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Motion & dynamical systems
Double Pendulum & Chaos
How long can nearly identical starts share one trajectory?
Open LabHow Orbits Take Shape
How can one force law draw three different conic sections?
Open LabHow Coupled Springs Move Together
Can collective motion be decomposed into clean modes?
Open LabBinary Neutron Star Merger
How does a rising chirp foretell tidal collision, kilonova ejecta, and a compact remnant?
Open LabHow a Black Hole Bends Light
Why can one thin accretion disk appear both above and below the black-hole shadow?
Open LabThe Three-Body Dance
Why does one extra body remove the general orbit formula?
Open Lab
Waves & optics
When Two Waves Meet
Why do passing waves leave a stable fringe pattern?
Open LabDraw Any Wave with Circles
How can steady rotations rebuild almost any periodic signal?
Open LabLight after a Narrow Slit
Why does a narrower opening spread light farther?
Open LabHow a Lens Redirects Light
How do three principal rays locate and size an image?
Open LabListen to Spacetime with Light
How can a sub-proton length change become a readable signal?
Open LabHow One Opening Redraws a Water Wave
Why does narrowing an opening spread the transmitted wave through a wider angle?
Open LabTwo Refractions inside a Thick Lens
What does the thin-lens model miss when thickness matters?
Open LabA Rainbow Only Nanometres Thick
Why does a colorless film only hundreds of nanometres thick develop flowing color?
Open LabHow a Laser Builds inside a Cavity
Which waves return between two mirrors and keep growing?
Open LabOptical Boundary Explorer
How do angle, polarization, speed, and energy change together at one boundary?
Open LabHall of Mirrors
Which virtual images can an observer actually see as mirrors move?
Open LabMirror Engineering Challenge
Can a compact mirror network steer a beam without losing field of view?
Open LabCurved Mirror Observatory
How does mirror shape move the focus and change off-axis image quality?
Open LabCaustic Factory
How does a smooth family of rays collapse into a brilliant singular envelope?
Open LabFloating Image Mirascope
Where must two parabolic mirrors place a real image that can be seen but not touched?
Open LabFermat Path Finder
Why does a stationary travel-time path reproduce reflection, refraction, and curved rays?
Open LabUnderwater Vision Observatory
How can one flat water boundary move a fish, mislead a spear, compress the whole sky, and distort a camera port?
Open LabWindow Ghost Observatory
Why is the emerging ray parallel yet displaced, and why do windows make ghost images at night?
Open LabN-BK7 Prism Spectrometer Observatory
How can minimum deviation turn a glass prism into a calibrated wavelength instrument?
Open LabRainbow Caustic Observatory
How can one water drop create primary and secondary bows with a dark band between them?
Open LabMirage & Green-Flash Observatory
How do measured air dispersion and a prescribed thermal profile bend one horizon into depressed, loomed, and multiply imaged views?
Open LabGRIN Geometry Observatory
How can one continuous index field relay a ray, focus every direction, or turn plane curves into great circles without a hidden interface?
Open LabEclipse & Transit Shadow Observatory
How do two measured apparent disks generate sharp point-source shadow, umbra, penumbra, antumbra, eclipse contacts, and a transit light curve from one geometry?
Open LabUnilluminable Room
Can a mirrored room keep a finite region dark from one point source after many exact reflections?
Open LabSolar Concentrator & Étendue
Why can no passive concentrator squeeze every incoming direction into an arbitrarily small hot spot?
Open LabIllumination & Radiometry Studio
How can source size, distance, and surface angle create uniform illumination?
Open LabRay Cloaking Challenge
Can an optical train route rays around an object and restore the background afterward?
Open LabBranched Light in Random Media
Why does weak smooth disorder focus parallel rays into branches instead of simple diffusion?
Open LabGravitational Lens Telescope
How can image positions, arcs, and brightness reveal an invisible lens mass?
Open LabThin Lens Imaging Bench
How do three principal rays locate every real and virtual thin-lens image?
Open LabThick Lens Designer
What does the thin-lens approximation miss when curvature and thickness are both adjustable?
Open LabCompound Optics Workbench
How can one matrix predict imaging, magnification, and afocal behavior in a whole optical train?
Open LabParfocal Zoom Challenge
Can moving lens groups change focal length while the image plane stays fixed?
Open LabCamera Obscura
Which pinhole balances geometric blur against diffraction blur for the sharpest image?
Open LabPhotography Optics Playground
How do focal length, aperture, focus distance, and sensor size trade perspective against depth of field?
Open LabLens Aberration Clinic
Which optical correction cures each spot-diagram signature without creating a worse one elsewhere?
Open LabAnamorphic & Cylindrical Optics
How can orthogonal optical power reshape one image axis without focusing the other?
Open LabHuman Eye & Corrective Optics
Which correction returns the retinal point-spread function for each refractive error?
Open LabBuild a Microscope
How should objective, illumination, and detector share numerical aperture to resolve a tiny object?
Open LabBuild a Telescope
How do aperture, optical layout, and obstruction determine what a telescope can resolve?
Open LabBinocular Prism Lab
How do prism geometry and phase errors erect an image while preserving contrast?
Open LabTelecentric Metrology Camera
How can stop placement make magnification insensitive to object depth?
Open LabTilt-Shift & Scheimpflug Studio
How does tilting the lens rotate the plane of focus and reshape depth of field?
Open LabPupils, Stops & Vignetting
Which stop limits aperture, which limits field, and where do their pupils appear?
Open LabProjector Optics Lab
How must illumination, imaging, and étendue match to make a bright, sharp projection?
Open LabSmartphone Camera Module
Which optical trade-offs fit wide, telephoto, periscope, and macro imaging into a thin phone?
Open LabVR Headset Optics
How do display distance, eye box, and lens design trade field of view against comfort and distortion?
Open LabGhost Image, Pepper’s Ghost & HUD
How can a tilted combiner place a bright virtual overlay at the right apparent distance?
Open LabLight-Field Camera & Display
How does recording direction as well as position enable refocus and viewpoint change after capture?
Open LabCoherent Wave Composer
How do phasors, wavefronts, and detector intensity tell the same superposition story?
Open LabYoung Double-Slit Bench
How do slit width, separation, phase, and coherence jointly shape one fringe pattern?
Open LabThin-Film Color Studio
How can one editable layer stack produce bubbles, coatings, mirrors, and structural color?
Open LabInterference Surface Metrology
How can fringe geometry reveal thickness, curvature, and tiny surface defects?
Open LabMichelson Precision Lab
How can counting fringes measure displacement, wavelength, and refractive index?
Open LabLIGO Interferometer
How does a power-recycled kilometer-scale interferometer turn strain into a dark-port signal?
Open LabMach–Zehnder Sensor
How do complementary outputs separate phase, absorption, and which-path information?
Open LabFabry–Pérot Passive Cavity
How do mirror reflectivity and round-trip phase create narrow passive-cavity resonances?
Open LabSagnac Gyroscope
Why does rotation create a nonreciprocal phase between counterpropagating beams?
Open LabDivision-of-Wavefront Interferometers
How do different virtual-source constructions change phase, overlap, and usable fringe area?
Open LabLow-Coherence Interferometry & OCT
How does a short coherence gate turn reflected light into a depth-resolved image?
Open LabStellar Interferometer
How can visibility versus baseline reveal a star too small for either telescope to resolve?
Open LabSpeckle Lab
How does random coherent phase create structured grains with predictable statistics?
Open LabHolography Studio
How can an intensity-only plate preserve enough phase information to reconstruct a three-dimensional wavefront?
Open LabMoiré & Fringe Metrology
How can coarse fringe motion amplify and recover tiny displacement or surface shape?
Open LabHuygens–Fresnel Propagation Lab
How does a field evolve continuously from near-field wavelets to a far-field diffraction pattern?
Open LabAperture Diffraction Studio
How does drawing a new aperture rewrite its entire far-field intensity pattern?
Open LabCrystal Diffraction & Reciprocal Space
How can reciprocal-space spots and rings reveal an unknown real-space lattice?
Open LabDiffraction-Grating Spectrometer
How do groove count, blaze, slit width, and order overlap set spectral resolution?
Open LabDiffractive Lens Workshop
How do zone placement and phase quantization trade focal efficiency against chromatic behavior?
Open LabTalbot Carpet
Why does a periodic grating reproduce shifted and multiplied copies of itself during propagation?
Open LabOptical Fourier Processor
How does moving one filter in a Fourier plane rewrite edges, blur, and repeated texture in an image?
Open LabAbbe Resolution Lab
Which spatial frequencies must enter the pupil before two points or grating lines become resolvable?
Open LabPSF–OTF–MTF Imaging Lab
How do pupil shape and wavefront error become blur, contrast loss, and an image transfer curve?
Open LabPhase Microscopy Lab
How can pupil manipulation turn an invisible phase object into visible intensity contrast?
Open LabSchlieren Flow Viewer
Which optical cutoff makes temperature, density, and shock gradients visible?
Open LabPupil Engineering & Coronagraph
How can masks and apodizers suppress a star without erasing a nearby planet?
Open LabPhase Retrieval Challenge
Can intensity-only measurements recover a complex field despite ambiguity and noise?
Open LabCoded-Aperture Camera
How can a patterned shadow encode a scene without a conventional lens?
Open LabComputational Deblurring Lab
When does deconvolution recover detail, and when does it only amplify noise or model error?
Open LabAdaptive Optics Observatory
How can measured wavefront slopes drive a mirror fast enough to sharpen a turbulent star image?
Open LabPtychography & Coherent Diffraction Imaging
How does overlapping illumination make a lensless amplitude-and-phase reconstruction possible?
Open LabPolarization State Explorer
How do intensity, ellipse shape, Jones vectors, and Stokes measurements encode the same polarization state?
Open LabPolarized Reflections & Sky
Why can one rotating filter darken water glare and blue sky in different directions?
Open LabBirefringent Crystal Lab
How does crystal orientation split one ray into ordinary and extraordinary propagation?
Open LabWaveplate & Poincaré Sphere Lab
How does each retarder rotate a polarization state along a precise path on the Poincaré sphere?
Open LabOptical Activity Polarimeter
How can a crossed analyzer determine concentration and handedness in a chiral sample?
Open LabPhotoelastic Stress Viewer
How do colorful polarization fringes map the principal-stress difference inside a loaded object?
Open LabLCD Pixel Microscope
How does voltage-controlled liquid-crystal rotation become RGB brightness and viewing-angle leakage?
Open LabTIR Phase & Fresnel Rhomb
How can total reflection create broadband retardance even though no power is transmitted?
Open LabFaraday Isolator
Why does a nonreciprocal rotation transmit forward light yet reject the same light on return?
Open LabElectro-Optic Modulator
How does an electric field become controllable optical phase and then measurable intensity modulation?
Open LabOptical Fiber: Rays to Modes
When must the total-reflection ray picture be replaced by a guided-mode picture?
Open LabFiber Pulse Propagation
How do dispersion and chirp broaden, compress, or reshape an ultrashort pulse in fiber?
Open LabEvanescent Directional Coupler
How do gap and interaction length transfer power between neighboring waveguides?
Open LabMicroring & Whispering-Gallery Resonator
How do ring size, loss, and bus coupling create a sharp resonance dip and circulating field?
Open LabPhotonic Crystal Band Structure
How does periodic dielectric structure create band gaps, defect states, and guided channels?
Open LabBoundary Wave Tunnel
How can an evanescent field cross a narrow gap and restore transmission beyond total reflection?
Open LabBeam Shift Microscope
How do finite beam width and polarization reveal tiny longitudinal and transverse interface shifts?
Open LabGaussian Beam & Gouy Phase
How do waist, divergence, lens transformation, and Gouy phase describe one focused beam?
Open LabSelf-Healing Beam Arena
How can Bessel and Airy beams reconstruct after an obstacle, and what energy trade-off pays for it?
Open LabLight in Disorder
How does increasing disorder move wave transport from scattering to diffusion and localization?
Open LabOptical Vortex & OAM
How does a phase singularity create a dark core, helical wavefront, and measurable orbital angular momentum?
Open LabVector Beams & Optical Skyrmions
How can a spatial polarization field wrap the Poincaré sphere and acquire a topological number?
Open LabPhotonic Nanojet & Hook
How do particle shape and index create a subwavelength jet or a sharply curved optical hook?
Open LabSuperoscillation Designer
How can a band-limited field make a tiny hotspot while paying in sidelobes, efficiency, and field of view?
Open LabSurface Plasmon Resonance Lab
How does phase matching transfer prism light into a lossy surface wave that senses refractive index?
Open LabNegative Refraction & Superlens
How can a negative-index slab reverse refraction and recover normally lost evanescent detail?
Open LabTopological Photonic Edge State
Why can an edge mode cross defects and corners with much less backscattering than an ordinary guide?
Open LabNonlinear Light Shapes Its Own Medium
When does optical intensity write an index profile strong enough to focus or guide the beam itself?
Open LabAbsorption, Spontaneous & Stimulated Emission
When does resonant light cause net absorption, random emission, or coherent amplification?
Open LabPumping & Population Inversion
Why is continuous inversion difficult in two levels but practical in three- and four-level schemes?
Open LabLaser Startup from Noise
How does spontaneous-emission noise become a saturated, mode-selected laser field above threshold?
Open LabStable Resonator & Transverse Modes
Which mirror geometry produces a stable low-loss cavity dominated by the fundamental transverse mode?
Open LabQ-Switched Giant Pulse
How can stored inversion be released as one giant pulse instead of leaking into premature lasing?
Open LabMode Locking & Frequency Comb
How does locking many longitudinal phases transform continuous output into a pulse train and frequency comb?
Open Lab
Fields, fluids & matter
How an Offset Circle Becomes a Lifting Airfoil
How do geometry, angle of attack, and the Kutta condition select circulation and pressure difference?
Open LabMake an Electric Field Visible
How does the shape of potential predict the next force?
Open LabBillions of Collisions in a Gas
How do random collisions become stable macroscopic laws?
Open LabA Charge Bending through Fields
How can a magnetic field turn motion without changing speed?
Open LabWhy a Spinning Ball Curves
How does spin rearrange flow and create a sideways force?
Open LabHow One Moving Wall Drives an Entire Fluid
Why does a right-moving lid create one giant clockwise circulation inside a sealed cavity?
Open LabPush a Numerical Jet by Hand
How do advection, diffusion, and pressure projection separately change dye, vortices, and divergence?
Open LabHow Phase Turns Flapping into Propulsion
How does the phase between heave and pitch change unsteady lift, wake direction, and cycle-averaged thrust?
Open LabWhy a Symmetric Wake Breaks Itself
Why do the two shear layers shed alternately even when the cylinder remains fixed?
Open LabHow a Thermal Gradient Organizes into Rolls
When can buoyancy defeat viscous and thermal diffusion to destabilize a quiet conducting layer?
Open LabImmune Design from Molecule to Organoid
How can one molecular recognition event cross a cell threshold and become tissue-wide clearance?
Open LabFrom Hard Spheres to Boltzmann
How can deterministic collisions be compressed into a reliable kinetic equation while controlling recollision correlations?
Open LabWhy a Smoke Ring Propels Itself
If fluid rotates around the toroidal core, why does the whole vortex ring travel along the nozzle axis?
Open LabHow Rotating Shear Fractures into Taylor Cells
Why does purely azimuthal Couette flow grow radial–axial secondary circulation?
Open LabWBE and the Quarter-Power Pace of Life
How can a space-filling delivery network connect body mass to metabolism and biological time?
Open LabHow Stars Build Elements up to Iron
Why does fusion release energy only until nuclei approach iron?
Open Lab
Quantum & fields
How Cooper Pairs Condense
How can a fermion pair evolve continuously from a cloud-wide correlation into a composite bosonic molecule that condenses?
Open LabRotate a Qubit
Where does phase hide when Z-basis probabilities stay fixed?
Open LabCan a Particle Cross an Impossible Wall?
When classical transmission is zero, why can a quantum detector still click beyond the barrier?
Open LabCan One Particle Interfere?
How do unpredictable hits accumulate into stable fringes?
Open LabHow a Field Becomes Quantized
How can a continuous field produce discrete particle excitations?
Open LabHow One-Dimensional Bulk Topology Creates an Edge
Why can exchanging two bond strengths pin a zero-energy state to the end of a chain?
Open LabWhy an Edge Packet Routes Around a Defect
How does a Chern number convert bulk-band geometry into one-way edge transport?
Open LabHall Topology at Zero Net Flux
How do the signs of two Dirac-valley masses decide whether a honeycomb lattice is trivial or Chern insulating?
Open LabHow One Band Splits into the Hofstadter Butterfly
How does a rational-flux denominator enlarge the magnetic cell and reorganize bands and Hall gaps?
Open LabHow to Read a Particle Collision
How can curved tracks, energy clusters, and momentum imbalance reconstruct an unseen collision?
Open LabHow a Knot Becomes a Quantum-Field Observable
Why can a knot diagram change while a Wilson-loop expectation depends only on its topology?
Open Lab