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Sandbox Physics

Optics 058 · Diffraction, Fourier optics, and computational imaging

Crystal Diffraction & Reciprocal Space

An independently initialized three-dimensional apparatus connects Rotating Laue pattern, Reciprocal-lattice construction, Powder diffraction rings. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelCrystal Diffraction & Reciprocal Space
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 Crystal Diffraction & Reciprocal Space

BackgroundCrystal Diffraction & Reciprocal Space is one independently initialized apparatus with three linked investigations: Rotating Laue pattern, Reciprocal-lattice construction, Powder diffraction rings. Its two controls—Lattice spacing and Crystal rotation—feed the governing relation 2dsin⁡θ=mλ2d\sin\theta=m\lambda. Scalar, paraxial, or sampled-field assumptions are stated by the validity indicator; vector and nonparaxial effects are outside that boundary.

Why it mattersHow can reciprocal-space spots and rings reveal an unknown real-space lattice?

Start with the essentials

Focus question
How can reciprocal-space spots and rings reveal an unknown real-space lattice?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from 2dsin⁡θ=mλ2d\sin\theta=m\lambda. 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

2dsin⁡θ=mλ2d\sin\theta=m\lambda

The implementation evaluates this relation with dimensional inputs and an executable analytic or numerical benchmark. Scalar, paraxial, or sampled-field assumptions are stated by the validity indicator; vector and nonparaxial effects are outside that boundary.

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: Rotating Laue pattern

    Select Rotating Laue pattern. Sweep Lattice spacing, hold Crystal rotation 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: Reciprocal-lattice construction

    Select Reciprocal-lattice construction. Sweep Lattice spacing, hold Crystal rotation 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: Powder diffraction rings

    Select Powder diffraction rings. Sweep Lattice spacing, hold Crystal rotation 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.