Skip to main content
Sandbox Physics

Optics 009 · Ray worlds, boundaries, and natural optics

Window & Glass Slab Lab

An independently initialized three-dimensional apparatus connects Parallel-plate displacement, Double-pane ghosts, Tilted coated window. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelWindow & Glass Slab 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 Window & Glass Slab Lab

BackgroundWindow & Glass Slab Lab is one independently initialized apparatus with three linked investigations: Parallel-plate displacement, Double-pane ghosts, Tilted coated window. Its two controls—Slab thickness and Incident angle—feed the governing relation d=t sin⁡(θi−θt)cos⁡θtd=t\,\frac{\sin(\theta_i-\theta_t)}{\cos\theta_t}. The validity indicator marks the paraxial, lossless, weak-field, or steady-state assumption used by this apparatus.

Why it mattersWhy is the emerging ray parallel yet displaced, and why do windows make ghost images at night?

Start with the essentials

Focus question
Why is the emerging ray parallel yet displaced, and why do windows make ghost images at night?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from d=t sin⁡(θi−θt)cos⁡θtd=t\,\frac{\sin(\theta_i-\theta_t)}{\cos\theta_t}. 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

d=t sin⁡(θi−θt)cos⁡θtd=t\,\frac{\sin(\theta_i-\theta_t)}{\cos\theta_t}

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: Parallel-plate displacement

    Select Parallel-plate displacement. Sweep Slab thickness, hold Incident 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: Double-pane ghosts

    Select Double-pane ghosts. Sweep Slab thickness, hold Incident 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: Tilted coated window

    Select Tilted coated window. Sweep Slab thickness, hold Incident 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.