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Sandbox Physics

Optics 015 · Ray worlds, boundaries, and natural optics

Unilluminable Room

An independently initialized three-dimensional apparatus connects Visibility graph, Penrose room, Specular versus diffuse walls. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelUnilluminable Room
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 Unilluminable Room

BackgroundUnilluminable Room is one independently initialized apparatus with three linked investigations: Visibility graph, Penrose room, Specular versus diffuse walls. Its two controls—Source horizontal position and Diffuse fraction—feed the governing relation θi=θr\theta_{\mathrm i}=\theta_{\mathrm r}. The validity indicator marks the paraxial, lossless, weak-field, or steady-state assumption used by this apparatus.

Why it mattersCan a room contain points with line of sight but no valid specular light path?

Start with the essentials

Focus question
Can a room contain points with line of sight but no valid specular light path?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from θi=θr\theta_{\mathrm i}=\theta_{\mathrm r}. 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

θi=θr\theta_{\mathrm i}=\theta_{\mathrm r}

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: Visibility graph

    Select Visibility graph. Sweep Source horizontal position, hold Diffuse fraction 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: Penrose room

    Select Penrose room. Sweep Source horizontal position, hold Diffuse fraction 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: Specular versus diffuse walls

    Select Specular versus diffuse walls. Sweep Source horizontal position, hold Diffuse fraction 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.