Skip to main content
Sandbox Physics

Optics 011 · Ray worlds, boundaries, and natural optics

Rainbow Laboratory

An independently initialized three-dimensional apparatus connects Primary bow, Secondary bow, Supernumerary wave correction. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelRainbow Laboratory
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 Rainbow Laboratory

BackgroundRainbow Laboratory is one independently initialized apparatus with three linked investigations: Primary bow, Secondary bow, Supernumerary wave correction. Its two controls—Droplet radius and Wavelength—feed the governing relation nsin⁡r=sin⁡in\sin r=\sin i. The validity indicator marks the paraxial, lossless, weak-field, or steady-state assumption used by this apparatus.

Why it mattersHow can one water drop create primary and secondary bows with a dark band between them?

Start with the essentials

Focus question
How can one water drop create primary and secondary bows with a dark band between them?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from nsin⁡r=sin⁡in\sin r=\sin i. 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

nsin⁡r=sin⁡in\sin r=\sin i

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: Primary bow

    Select Primary bow. Sweep Droplet radius, hold Wavelength 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: Secondary bow

    Select Secondary bow. Sweep Droplet radius, hold Wavelength 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: Supernumerary wave correction

    Select Supernumerary wave correction. Sweep Droplet radius, hold Wavelength 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.