A healthy lens is packed with crystallin proteins at ~35% volume fraction yet stays optically clear, because Benedek's fluctuation theory shows that closely-spaced small scatterers (short-range order, spacing ≪ wavelength) interfere destructively and cancel almost all scattered light. A cataract begins when crystallins denature and coalesce into much larger aggregates — that short-range order breaks down and the lens turns hazy.
Rayleigh cross-section (dipole, radius a ≪ λ):
σ(a,λ) = (8π/3)·(2π/λ)⁴·a⁶·((m²−1)/(m²+2))², m = n_protein / n_cytoplasm
Volume-conserving coarsening (N monomers → fewer, bigger clusters):
N(a) = N₀·(a₀/a)³
Beer–Lambert turbidity and transmission over path L:
τ = N(a)·σ(a,λ), T = exp(−τL)
- Aggregation slider — advances the mean aggregate radius a from ~5 nm (small oligomers) toward ~140 nm (mature aggregates), the size range where scattering becomes visually significant.
- Wavelength slider — σ scales as λ⁻⁴, so shorter (blue) wavelengths scatter far more strongly than red — the same reason cataracts often shift perceived color toward yellow/brown.
- Animate aging — advances the aggregation slider automatically, like a lens aging over years compressed into seconds.
- The instanced spheres show relatively fewer, larger aggregates as merging proceeds (volume is conserved); the light rays bend more as they cross the lens, and the beam dims as computed transmission drops.
The cross-section is smoothly capped near the geometric limit (πa²) once a approaches λ, standing in for the transition out of the simple dipole (Rayleigh) regime — a physically-motivated approximation, not full Mie theory. Refractive indices (n≈1.45 protein, 1.336 cytoplasm), protein volume fraction and lens path length are set to realistic human-lens values; the overall calibration constant is tuned for a clear interactive range rather than absolute clinical accuracy.