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Sandbox Physics

Optics 008 · Ray worlds, boundaries, and natural optics

Underwater Vision

An independently initialized three-dimensional apparatus connects Apparent depth, Fishing aim correction, Snell window. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelUnderwater Vision
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 Underwater Vision

BackgroundUnderwater Vision is one independently initialized apparatus with three linked investigations: Apparent depth, Fishing aim correction, Snell window. Its two controls—Object depth and Water refractive index—feed the governing relation nwsin⁡θw=nasin⁡θan_{\mathrm w}\sin\theta_{\mathrm w}=n_{\mathrm a}\sin\theta_{\mathrm a}. The validity indicator marks the paraxial, lossless, weak-field, or steady-state assumption used by this apparatus.

Why it mattersWhy do depth, aiming, and the visible sky all change across the water surface?

Start with the essentials

Focus question
Why do depth, aiming, and the visible sky all change across the water surface?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from nwsin⁡θw=nasin⁡θan_{\mathrm w}\sin\theta_{\mathrm w}=n_{\mathrm a}\sin\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

nwsin⁡θw=nasin⁡θan_{\mathrm w}\sin\theta_{\mathrm w}=n_{\mathrm a}\sin\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: Apparent depth

    Select Apparent depth. Sweep Object depth, hold Water 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: Fishing aim correction

    Select Fishing aim correction. Sweep Object depth, hold Water 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: Snell window

    Select Snell window. Sweep Object depth, hold Water 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.