Ocular optics: the reduced eye, accommodation, and presbyopia

Ocular optics is classical, not an R19 claim: the reduced eye focuses a roughly 60-diopter system onto a 22.27 mm axial length, giving a clinical 2.69 D/mm sensitivity that this package reproduces arithmetically. Accommodation falls from 19 D at age 15 to 1 D at 60 by Hofstetter's formula — presbyopia. Refractive error is a focal–axial mismatch.

The Gullstrand reduced eye (total power ≈60 D, n′=1.336) is emmetropic at axial length 22.27 mm; the model reproduces this and the clinical 2.69 D/mm axial–refraction sensitivity. Hofstetter's age formula gives amplitude 25 − 0.40·age, i.e. ≈1 D at age 60 (presbyopia). These are classical-optics anchors reproduced by arithmetic [V-arith], documented and linked, not re-derived from the substrate.

The eye's optics belong to classical physics, and this package treats them that way: it documents and links the lensmaker and dioptric relations rather than re-deriving them from the jamming substrate. Drawing that boundary clearly is part of the program's discipline, not a gap — see the no-tuning method.

The reduced eye is a documented instrument

Gullstrand's reduced (schematic) eye lumps the cornea and lens into a single refracting surface of total power about 60 diopters with image-space index 1.336, emmetropic at an axial length of 22.27 mm — the value the model returns. It is the standard first-order model of the eye as an optical instrument.

Why one millimetre of eye length matters so much

The geometry implies an axial–refraction sensitivity of 2.69 D/mm: each extra millimetre of axial length is worth about 2.69 diopters of refraction, matching the clinical 2.7–3.0 D/mm. A longer eye is therefore more myopic by this fixed conversion, which is exactly why small differences in eye growth translate into large differences in spectacle prescription.

Presbyopia: accommodation declines linearly with age

Accommodation is the eye's ability to refocus on near objects. Hofstetter's formula, amplitude = 25 − 0.40·age, gives about 19 D at age 15 and only about 1 D at 60 — the near point recedes to arm's length, which is presbyopia. The decline is steady and predictable, and the model reproduces both endpoints.

Classical, reproduced by arithmetic [V-arith]. Reduced-eye power, axial length, the D/mm conversion, and the Hofstetter decline are cited classical-optics anchors that the package reproduces numerically; they are explicitly not derived from the substrate, and saying so is what keeps the [V] grade honest.

Refractive error follows directly: myopia is an axial length too long for the eye's power, and hyperopia too short. The growth-control loop that should defend the focal–axial match — emmetropization — is what fails in progressive myopia, and that loop is treated in the disease law and therapy program.