Eye Refraction Lab: Myopia, Hyperopia & Accommodation

Eye Anatomy

Axial length 23.5 mm

Accommodation (ciliary muscle) 0.0 D

Object distance 6.0 m

Correction

Corrective lens power 0.0 D

Diagnosis

—

Total eye power

60.0 D

Defocus at retina

0.00 D

Focus falls at

23.5 mm

Retina at

23.5 mm

How it works

This is the classic reduced (schematic) eye used in optometry: a single refracting system of power P (cornea ≈ 43 D fixed + crystalline lens, which the ciliary muscle can add up to ≈ 12 D of extra power to for near focus — accommodation) sitting in front of a vitreous chamber of refractive index n′ = 1.336, with the retina at the back, at distance = axial length.

Vergence equation:  L' = L + P
  L  = n / (-u)      incident vergence from an object at distance u (n=1 in air)
  P  = P_cornea + P_accom + P_correction   total dioptric power (diopters, D)
  L' = n' / v        vergence of the image-forming ray bundle
  →  v = n' / L'      distance from the eye where light actually converges

Defocus (D) = L' − n'/AL   (AL = axial length, i.e. where the retina sits)

Axial length — an eyeball that is too long focuses light in front of the retina (myopia / nearsightedness); too short focuses it behind (hyperopia / farsightedness). This is the single biggest anatomical cause of refractive error.
Accommodation — the ciliary muscle contracts, the lens bulges and its power rises, pulling the focal point forward for near objects. Presbyopia is the age-related loss of this range.
Object distance — moving the target changes its vergence L; a distant object arrives as nearly parallel rays (L≈0), a near object as strongly diverging rays.
Corrective lens — a diverging (negative D) spectacle lens reduces excess positive power for myopia; a converging (positive D) lens adds power for hyperopia. Glasses correction ≈ −(defocus in diopters) restores focus onto the retina.

Real-world relevance: this vergence formalism is exactly how optometrists compute a spectacle or contact-lens prescription from axial length and refractive power measurements (biometry + keratometry).

Light rays Retina (image plane target) Focus point of the bundle

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