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Sandbox Physics

Optics 024 · Imaging, instruments, and visual systems

Parfocal Zoom Challenge

An independently initialized three-dimensional apparatus connects Wide-angle endpoint, Parfocal trajectory, Telephoto endpoint. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelParfocal Zoom Challenge
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 Parfocal Zoom Challenge

BackgroundParfocal Zoom Challenge is one independently initialized apparatus with three linked investigations: Wide-angle endpoint, Parfocal trajectory, Telephoto endpoint. Its two controls—Zoom group separation and Compensator position—feed the governing relation B(Mzoom)=0B(\mathbf M_{\mathrm{zoom}})=0. The validity indicator marks the paraxial, lossless, weak-field, or steady-state assumption used by this apparatus.

Why it mattersCan moving lens groups change focal length while the image plane stays fixed?

Start with the essentials

Focus question
Can moving lens groups change focal length while the image plane stays fixed?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from B(Mzoom)=0B(\mathbf M_{\mathrm{zoom}})=0. 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

B(Mzoom)=0B(\mathbf M_{\mathrm{zoom}})=0

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: Wide-angle endpoint

    Select Wide-angle endpoint. Sweep Zoom group separation, hold Compensator position 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: Parfocal trajectory

    Select Parfocal trajectory. Sweep Zoom group separation, hold Compensator position 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: Telephoto endpoint

    Select Telephoto endpoint. Sweep Zoom group separation, hold Compensator position 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.