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Sandbox Physics

Optics 028 · Imaging, instruments, and visual systems

Anamorphic & Cylindrical Optics

An independently initialized three-dimensional apparatus connects Cylindrical line focus, Anamorphic squeeze, Elliptic bokeh and laser line. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelAnamorphic & Cylindrical Optics
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 Anamorphic & Cylindrical Optics

BackgroundAnamorphic & Cylindrical Optics is one independently initialized apparatus with three linked investigations: Cylindrical line focus, Anamorphic squeeze, Elliptic bokeh and laser line. Its two controls—Horizontal focal length and Vertical focal length—feed the governing relation Aanam=MxMyA_{\mathrm{anam}}=\frac{M_x}{M_y}. The validity indicator marks the paraxial, lossless, weak-field, or steady-state assumption used by this apparatus.

Why it mattersHow can orthogonal optical power reshape one image axis without focusing the other?

Start with the essentials

Focus question
How can orthogonal optical power reshape one image axis without focusing the other?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from Aanam=MxMyA_{\mathrm{anam}}=\frac{M_x}{M_y}. 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

Aanam=MxMyA_{\mathrm{anam}}=\frac{M_x}{M_y}

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: Cylindrical line focus

    Select Cylindrical line focus. Sweep Horizontal focal length, hold Vertical 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: Anamorphic squeeze

    Select Anamorphic squeeze. Sweep Horizontal focal length, hold Vertical 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: Elliptic bokeh and laser line

    Select Elliptic bokeh and laser line. Sweep Horizontal focal length, hold Vertical 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.