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Waves & Optics · Physics

Oscillations lead to waves. Rays lead to images. Waves explain light.

Build the foundations: simple harmonic motion and waves, then connect to geometrical optics and the wave nature of light.

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Waves & Optics

Each topic is a set of nano-lessons designed for mastery: clear concepts, compact worked examples, and practice prompts.

1
Simple Harmonic Motion
The universal model of small oscillations: restoring forces, sinusoidal motion, and energy exchange.
  • Restoring force and equilibrium
  • SHM equations, period, frequency
  • Energy in SHM
Start topic Small oscillations behave predictably.
2
Pendulums
A classic oscillator: small-angle approximation, period, and energy methods.
  • Simple pendulum model
  • Small-angle approximation
  • Physical pendulum (intro)
Start topic Approximation is the key step.
3
Damped Oscillations
Real oscillators lose energy. Classify motion and connect to practical systems.
  • Underdamped, critical, overdamped
  • Energy loss and decay
  • Practical damping examples
Start topic Decay rate matters as much as frequency.
4
Driven Oscillations and Resonance
External driving produces steady-state response, phase shifts, and resonance peaks.
  • Driving forces and response
  • Resonance condition
  • Amplitude and phase
Start topic Resonance is a matched-frequency effect.
5
Mechanical Waves
Describe waves in media: types, parameters, propagation, and basic mathematical form.
  • Transverse vs longitudinal
  • λ, f, v relationships
  • Wave description in space and time
Start topic Waves transport energy, not matter.
6
Wave Equation and Wave Speed
Link the 1D wave equation to physical wave speed and energy transport.
  • 1D wave equation
  • Speed on a string
  • Tension and linear density
Start topic Speed depends on medium properties.
7
Superposition Principle
Linear addition of waves produces interference patterns and pulse overlap behavior.
  • Constructive/destructive interference
  • Pulse overlap
  • Linearity assumptions
Start topic Add waves point-by-point.
8
Interference of Waves
Use phase and path difference to predict maxima/minima and beats (intro).
  • Path/phase difference
  • Two-source interference
  • Beats (intro)
Start topic Phase controls the pattern.
9
Standing Waves
Boundary conditions create nodes/antinodes and quantized harmonics.
  • Nodes and antinodes
  • Harmonics and normal modes
  • Boundary conditions
Start topic Modes are selected by boundaries.
10
Energy and Power in Waves
Quantify energy flow: power, intensity, and attenuation.
  • Energy transport
  • Power and intensity
  • Attenuation and losses
Start topic Amplitude often sets energy flow.
11
Geometrical Optics
Use rays when wavelength is small compared with system size; learn where the approximation breaks.
  • Ray approximation
  • Reflection and refraction as rays
  • Validity limits
Start topic Rays are a modeling choice.
12
Reflection and Mirrors
Apply the law of reflection to plane and spherical mirrors and predict image properties.
  • Plane mirrors
  • Spherical mirrors
  • Image characteristics
Start topic Ray diagrams keep sign confusion away.
13
Refraction and Snell’s Law
Predict bending at boundaries using refractive index, and preview dispersion.
  • Index of refraction
  • Snell’s law
  • Dispersion (intro)
Start topic Angles are measured from the normal.
14
Total Internal Reflection
Learn the critical angle, when TIR occurs, and why fibers guide light efficiently.
  • Critical angle
  • TIR conditions
  • Optical fibers
Start topic TIR is refraction at its limit.
15
Thin Lenses and Image Formation
Use the thin lens equation and ray diagrams to locate images and compute magnification.
  • Converging vs diverging lenses
  • Thin lens equation
  • Magnification and ray diagrams
Start topic One equation, many interpretations.
16
Optical Instruments
Apply lenses to devices: the eye, magnifiers, microscopes, and telescopes.
  • Human eye
  • Magnifier
  • Microscope and telescope
Start topic Systems are built from simple elements.
17
Wave Nature of Light
Treat light as an electromagnetic wave; introduce coherence and when wave optics is required.
  • Light as EM wave
  • Coherence and monochromaticity
  • Ray-to-wave transition
Start topic Wavelength starts to matter.
18
Interference of Light
Double-slit and thin-film interference: fringe spacing, phase conditions, and coherence constraints.
  • Young’s double slit
  • Thin-film interference
  • Coherence conditions
Start topic Phase creates bright and dark.
19
Diffraction
Single-slit patterns, gratings, and why diffraction limits resolution.
  • Single-slit diffraction
  • Diffraction gratings
  • Resolution limits
Start topic Edges and apertures spread waves.
20
Polarization of Light
Use polarization to reveal light’s transverse nature and apply Malus’ law.
  • Transverse nature of light
  • Polarizers
  • Malus’ law and applications
Start topic Polarization is directional filtering.
Practice
Practice & Exercises
Reinforce the full track with mixed conceptual checks and exam-style problems.
  • SHM and resonance drills
  • Wave superposition and standing wave sets
  • Ray diagrams and thin lens problems
  • Interference and diffraction practice
  • Polarization and intensity questions
Open practice Mix skills across the track.