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Sandbox Physics

Optics 022 · Imaging, instruments, and visual systems

Thick Lens Designer

An independently initialized three-dimensional apparatus connects Two spherical refractions, Principal-plane tracking, Thin-lens error map. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelThick Lens Designer
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 Thick Lens Designer

BackgroundThick Lens Designer is one independently initialized apparatus with three linked investigations: Two spherical refractions, Principal-plane tracking, Thin-lens error map. Its two controls—Centre thickness and Refractive index—feed the governing relation 1f=(n−1) ⁣(1R1−1R2+(n−1)dnR1R2)\frac{1}{f}=(n-1)\!\left(\frac{1}{R_1}-\frac{1}{R_2}+\frac{(n-1)d}{nR_1R_2}\right). The validity indicator marks the paraxial, lossless, weak-field, or steady-state assumption used by this apparatus.

Why it mattersWhat does the thin-lens approximation miss when curvature and thickness are both adjustable?

Start with the essentials

Focus question
What does the thin-lens approximation miss when curvature and thickness are both adjustable?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from 1f=(n−1) ⁣(1R1−1R2+(n−1)dnR1R2)\frac{1}{f}=(n-1)\!\left(\frac{1}{R_1}-\frac{1}{R_2}+\frac{(n-1)d}{nR_1R_2}\right). 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

1f=(n−1) ⁣(1R1−1R2+(n−1)dnR1R2)\frac{1}{f}=(n-1)\!\left(\frac{1}{R_1}-\frac{1}{R_2}+\frac{(n-1)d}{nR_1R_2}\right)

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: Two spherical refractions

    Select Two spherical refractions. Sweep Centre thickness, hold Refractive index 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: Principal-plane tracking

    Select Principal-plane tracking. Sweep Centre thickness, hold Refractive index 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: Thin-lens error map

    Select Thin-lens error map. Sweep Centre thickness, hold Refractive index 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.