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Sandbox Physics

Optics 030 · Imaging, instruments, and visual systems

Build a Microscope

An independently initialized three-dimensional apparatus connects Geometric magnification, Köhler illumination, Diffraction-limited resolution. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelBuild a Microscope
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 Build a Microscope

BackgroundBuild a Microscope is one independently initialized apparatus with three linked investigations: Geometric magnification, Köhler illumination, Diffraction-limited resolution. Its two controls—Objective numerical aperture and Wavelength—feed the governing relation d≈0.61λNAd\approx\frac{0.61\lambda}{\mathrm{NA}}. The validity indicator marks the paraxial, lossless, weak-field, or steady-state assumption used by this apparatus.

Why it mattersHow should objective, illumination, and detector share numerical aperture to resolve a tiny object?

Start with the essentials

Focus question
How should objective, illumination, and detector share numerical aperture to resolve a tiny object?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from d≈0.61λNAd\approx\frac{0.61\lambda}{\mathrm{NA}}. 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

d≈0.61λNAd\approx\frac{0.61\lambda}{\mathrm{NA}}

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: Geometric magnification

    Select Geometric magnification. Sweep Objective numerical aperture, hold Wavelength 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: Köhler illumination

    Select Köhler illumination. Sweep Objective numerical aperture, hold Wavelength 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: Diffraction-limited resolution

    Select Diffraction-limited resolution. Sweep Objective numerical aperture, hold Wavelength 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.