Optical Power (Diopters)
Optical power in dioptres from focal length, and a two-element eye: total power by Gullstrand's equation, refractive error from the axial length, and contact-lens and spectacle corrections.
Lens power
Result
1 dioptre (D) = 1 m⁻¹. Powers of thin lenses in contact add.
Two-element eye
Results
Refraction vs axial length
Model
P = 1/f; two elements in index n: φ = φ₁ + φ₂ − (t/n)φ₁φ₂ (Gullstrand)
Back from the retina: V₃ = n/(L − t), V₂ = V₃ − φ₂, V₁ = V₂/(1 + (t/n)V₂), K = V₁ − φ₁
Spectacle lens at vertex distance d: F = K/(1 + dK)
Paraxial eye of two thin elements: the cornea at the vertex and the crystalline lens t behind it, unaccommodated. The defaults are Gullstrand's exact eye (43.05 D and 19.11 D, principal planes 5.73 mm apart, 58.64 D in all) with a typical 24 mm axial length. This eye is emmetropic at 24.31 mm, so the 24 mm default is slightly short and reads ≈ +0.8 D (hyperopic). K is the vergence at the cornea that focuses on the retina: negative for myopia (far point in front of the eye), positive for hyperopia, and it is the contact-lens correction. Thin elements put the rear focal point about 0.1 mm in front of the thick-lens eye's, so refractions read about 0.2 D more myopic than in the full schematic eye.
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
Paraxial, unaccommodated eye of two thin elements in one medium, with Gullstrand's exact-eye powers as defaults. Thin elements shift the rear focal point about 0.1 mm forward of the thick-lens eye's, about 0.2 D of refraction.
- Greivenkamp J. E. (2004). Field Guide to Geometrical Optics. SPIE Press. Optical power and the two-lens (Gullstrand) equation. doi:10.1117/3.547461
- Atchison D. A., Smith G. (2000). Optics of the Human Eye. Butterworth-Heinemann. Gullstrand number 1 schematic eye (appendix 1), refractive errors and spectacle-lens effectivity.