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Sandbox Physics

Optics 012 · Ray worlds, boundaries, and natural optics

Atmospheric Refraction Theatre

An independently initialized three-dimensional apparatus connects Inferior mirage, Superior mirage and looming, Fata Morgana and green flash. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelAtmospheric Refraction Theatre
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 Atmospheric Refraction Theatre

BackgroundAtmospheric Refraction Theatre is one independently initialized apparatus with three linked investigations: Inferior mirage, Superior mirage and looming, Fata Morgana and green flash. Its two controls—Index gradient per and Launch angle—feed the governing relation dds ⁣(nt^)=∇n\frac{\mathrm d}{\mathrm ds}\!\left(n\hat{\mathbf t}\right)=\nabla n. The validity indicator marks the paraxial, lossless, weak-field, or steady-state assumption used by this apparatus.

Why it mattersWhat vertical refractive-index profile produces each mirage and horizon distortion?

Start with the essentials

Focus question
What vertical refractive-index profile produces each mirage and horizon distortion?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from dds ⁣(nt^)=∇n\frac{\mathrm d}{\mathrm ds}\!\left(n\hat{\mathbf t}\right)=\nabla n. 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

dds ⁣(nt^)=∇n\frac{\mathrm d}{\mathrm ds}\!\left(n\hat{\mathbf t}\right)=\nabla n

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: Inferior mirage

    Select Inferior mirage. Sweep Index gradient per, hold Launch angle 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: Superior mirage and looming

    Select Superior mirage and looming. Sweep Index gradient per, hold Launch angle 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: Fata Morgana and green flash

    Select Fata Morgana and green flash. Sweep Index gradient per, hold Launch angle 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.