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Sandbox Physics

Optics 050 · Interference, coherence, cavities, and metrology

Division-of-Wavefront Interferometers

An independently initialized three-dimensional apparatus connects Lloyd mirror, Fresnel biprism, Fresnel mirrors. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelDivision-of-Wavefront Interferometers
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 Division-of-Wavefront Interferometers

BackgroundDivision-of-Wavefront Interferometers is one independently initialized apparatus with three linked investigations: Lloyd mirror, Fresnel biprism, Fresnel mirrors. Its two controls—Virtual source separation and Reflection phase—feed the governing relation Δϕ=2πλΔL+ϕr\Delta\phi=\frac{2\pi}{\lambda}\Delta L+\phi_{\mathrm r}. The validity indicator marks the paraxial, lossless, weak-field, or steady-state assumption used by this apparatus.

Why it mattersHow do different virtual-source constructions change phase, overlap, and usable fringe area?

Start with the essentials

Focus question
How do different virtual-source constructions change phase, overlap, and usable fringe area?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from Δϕ=2πλΔL+ϕr\Delta\phi=\frac{2\pi}{\lambda}\Delta L+\phi_{\mathrm r}. 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

Δϕ=2πλΔL+ϕr\Delta\phi=\frac{2\pi}{\lambda}\Delta L+\phi_{\mathrm r}

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: Lloyd mirror

    Select Lloyd mirror. Sweep Virtual source separation, hold Reflection 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: Fresnel biprism

    Select Fresnel biprism. Sweep Virtual source separation, hold Reflection 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: Fresnel mirrors

    Select Fresnel mirrors. Sweep Virtual source separation, hold Reflection 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.