Optics & Light
Reflection, refraction, lenses, prisms, and diffraction patterns
Eye: Myopia & Hyperopia
Reduced eye + glasses; retina blur cue; presets and suggested ΔP.
Fresnel vs Fraunhofer
Slit diffraction: N = a²/(λL); Cornu spiral; Fresnel integral vs sinc².
Three Polarizers (paradox)
P₁–P₂–P₃ Malus chain; crossed P₁⊥P₃ plus P₂ at 45° lets light through.
Airy Disk & Rayleigh Limit
Circular aperture Fraunhofer pattern; first dark ring; two-point resolution.
Optical Bench (sandbox)
Up to 4 elements: thin lenses, vertical mirrors, wedge δ; paraxial ray trace.
Telescope & Microscope (2 lenses)
Kepler / Galileo / microscope presets; paraxial rays, M, f_obj/f_eye hint.
Whispering Gallery (Rays)
Circular mirror: shallow chords refocus acoustic energy opposite the source (geometric optics).
Fiber Bragg Grating
λ_B = 2 n_eff Λ; Lorentzian toy reflectivity vs λ and probe wavelength.
Laser Speckle
Random phased waves: |Σ e^{i(k·r+φ)}|² grain pattern (qualitative).
Bragg’s Law (X-ray)
2d sin θ = nλ vs θ; crystal planes and constructive reflection (schematic).
Kaleidoscope
N-fold rotation + optional mirror: one bead etches a symmetric mandala trail.
Coffee-Cup Caustics
Parallel beam, circular cup segment, reflected-ray density on a table line.
Soap Film (Minimal Surface)
Non-planar wire: discrete Laplace relaxation on z; iridescent mesh — Plateau sketch.
CD / Grating Rainbow
Lines/mm and incidence: scalar grating orders painted as λ-colored fans.
Moiré (Line Gratings)
Two translucent rulings: spacing, tilt, shift — spatial beats and envelopes.
Fiber: Numerical Aperture
NA from n_core, n_clad; acceptance angle and bend loss cue.
Fiber Bend & TIR Loss
Curved core: outer-wall incidence vs θ_c; tight R leaks (meridional sketch).
Evanescent Wave (TIR)
Beyond θ_c: penetration depth scale in the rarer medium vs λ.
Retina & Diffraction
Order-of-magnitude θ ~ λ/D and cone spacing scale.
Pinhole Camera
Camera obscura: similar triangles, image size h_i = h_o · v/u.
Rainbow in a Droplet
Snell in a sphere: primary (1× internal reflection ~42°) and secondary (2× ~51°, reversed spectrum); scan b/R and n.
Rayleigh Sky (blue)
Scattered intensity ∝ λ⁻⁴; compare blue vs red and qualitative sky gradient.
Inferior Mirage (hot road)
n(y) gradient above hot asphalt: rays bend — sky light looks like a wet patch.
Reflection
Flat, concave, and convex mirrors with auto-drawn ray diagrams.
Refraction
Light crossing boundaries. Snell's law with angle measurements.
Total Internal Reflection
Find the critical angle. Fiber optics analogy.
Lens Simulator
Converging and diverging lenses with ray diagrams and image formation.
Simple Eye (Thin Lens)
P_total = P_eye + P_glasses; 1/v = P − 1/u vs retina; blur cue.
Thin Lens Equation
Hyperbola d_i(d_o), pole at d_o = f, schematic + 1/d check.
Prism & Dispersion
White light through a prism creating a rainbow spectrum.
Thin-Film Interference
Wedge fringes: n, d, θ; cos²(δ/2) colors and I(λ) at mid thickness.
Newton’s Rings
Spherical lens on flat glass: air-film thickness fringes; optional π phase on reflection.
Anti-Reflection Coating
Air–film–glass at normal incidence: R(λ) from two-interface interference; quarter-wave design.
Michelson Interferometer
I(Δ) = V cos²(πΔ/λ); tilt fringes; coherence length envelope.
Mach–Zehnder Interferometer
Two-beam recombination; I ∝ cos²(πΔ/λ) vs one-arm OPD; schematic + fringe plot.
Sagnac (Ring) Interferometer
Δφ ∝ Ω·A/λ for counter-propagating beams in a rotating loop — optical gyro idea.
Brewster Angle
tan θ_B = n₂/n₁; R_p→0; θᵢ+θₜ=90°; Fresnel R_s, R_p vs θᵢ.
Fermat's Principle
OPL = n₁AP+n₂PB vs hit point; minimum = Snell path.
Chromatic Aberration
Cauchy n(λ); thin-lens f(λ); paraxial rays R/G/B.
Diffraction
Single and double slit with interference patterns.
Color Mixing
Additive (RGB) and subtractive (CMY) interactive color mixing.
Polarization (Malus)
Two polarizers. Rotate θ, see I = I₁ cos²θ and extinction.
Birefringence (Calcite sketch)
Two scalar Snell paths for n_o and n_e — double refraction cartoon (not full optic-axis walk-off).
Holography (Recording principle)
Toy 2D interference |E_ref + E_obj|²: fringes encode phase; readout diffraction not simulated.