings with d'Alembert's solution, wave speeds in strings, gases and solids, power, impedance, reflection and transmission, standing waves on strings and in open and closed pipes, the harmonics of plucked strings, beats and equal temperament, Fourier series and transforms, the Gibbs phenomenon, Parseval's theorem, the bandwidth theorem, sampling and aliasing, and phase and group velocity in dispersive media, electromagnetic waves from Maxwell's equations with intensity, radiation pressure, Jones calculus, Malus's law, Fresnel's equations, Brewster's angle and wave plates, coherence and interference in Young's slits, thin films, anti-reflection coatings, Newton's rings and Michelson and Fabry–Pérot interferometers, single-slit, multi-slit and circular-aperture diffraction with grating resolving power, the Rayleigh criterion and Bragg's law, geometrical optics from Fermat's principle with total internal reflection, rainbows, thin lenses, mirrors, ray transfer matrices and aberrations, and a capstone on the eye, cameras, microscopes, telescopes, optical fibres and lasers and the limits that diffraction sets on them.
Part of the Science stream, typically taken in year 2.