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Sandbox Physics

Optics 025 · Imaging, instruments, and visual systems

Camera Obscura

An independently initialized three-dimensional apparatus connects Large bright pinhole, Optimal aperture, Diffraction-limited pinhole. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelCamera Obscura
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 Camera Obscura

BackgroundCamera Obscura is one independently initialized apparatus with three linked investigations: Large bright pinhole, Optimal aperture, Diffraction-limited pinhole. Its two controls—Pinhole diameter and Screen distance—feed the governing relation dopt≈1.9λLd_{\mathrm{opt}}\approx1.9\sqrt{\lambda L}. The validity indicator marks the paraxial, lossless, weak-field, or steady-state assumption used by this apparatus.

Why it mattersWhich pinhole balances geometric blur against diffraction blur for the sharpest image?

Start with the essentials

Focus question
Which pinhole balances geometric blur against diffraction blur for the sharpest image?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from dopt≈1.9λLd_{\mathrm{opt}}\approx1.9\sqrt{\lambda 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

dopt≈1.9λLd_{\mathrm{opt}}\approx1.9\sqrt{\lambda 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: Large bright pinhole

    Select Large bright pinhole. Sweep Pinhole diameter, hold Screen distance 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: Optimal aperture

    Select Optimal aperture. Sweep Pinhole diameter, hold Screen distance 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 pinhole

    Select Diffraction-limited pinhole. Sweep Pinhole diameter, hold Screen distance 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.