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Sandbox Physics

Optics 036 · Imaging, instruments, and visual systems

Projector Optics Lab

An independently initialized three-dimensional apparatus connects Condenser uniformity, Projection focus and throw, Keystone and étendue limit. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelProjector Optics 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 Projector Optics Lab

BackgroundProjector Optics Lab is one independently initialized apparatus with three linked investigations: Condenser uniformity, Projection focus and throw, Keystone and étendue limit. Its two controls—Throw distance and Projection focal length—feed the governing relation TR=LW\mathrm{TR}=\frac{L}{W}. The validity indicator marks the paraxial, lossless, weak-field, or steady-state assumption used by this apparatus.

Why it mattersHow must illumination, imaging, and étendue match to make a bright, sharp projection?

Start with the essentials

Focus question
How must illumination, imaging, and étendue match to make a bright, sharp projection?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from TR=LW\mathrm{TR}=\frac{L}{W}. 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

TR=LW\mathrm{TR}=\frac{L}{W}

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: Condenser uniformity

    Select Condenser uniformity. Sweep Throw distance, hold Projection focal length 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: Projection focus and throw

    Select Projection focus and throw. Sweep Throw distance, hold Projection focal length 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: Keystone and étendue limit

    Select Keystone and étendue limit. Sweep Throw distance, hold Projection focal length 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.