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Sandbox Physics

Optics 046 · Interference, coherence, cavities, and metrology

LIGO Interferometer

An independently initialized three-dimensional apparatus connects Dark-port Michelson, Fabry–Pérot arm gain, Noise-budget chirp. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelLIGO Interferometer
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 LIGO Interferometer

BackgroundLIGO Interferometer is one independently initialized apparatus with three linked investigations: Dark-port Michelson, Fabry–Pérot arm gain, Noise-budget chirp. Its two controls—Strain exponent and Signal frequency—feed the governing relation h=ΔLLh=\frac{\Delta L}{L}. The validity indicator marks the paraxial, lossless, weak-field, or steady-state assumption used by this apparatus.

Why it mattersHow does a power-recycled kilometer-scale interferometer turn strain into a dark-port signal?

Start with the essentials

Focus question
How does a power-recycled kilometer-scale interferometer turn strain into a dark-port signal?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from h=ΔLLh=\frac{\Delta L}{L}. 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

h=ΔLLh=\frac{\Delta L}{L}

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: Dark-port Michelson

    Select Dark-port Michelson. Sweep Strain exponent, hold Signal frequency 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: Fabry–Pérot arm gain

    Select Fabry–Pérot arm gain. Sweep Strain exponent, hold Signal frequency 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: Noise-budget chirp

    Select Noise-budget chirp. Sweep Strain exponent, hold Signal frequency 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.