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Accommodation and Its Optical Basis
Optics & Refraction
Teaching images
81. Optics of the Eye
Clinical Analogy
- Think of the eye as a two-lens camera system: the cornea is the wide-angle primary lens providing ~2/3 of the total power (~43D), and the crystalline lens is a variable-zoom secondary lens (~20D at rest) that fine-tunes focus. The vitreous and aqueous are the optical media - essentially flat glass - through which images must pass without distortion.
Reduced Eye (Listing's Schematic Eye)
Teaching image
1To simplify calculations, Listing proposed the reduced eye - a single refracting surface separating air (n=1.0) from a uniform medium (n=1.336), placed at the principal plane of the eye.
- Equivalent power: +60D (cornea 43D + lens 17D)
- Anterior focal length (f): ~17mm (in air)
- Posterior focal length (f'): ~22.7mm (in vitreous, n=1.336)
- Nodal point: ~7 mm behind cornea - paraxial rays directed toward it emerge at the same angle
- Centre of rotation: ~13.5 mm behind cornea (Gullstrand schematic eye)
Cardinal Points of the Eye
| Cardinal Point | Location from Cornea | Clinical Relevance |
|---|---|---|
| First Principal Plane (H) | 1.35mm behind cornea | • Object vergence measured here |
| Second Principal Plane (H') | 1.60mm behind cornea | • Image vergence measured here |
| First Nodal Point (N) | 7.08mm behind cornea | • Angle of visual field • retinal image size calculation |
| Second Nodal Point (N') | 7.33mm behind cornea | • Almost coincide - can be treated as single nodal point |
| First Focal Point (F) | 15.7mm in front of cornea | • Divergent rays from the First Focal Point (F) emerge parallel to the optical axis after passing through the eye. |
| Second Focal Point (F') | 24.13mm behind cornea | • Parallel incident rays focus here • retina in emmetropia |
| Cardinal Point | Location from Cornea | Clinical Relevance |
|---|---|---|
| First Principal Plane (H) | 1.35mm behind cornea | • Object vergence measured here |
| Second Principal Plane (H') | 1.60mm behind cornea | • Image vergence measured here |
| First Nodal Point (N) | 7.08mm behind cornea | • Angle of visual field • retinal image size calculation |
| Second Nodal Point (N') | 7.33mm behind cornea | • Almost coincide - can be treated as single nodal point |
| First Focal Point (F) | 15.7mm in front of cornea | • Divergent rays from the First Focal Point (F) emerge parallel to the optical axis after passing through the eye. |
| Second Focal Point (F') | 24.13mm behind cornea | • Parallel incident rays focus here • retina in emmetropia |
Oral-exam tip
- The nodal point is clinically used to calculate retinal image size: for a small-angle object in the reduced-eye approximation, Image size ≈ Object size × (distance from nodal point to retina / object distance from nodal point). Retinal-image-size and visual-angle principles underlie magnification with low-vision aids.
Corneal Optics
- Anterior cornea: radius of curvature = 7.8mm, power ≈ +48.8D
- Posterior cornea: radius = 6.5mm, power ≈ –5.8D (back surface acts as diverging lens)
- Net corneal power ≈ +43D
- Keratometric power assumes a single refracting surface; uses fictitious index 1.3375 to account for posterior cornea
- This is why conventional keratometry can overestimate actual corneal power after myopic LASIK - an error that is clinically relevant for post-LASIK IOL calculations.
Crystalline Lens Optics
- Biconvex lens; anterior radius 10mm, posterior radius 6mm at rest
- Refractive index: cortex 1.386, nucleus 1.406 - gradient index (GRIN) creates a 'lenslet stack' effect
- GRIN lens reduces spherical aberration significantly compared to a uniform-index equivalent
- Power at rest: ~20D; during maximum accommodation: ~33D
- Purkinje-Sanson images: P-I (anterior cornea, bright upright), P-II (posterior cornea, faint upright), P-III
- (anterior lens, large upright), P-IV (posterior lens, small inverted) - P-III and P-IV move with accommodation
Exam pearl
- Keratometry measures anterior corneal curvature only.
- In post-LASIK eyes, the relationship between anterior and posterior cornea changes.
- In post-myopic LASIK eyes, using standard K for IOL power calculation can lead to hyperopic surprise.
- Use designated post-refractive methods, such as the ASCRS post-refractive calculator.
- Haigis-L is useful for myopic LASIK, and Barrett True-K can be used with or without historical data.
Oral-exam tip
- Purkinje image IV is inverted (posterior lens is a concave mirror).
- Changes in P-III and P-IV with accommodation can be used to estimate lens-surface curvature.
- Dynamic retinoscopy assesses accommodative response from the retinoscopic reflex.
- Scheimpflug imaging independently measures lens-curvature changes.
2. Vergence, Refraction & Snell's Law
Vergence (V)
Vergence = the degree of convergence or divergence of a pencil of light rays. V = n/distance (in metres), where n = refractive index of medium.
- Diverging pencil (real object in front of lens): negative vergence
- Converging pencil (converging towards a focus): positive vergence
- Vergence equation: V' = V + F, where F = lens power, V = incident vergence, V' = emergent vergence
- This is fundamental to many of the equations that follow in ophthalmic optics.
Clinical Example: A +5D lens. Object at 25cm (V = –1/0.25 = –4D). V' = –4 + 5 = +1D. Image forms at +1m behind lens. This forms the basis of near addition calculations.
Snell's Law & Total Internal Reflection
n₁ sin θ₁ = n₂ sin θ₂. When light travels from denser to rarer medium, critical angle (θc) = sin⁻¹(n₂/n₁).
- Cornea-air critical angle: ~48.5° - basis of total internal reflection in gonioscopy
- Without goniolens, angle structures not visible (rays undergo TIR at cornea-air interface)
- Goldmann gonioscopy lens: eliminates TIR by placing viscous coupling fluid, such as methylcellulose, against the cornea, coupling out the light
- Koeppe lens: direct gonioscopy - patient supine; child gonioscopy
Prism Optics
- Prism deviates light towards its base; image appears displaced towards apex
- Prentice's Rule: Prismatic effect (∆) = F × d, where F = lens power, d = decentration in cm
- 1 prism dioptre = 1cm displacement at 1 metre
- Minimum deviation occurs when ray passes symmetrically through prism
- Clinical use: measurement/correction of strabismus, Fresnel prisms, prism in spectacles
MCQ Trap
- The anterior chamber angle is NOT visible directly because of TIR at the cornea-air interface.
- NOT because of the curve of the cornea. This distinction is often tested.
Oral-exam tip
- Prentice's Rule calculates induced prism as P = cF; a −10D lens produces significant unwanted prism when viewed away from its optical center.
- The base direction depends on which side of the optical center is viewed; a −10D lens does not inherently produce base-out prism merely because the wearer views through an edge.
- Base-out prism produces a convergence demand and is used to neutralize esophoria/esotropia; base-in prism is used for exophoria/exotropia.
- This is why strong myopes need careful centration.
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Keep reading Accommodation and Its Optical Basis
8 more sections are included with the Clinical plan.
- Mechanism of Accommodation
- Amplitude, Range & Measurement of Accommodation
- Presbyopia
- Anomalies of Accommodation
- Clinical Refraction - Principles & Techniques
- Optical Instruments & Low Vision Aids