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Sandbox Physics

Optics 023 · Imaging, instruments, and visual systems

Compound Optics Workbench

An independently initialized three-dimensional apparatus connects Afocal telescope, Beam expander, Relay imaging chain. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelCompound Optics Workbench
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 Compound Optics Workbench

BackgroundCompound Optics Workbench is one independently initialized apparatus with three linked investigations: Afocal telescope, Beam expander, Relay imaging chain. Its two controls—First focal length and Lens separation—feed the governing relation (y2θ2)=(ABCD)(y1θ1)\begin{pmatrix}y_2\\\theta_2\end{pmatrix}=\begin{pmatrix}A&B\\C&D\end{pmatrix}\begin{pmatrix}y_1\\\theta_1\end{pmatrix}. The validity indicator marks the paraxial, lossless, weak-field, or steady-state assumption used by this apparatus.

Why it mattersHow can one matrix predict imaging, magnification, and afocal behavior in a whole optical train?

Start with the essentials

Focus question
How can one matrix predict imaging, magnification, and afocal behavior in a whole optical train?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from (y2θ2)=(ABCD)(y1θ1)\begin{pmatrix}y_2\\\theta_2\end{pmatrix}=\begin{pmatrix}A&B\\C&D\end{pmatrix}\begin{pmatrix}y_1\\\theta_1\end{pmatrix}. 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

(y2θ2)=(ABCD)(y1θ1)\begin{pmatrix}y_2\\\theta_2\end{pmatrix}=\begin{pmatrix}A&B\\C&D\end{pmatrix}\begin{pmatrix}y_1\\\theta_1\end{pmatrix}

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: Afocal telescope

    Select Afocal telescope. Sweep First focal length, hold Lens separation 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: Beam expander

    Select Beam expander. Sweep First focal length, hold Lens separation 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: Relay imaging chain

    Select Relay imaging chain. Sweep First focal length, hold Lens separation 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.