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Sandbox Physics

Optics 018 · Ray worlds, boundaries, and natural optics

Ray Cloaking Challenge

An independently initialized three-dimensional apparatus connects Four-lens Rochester cloak, Prismatic bypass, Finite-aperture failure. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelRay Cloaking Challenge
Primary prediction P1\mathcal P_10.500.50
Physical scale P2\mathcal P_250%50\%
Limit check V\mathcal V0.00π0.00\pi
Model regimevalid model regime\text{valid model regime}

Physics tutorial

How to investigate Ray Cloaking Challenge

BackgroundRay Cloaking Challenge is one independently initialized apparatus with three linked investigations: Four-lens Rochester cloak, Prismatic bypass, Finite-aperture failure. Its two controls—Outer focal length and Inner focal length—feed the governing relation Mcloak≈(1L01)\mathbf M_{\mathrm{cloak}}\approx\begin{pmatrix}1&L\\0&1\end{pmatrix}. The validity indicator marks the paraxial, lossless, weak-field, or steady-state assumption used by this apparatus.

Why it mattersCan an optical train route rays around an object and restore the background afterward?

Start with the essentials

Focus question
Can an optical train route rays around an object and restore the background afterward?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from Mcloak≈(1L01)\mathbf M_{\mathrm{cloak}}\approx\begin{pmatrix}1&L\\0&1\end{pmatrix}. Geometry and glow are presentation encodings; the equation, units, conservation or limit check, and validity indicator are the quantitative evidence.

Core mathematical model

Governing relation

Mcloak≈(1L01)\mathbf M_{\mathrm{cloak}}\approx\begin{pmatrix}1&L\\0&1\end{pmatrix}

The implementation evaluates this relation with dimensional inputs and an executable analytic or numerical benchmark. The validity indicator marks the paraxial, lossless, weak-field, or steady-state assumption used by this apparatus.

Common difficulties

Mistaking glow for measured power

Typical misconceptionA brighter cinematic trail must represent proportionally more optical power.

Better mental modelUse the detector and normalized readouts for comparison. Glow is deliberately nonlinear so weak structure stays visible.

Run the experiment

  1. 01

    Scene 1: Four-lens Rochester cloak

    Select Four-lens Rochester cloak. Sweep Outer focal length, hold Inner focal length fixed, and then reverse the roles. Drag the stage probe to repeat the first sweep directly.

    What to observe: Read the primary prediction, physical scale, limit check, and validity indicator together. Record where the approximation boundary changes.
  2. 02

    Scene 2: Prismatic bypass

    Select Prismatic bypass. Sweep Outer focal length, hold Inner focal length fixed, and then reverse the roles. Drag the stage probe to repeat the first sweep directly.

    What to observe: Read the primary prediction, physical scale, limit check, and validity indicator together. Record where the approximation boundary changes.
  3. 03

    Scene 3: Finite-aperture failure

    Select Finite-aperture failure. Sweep Outer focal length, hold Inner focal length fixed, and then reverse the roles. Drag the stage probe to repeat the first sweep directly.

    What to observe: Read the primary prediction, physical scale, limit check, and validity indicator together. Record where the approximation boundary changes.