Refraction, Prism, Lacrimal Lens, Accommodation & Transposition

Refraction, Prism, Lacrimal Lens, Accommodation & Transposition

Quick Answer: Contact lens optics differ from spectacle optics because the lens sits on the tear film at the corneal plane. The lacrimal (tear) lens formed behind an RGP masks corneal astigmatism; decentration prism is negligible because the lens moves with the eye; and accommodative demand differs from spectacles because vertex distance is zero. The SAM/FAP rule and transposition formulas let you adjust power reliably.

Refraction Principles

When light crosses an interface between media of different refractive indices, it bends according to Snell's law: n₁ sin θ₁ = n₂ sin θ₂. A contact lens's refractive index (~1.40 for soft hydrogel, ~1.49 for RGP) and the curvature of its optic zone combine with the tear film and cornea to focus light on the retina.

Total corneal power is approximately +43 D (dominated by the steep anterior surface); the crystalline lens adds ~+19 D. The contact lens adds or subtracts the residual refractive error needed to bring the image to focus on the retina. Because the CL sits millimeters from the corneal apex, its effective power and its interactions with the tear film differ fundamentally from a spectacle lens at 12 mm.

Prismatic Effects

Prentice's rule: P = c × F, where P is prism in prism diopters (Δ), c is decentration in centimeters, and F is lens power in diopters.

With spectacles, off-axis gaze through the lens periphery induces prism — a -10.00 D lens decentered 1 cm produces 10Δ of base-in prism. In anisometropia, this causes vertical imbalance in down-gaze (often symptomatic above 1.5Δ of vertical differential prism).

With contact lenses, the lens moves with the eye. The optical center stays aligned with the visual axis under all gaze positions, so decentration prism is essentially eliminated. This is why anisometropic patients tolerate CLs far better than spectacles and why spectacle-only prescriptions can fail in high anisometropia.

Diffraction (Domain II Optics Terminology)

Diffraction is the bending and spreading of light waves as they pass an aperture or edge — for example, the pupil margin or a multifocal zone transition. Diffraction limits how finely an optical system can resolve detail (Airy disk) and contributes to night glare/halos when pupils dilate. On the CLRE, distinguish:

Know the word diffraction as an optics principle related to contact lenses — not only as a marketing label on "diffractive" multifocal designs.

Residual Astigmatism: What RGP Masks vs. Soft Reveals

The lacrimal lens (tear lens) is the thin tear layer between the back surface of an RGP and the front surface of the cornea. Because the RGP is rigid, the tear layer fills in any irregular or toric corneal shape — optically, the corneal surface becomes the smooth back curve of the RGP.

Lenticular astigmatism (from the crystalline lens) cannot be masked by any contact lens — it remains as residual astigmatism regardless of lens type. If a patient has more than ~0.75 D of residual astigmatism with an RGP, a toric CL (soft toric or RGP back-surface toric) is typically required.

The Lacrimal Lens & SAM/FAP Rule

The lacrimal lens has refractive power that depends on the relationship between the RGP base curve and the corneal curvature (K readings).

• If RGP base curve is steeper than the flat K → tear lens is plus power → must add minus to the CL to compensate (SAM = Steep Add Minus)
• If RGP base curve is flatter than the flat K → tear lens is minus power → must add plus to the CL (FAP = Flat Add Plus)
• If RGP base curve matches the flat K → no tear lens power adjustment needed

Worked Example A (SAM)

Corneal Ks: 43.00 / 44.50 D (1.50 D WTR astigmatism)

• RGP fitted "on flat K" with base curve = 43.00 D → no tear lens adjustment; the 1.50 D of corneal astigmatism is masked by the tear lens and needs no cyl in the CL.
• RGP fitted 0.50 D steeper, base curve = 43.50 D → tear lens is +0.50 D → add −0.50 D to the CL power (SAM).

Worked Example B (FAP)

RGP fitted 0.75 D flatter than flat K, base curve = 42.25 D → tear lens is −0.75 D → add +0.75 D to the CL power (FAP).

Memory aid: SAM the FAP — "Steep Add Minus, Flat Add Plus." Always reference the flat K (not the steep K) when computing the difference.

Accommodation Differences: CL vs. Spectacle

Because contact lenses sit at the corneal plane (vertex distance ≈ 0) and spectacles sit ~12 mm away, effective power at the eye differs — and so does the accommodative demand for near work.

• Myopes: contact lens wearers accommodate more than spectacle wearers. The spectacle minus lens at 12 mm has less minus at the corneal plane, effectively reducing near demand; the CL delivers full minus to the cornea, removing that assist.
• Hyperopes: contact lens wearers accommodate less than spectacle wearers. The spectacle plus lens at 12 mm has more plus at the corneal plane than its labeled power, and base-out prism at near drives vergence-accommodation; CLs remove both effects.

Clinical implication: a 40-year-old emerging presbyope who is a high myope in spectacles may not yet need a near add, but may need one when refit with CLs because the accommodative "help" from the spectacles is gone. Conversely, a high hyperope may find near tasks easier in CLs than in spectacles.

Transposition of Prescriptions

Ophthalmic prescriptions can be written in plus-cylinder (ophthalmology convention) or minus-cylinder (optometry and CL convention). Contact lens manufacturers specify prescriptions in minus cylinder. To convert plus-cyl to minus-cyl:

1. New sphere = old sphere + old cylinder
2. New cylinder = −(old cylinder) (sign flipped, magnitude same)
3. New axis = old axis ± 90° (transpose 90°)

Worked Example

+1.00 +2.00 × 090 (plus cyl) →

• New sphere: +1.00 + 2.00 = +3.00
• New cyl: −2.00
• New axis: 090 + 90 = 180
• Result: +3.00 −2.00 × 180

Verify by computing the spherical equivalent (SE) of both forms — they must match: SE = +1.00 + 2.00/2 = +2.00 D, and SE = +3.00 + (−2.00)/2 = +2.00 D. ✓

Spherical Equivalent

The spherical equivalent collapses a spherocylindrical prescription into a single sphere value. It is used for trial lens fitting, soft CL power selection when only spherical lenses are available, and for vertex compensation calculations.

SE = sphere + (cylinder / 2)

Examples:

• −2.00 −1.00 × 180 → SE = −2.00 + (−0.50) = −2.50 D
• +1.50 +0.75 × 090 → SE = +1.50 + 0.375 = +1.875 D (round to +1.75 or +2.00)
• -5.00 -2.00 × 180 → SE = -5.00 + (-1.00) = -6.00 D