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Sandbox Physics

Optics 035 · Imaging, instruments, and visual systems

Pupils, Stops & Vignetting

An independently initialized three-dimensional apparatus connects Aperture-stop search, Entrance and exit pupils, Mechanical vignetting. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelPupils, Stops & Vignetting
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 Pupils, Stops & Vignetting

BackgroundPupils, Stops & Vignetting is one independently initialized apparatus with three linked investigations: Aperture-stop search, Entrance and exit pupils, Mechanical vignetting. Its two controls—Aperture radius and Field angle—feed the governing relation NA=nsin⁡θmax⁡\mathrm{NA}=n\sin\theta_{\max}. The validity indicator marks the paraxial, lossless, weak-field, or steady-state assumption used by this apparatus.

Why it mattersWhich stop limits aperture, which limits field, and where do their pupils appear?

Start with the essentials

Focus question
Which stop limits aperture, which limits field, and where do their pupils appear?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from NA=nsin⁡θmax⁡\mathrm{NA}=n\sin\theta_{\max}. 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

NA=nsin⁡θmax⁡\mathrm{NA}=n\sin\theta_{\max}

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: Aperture-stop search

    Select Aperture-stop search. Sweep Aperture radius, hold Field 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: Entrance and exit pupils

    Select Entrance and exit pupils. Sweep Aperture radius, hold Field 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: Mechanical vignetting

    Select Mechanical vignetting. Sweep Aperture radius, hold Field 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.