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Sandbox Physics

Optics 048 · Interference, coherence, cavities, and metrology

Fabry–Pérot Passive Cavity

An independently initialized three-dimensional apparatus connects Airy transmission, Finesse and linewidth, Critical coupling and lifetime. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelFabry–Pérot Passive Cavity
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 Fabry–Pérot Passive Cavity

BackgroundFabry–Pérot Passive Cavity is one independently initialized apparatus with three linked investigations: Airy transmission, Finesse and linewidth, Critical coupling and lifetime. Its two controls—Mirror reflectivity and Detuning phase—feed the governing relation T(δ)=11+Fsin⁡2(δ/2)T(\delta)=\frac{1}{1+F\sin^2(\delta/2)}. The validity indicator marks the paraxial, lossless, weak-field, or steady-state assumption used by this apparatus.

Why it mattersHow do mirror reflectivity and round-trip phase create narrow passive-cavity resonances?

Start with the essentials

Focus question
How do mirror reflectivity and round-trip phase create narrow passive-cavity resonances?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from T(δ)=11+Fsin⁡2(δ/2)T(\delta)=\frac{1}{1+F\sin^2(\delta/2)}. 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

T(δ)=11+Fsin⁡2(δ/2)T(\delta)=\frac{1}{1+F\sin^2(\delta/2)}

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: Airy transmission

    Select Airy transmission. Sweep Mirror reflectivity, hold Detuning phase 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: Finesse and linewidth

    Select Finesse and linewidth. Sweep Mirror reflectivity, hold Detuning phase 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: Critical coupling and lifetime

    Select Critical coupling and lifetime. Sweep Mirror reflectivity, hold Detuning phase 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.