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Sandbox Physics

Optics 014 · Ray worlds, boundaries, and natural optics

Shadow & Eclipse Lab

An independently initialized three-dimensional apparatus connects Point and extended sources, Solar and lunar eclipse, Transit and annular shadow. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelShadow & Eclipse Lab
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 Shadow & Eclipse Lab

BackgroundShadow & Eclipse Lab is one independently initialized apparatus with three linked investigations: Point and extended sources, Solar and lunar eclipse, Transit and annular shadow. Its two controls—Occluder radius and Observer distance—feed the governing relation αs≶αo\alpha_{\mathrm s}\lessgtr\alpha_{\mathrm o}. The validity indicator marks the paraxial, lossless, weak-field, or steady-state assumption used by this apparatus.

Why it mattersHow do source size and alignment divide space into umbra, penumbra, and antumbra?

Start with the essentials

Focus question
How do source size and alignment divide space into umbra, penumbra, and antumbra?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from αs≶αo\alpha_{\mathrm s}\lessgtr\alpha_{\mathrm o}. 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

αs≶αo\alpha_{\mathrm s}\lessgtr\alpha_{\mathrm o}

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: Point and extended sources

    Select Point and extended sources. Sweep Occluder radius, hold Observer distance 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: Solar and lunar eclipse

    Select Solar and lunar eclipse. Sweep Occluder radius, hold Observer distance 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: Transit and annular shadow

    Select Transit and annular shadow. Sweep Occluder radius, hold Observer distance 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.