The 3D version reduces the eye to a single combined dioptric power and one vergence equation. This 2D side view instead exactly ray-traces individual light rays — using real vector Snell's law — through each of the eye's three actual refracting surfaces in turn: the cornea, then the front and back surfaces of the crystalline lens, each with its own curvature and its own change in refractive index.
Vector Snell's law at each spherical surface (unit vectors d, N; indices n₁→n₂):
c₁ = −N·d (flip N if c₁<0)
η = n₁ / n₂
sin²θₜ = η²(1−c₁²) → total internal reflection if this exceeds 1
cosθₜ = √(1−sin²θₜ)
d' = η·d + (η·c₁ − cosθₜ)·N
Surfaces (schematic, mm from cornea vertex):
cornea z=0.0 R=+7.8mm air(1.000) → aqueous(1.336)
lens front z=3.6 R scales with accommodation aqueous → lens(1.406)
lens back z=7.2 R scales with accommodation lens → vitreous(1.336)
Because real rays at different heights through the pupil are traced independently rather than collapsed into one number, this model shows two things the 3D vergence version cannot: spherical aberration — rays entering near the pupil edge focus at a slightly different point than near-axis rays — and a genuine retinal blur spot diameter, the actual geometric spread of the ray bundle where it lands on the retina, which is what makes an out-of-focus image look blurred rather than just "wrong by some diopters".
- Axial length — moves the retina plane; ray-traced focus position is unaffected, so a longer eye increasingly overshoots the true focus (myopia) and a shorter one falls short (hyperopia).
- Accommodation — increases the curvature (decreases the radius) of both lens surfaces, the real Helmholtz mechanism, adding positive power traced surface-by-surface.
- Object distance — sets the entry angle of every traced ray at the cornea; a distant object sends nearly axis-parallel rays, a near one strongly diverging rays.
- Corrective lens — modeled as a real thin lens sitting 12 mm in front of the cornea (a real spectacle vertex distance), so its effect on the traced rays is not simply "−defocus": the further the lens sits from the eye, the more its effective power at the eye differs from its labeled power, a real, measurable effect called vertex distance. "Auto-correct" numerically searches for the corrective power that re-traces every ray back onto the retina, rather than only estimating it analytically.
Both models are correct optics — the ABCD paraxial-matrix method used to double-check this simulator agrees with its exact ray tracer to about 1 part in 10⁸ — they simply operate at different levels of detail, the same way a real ophthalmologist reasons about "spherical equivalent" power for a quick estimate but reaches for full ray-tracing software to predict actual image quality.