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Sandbox Physics

Optics 045 · Interference, coherence, cavities, and metrology

Michelson Precision Lab

An independently initialized three-dimensional apparatus connects Mirror displacement, Wavelength calibration, Gas-cell refractometry. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelMichelson Precision 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 Michelson Precision Lab

BackgroundMichelson Precision Lab is one independently initialized apparatus with three linked investigations: Mirror displacement, Wavelength calibration, Gas-cell refractometry. Its two controls—Mirror displacement and Cell index change—feed the governing relation m=2Δxλm=\frac{2\Delta x}{\lambda}. The validity indicator marks the paraxial, lossless, weak-field, or steady-state assumption used by this apparatus.

Why it mattersHow can counting fringes measure displacement, wavelength, and refractive index?

Start with the essentials

Focus question
How can counting fringes measure displacement, wavelength, and refractive index?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from m=2Δxλm=\frac{2\Delta x}{\lambda}. 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

m=2Δxλm=\frac{2\Delta x}{\lambda}

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: Mirror displacement

    Select Mirror displacement. Sweep Mirror displacement, hold Cell index change 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: Wavelength calibration

    Select Wavelength calibration. Sweep Mirror displacement, hold Cell index change 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: Gas-cell refractometry

    Select Gas-cell refractometry. Sweep Mirror displacement, hold Cell index change 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.