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Sandbox Physics

Optics 016 · Ray worlds, boundaries, and natural optics

Solar Concentrator & Étendue

An independently initialized three-dimensional apparatus connects Parabolic trough, Compound concentrator, Light-pipe acceptance limit. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelSolar Concentrator & Étendue
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 Solar Concentrator & Étendue

BackgroundSolar Concentrator & Étendue is one independently initialized apparatus with three linked investigations: Parabolic trough, Compound concentrator, Light-pipe acceptance limit. Its two controls—Acceptance half angle and Refractive index—feed the governing relation Cmax⁡=n2sin⁡2θaC_{\max}=\frac{n^2}{\sin^2\theta_{\mathrm a}}. The validity indicator marks the paraxial, lossless, weak-field, or steady-state assumption used by this apparatus.

Why it mattersWhy can no passive concentrator squeeze every incoming direction into an arbitrarily small hot spot?

Start with the essentials

Focus question
Why can no passive concentrator squeeze every incoming direction into an arbitrarily small hot spot?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from Cmax⁡=n2sin⁡2θaC_{\max}=\frac{n^2}{\sin^2\theta_{\mathrm a}}. 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

Cmax⁡=n2sin⁡2θaC_{\max}=\frac{n^2}{\sin^2\theta_{\mathrm a}}

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: Parabolic trough

    Select Parabolic trough. Sweep Acceptance half angle, hold Refractive index 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: Compound concentrator

    Select Compound concentrator. Sweep Acceptance half angle, hold Refractive index 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: Light-pipe acceptance limit

    Select Light-pipe acceptance limit. Sweep Acceptance half angle, hold Refractive index 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.