# Introduction to optics

## Michel Fich, Ph. D.

Course outline

1. Mathematical review
• Trigonometry and geometry
• Vectors
• Matrices
• Complex numbers
• Calculus
• Coordinate systems
2. Introduction to waves (In the first lecture following mathematical review)
• 1D wave equation
• Transverse & Longitudinal waves
• Simple harmonic oscillator (SHO) and sinusoidal waves
• Mechanical waves (including accoustic waves, transverse waves on a string)
• Harmonics
• superposition (using algebraic, complex and phasor representations)
• 2D waves
• Huygen’s principal
• 3D waves (Plane, spherical and cylindrical)
• Waveform synthesis by superposition of sinusoidal components
• Demonstrations (DEMOS): SHO, dependence of wave velocity on tension/density of medium
3. Wave & Particle duality (Light as a wave and as photons)
• Quantum nature of light
• Summary of wave theory (Electromagnetic theory, Electromagnetic waves, poynting vector, radiation mechanisms)
• Light & Matter interaction (Index of refraction, scattering, absorption, and dispersion)
• The electromagnetic spectrum (Wavelengths and colours)
• DEMO: Spectral division of white light
4. Reflection
• Plane and spherical mirrors (including sign conventions)
• Focal point and lengths
• Rotating mirror (relevance to micro-opto-electro-mechanical systems)
• DEMOS: Plane mirror, corner cube, and focal point of a spherical mirror
5. Refraction
• Snell's law
• Fermat’s principal
• Critical angle
• Apparent depth
• Prisms (small angle, general and compound, relevance to rainbows, atmospheric refraction and mirage)
• DEMOS: Critical angle, a variety of prisms, and image bending in liquids
6. Simple optical systems
• Refraction through a spherical surface
• the thin lens
• Ray tracing
• Matrix optics
• Fibre optics
• DEMOS: a variety of lenses, and combining optical elements
7. Wavefront splitting interference
• Path difference & Phase difference
• Young’s 2 slit experiment
• Multiple slit interference
• DEMOS: Interference of 2 lasers at various slit combinations
8. Amplitude splitting interference
• Introduction to thin film theory
• Multiple reflection
• Reflection & Transmission (Fresnel) coefficients
• Optical wedges
• Newton’s rings
• The Michelson interferometer (perpendicular case only).
• DEMOS: Wedges in air and water, Newton’s rings, and interference of an oil film on water
9. Diffraction
• Fraunhoffer diffraction (1D)
• Diffraction at one, two and many slits
• DEMOS: Interference of 2 lasers (of different colour) at various slit combination