Optics of the Eye and Schematic Eyes
On this page
Direct answer
Gullstrand's exact schematic eye assigns the unaccommodated eye a total power of +58.64 D (rising to +70.57 D fully accommodated), an axial length of 24 mm, about +43 D from the cornea and +19 D from the lens in situ, with refractive indices of 1.376 for cornea, 1.336 for aqueous and vitreous, and 1.386-1.406 for lens cortex and nucleus. Listing's reduced eye collapses all this into one refracting surface of about +60 D with index 4/3, its principal plane roughly 1.5-2 mm behind the cornea, giving anterior and posterior focal lengths of about 17 mm and 22.6-23 mm. From this scaffold fall out the far and near points, the amplitude of accommodation, and the arithmetic of presbyopia that optometrists use daily.
What you must remember
- Gullstrand numbers to quote: total +58.64 D relaxed, +70.57 D accommodated; cornea +43 D; lens +19 D relaxed rising to about +33 D accommodated; axial length 24 mm.
- Refractive indices: cornea 1.376; aqueous and vitreous 1.336; lens cortex 1.386, nucleus 1.406 — a gradient index that damps spherical aberration.
- Reduced eye: one surface, +60 D, n = 4/3, principal plane about 1.5-2 mm behind the corneal vertex; anterior focal length about 17 mm, posterior about 22.6 mm.
- Amplitude of accommodation: Hofstetter's average is 18.5 − 0.3 × age dioptres (maximum 25 − 0.4 × age, minimum 15 − 0.25 × age); classic near points run about 7 cm at 10 years, 10 cm at 20, 22 cm at 40, 1 m at 60.
- Far point logic: emmetropia — far point at infinity; −2.00 D myopia — far point 50 cm in front; hypermetropia — a virtual far point behind the eye.
- Correction-plane effects: myopes in spectacles accommodate less than emmetropes at near, hypermetropes more — a staple viva calculation with real contact-lens consequences.
- Purkinje images: four reflections — anterior cornea (brightest), posterior cornea, anterior lens, posterior lens (inverted, and shifting most in accommodation).
- Aberrations that matter clinically: positive spherical aberration at the pupillary margin, axial chromatic aberration of about 0.25-0.50 D between red and green (the entire basis of the duochrome test), and the Stiles-Crawford effect damping the peripheral contribution.
Worked optics: the 45-year-old near point
A tailor reports blur at her 33 cm needle point; her near point has receded to 40 cm, so monocular amplitude is 100/40 = 2.50 D. Reading at 33 cm demands 3.00 D, but the comfortable convention spends only half the available amplitude — 1.25 D — leaving reserve against fatigue. The addition is demand minus half amplitude: 3.00 − 1.25 = +1.75 D. Her working distance, not her age alone, decided the number; the age table (mid-40s +1.00 to +1.25, 50 years +1.50 to +1.75, 60 and beyond +2.50 to +3.00) merely predicts what the tape measure confirms.
Now the correction wrinkle: were she a −3.00 D myope in spectacles, the minus lens would shoulder part of the near demand, so she would accommodate less than an emmetrope; switched to contact lenses at 40-plus, the demand rises back toward emmetropic values — the classic reason presbyopic myopes grumble after converting. One schematic-eye diagram, two clinical consequences.
How the exam frames it
The cornea-versus-lens paradox leads: the cornea is flatter than the lens yet carries three-quarters of the power — answer with the index discontinuity at the tear-air interface. Second, why the lens accommodates and the cornea cannot: no muscle moves the cornea, while a gradient-index organ changes effective power by shape alone. Third, the far-point-to-prescription conversion: a far point at 25 cm means a −4.00 D eye, because the far point's reciprocal in metres is the myopia in dioptres. Candidates who quote 58.64 and 70.57 precisely and can derive near points from Hofstetter rather than reciting tables separate themselves cleanly.
Frequently asked questions
What is the total power of the Gullstrand schematic eye?
+58.64 D unaccommodated and +70.57 D fully accommodated, with the cornea supplying about +43 D and the lens about +19 D in situ.
What assumptions does Listing's reduced eye make?
A single refracting surface of about +60 D, index 4/3, principal plane roughly 1.5-2 mm behind the cornea, anterior focal length near 17 mm and posterior near 22.6 mm.
How is amplitude of accommodation estimated from age?
By Hofstetter's formulas — average 18.5 − 0.3 × age dioptres, bounded by 25 − 0.4 × age and 15 − 0.25 × age.
Why does a spectacle-wearing myope accommodate less at near than an emmetrope?
The minus spectacle lens adds negative vergence to incoming near light, reducing the eye's accommodative effort; the effect shrinks in contact lenses and vanishes at the corneal plane.
What chromatic aberration does the eye show, and which test exploits it?
About 0.25-0.50 D between red and green wavelengths, exploited by the duochrome test to polish the spherical end point of refraction.