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Sandbox Physics

Optics 020 · Ray worlds, boundaries, and natural optics

Gravitational Lens Telescope

An independently initialized three-dimensional apparatus connects Einstein ring, Multiple-image arcs, Microlensing light curve. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelGravitational Lens Telescope
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 Gravitational Lens Telescope

BackgroundGravitational Lens Telescope is one independently initialized apparatus with three linked investigations: Einstein ring, Multiple-image arcs, Microlensing light curve. Its two controls—Lens mass solar and Normalized alignment—feed the governing relation θE=4GMc2DLSDLDS\theta_{\mathrm E}=\sqrt{\frac{4GM}{c^2}\frac{D_{\mathrm{LS}}}{D_{\mathrm L}D_{\mathrm S}}}. The validity indicator marks the paraxial, lossless, weak-field, or steady-state assumption used by this apparatus.

Why it mattersHow can image positions, arcs, and brightness reveal an invisible lens mass?

Start with the essentials

Focus question
How can image positions, arcs, and brightness reveal an invisible lens mass?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from θE=4GMc2DLSDLDS\theta_{\mathrm E}=\sqrt{\frac{4GM}{c^2}\frac{D_{\mathrm{LS}}}{D_{\mathrm L}D_{\mathrm S}}}. 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

θE=4GMc2DLSDLDS\theta_{\mathrm E}=\sqrt{\frac{4GM}{c^2}\frac{D_{\mathrm{LS}}}{D_{\mathrm L}D_{\mathrm S}}}

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: Einstein ring

    Select Einstein ring. Sweep Lens mass solar, hold Normalized alignment 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: Multiple-image arcs

    Select Multiple-image arcs. Sweep Lens mass solar, hold Normalized alignment 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: Microlensing light curve

    Select Microlensing light curve. Sweep Lens mass solar, hold Normalized alignment 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.