This is the chapter candidates fear, and the one that separates a pass from a near miss. The outline lists "calculating prismatic effects" and eight ophthalmic formulas by name: Prentice's rule, vertical imbalance, vertex compensation, centration, power in oblique meridians, magnification, anisometropia and aniseikonia[1]. Every one of them is arithmetic you can do on the exam's on-screen scientific calculator[1].
The method for every problem in this chapter is the same:
- Write down what you are given, with units.
- Convert millimeters to centimeters (Prentice) or to meters (power and focal length).
- Find the power in the meridian that matters — horizontal for in/out prism, vertical for up/down prism.
- Calculate, then name the direction (base up, down, in or out; stronger or weaker).
- Sanity-check: does a bigger lens power or a bigger error give a bigger answer?
Work every example below with a pencil before reading the solution.
I.8 Calculating prismatic effects
What a prism does
A prism is a transparent wedge with an apex and a base. Light passing through it bends toward the base, but the image appears displaced toward the apex[2]. Prism power is measured in prism diopters (Δ): one prism diopter deviates a ray 1 cm, measured on a plane 1 m away[2]. A prism does not focus light; it only displaces it[3].
Two consequences you must hold onto:
- A lens is a stack of prisms. A plus lens has its bases toward the middle and its apexes at the edge; a minus lens has its apexes in the middle and bases at the edge[4].
- The optical center is the only point with no prism. Look through any other point and you are looking through prism[4].
Which way is the base?
From the stacked-prism picture you can work out the base direction for any point on a lens:
- Plus lens: the base points toward the optical center.
- Minus lens: the base points away from the optical center.
NAO's statements match: looking through the top of a minus lens or the bottom of a plus lens gives base-up prism; looking through the top of a plus lens or the bottom of a minus lens gives base-down prism[5].
For horizontal prism, "in" means toward the nose and "out" means toward the temple, for either eye[5]. When the lenses' optical centers are set wider than the patient's PD and the lenses are minus, the patient looks through base-in prism; with plus lenses the same error gives base-out prism[4].
| Where the eye looks relative to the OC | Plus lens | Minus lens |
|---|---|---|
| Below the OC | Base up | Base down |
| Above the OC | Base down | Base up |
| Nasal to the OC (OCs set too wide) | Base out | Base in |
| Temporal to the OC (OCs set too narrow) | Base in | Base out |
I.14.1 Prentice's rule
Prentice's rule: the prismatic effect at a point on a lens equals the distance from the optical center, in centimeters, multiplied by the lens power in diopters in that meridian[4].
P = c × F — P in prism diopters, c in centimeters, F in diopters. Because decentration is measured in millimeters, the working form is P = (mm × F) ÷ 10[4].
Worked example 1 (NAO's PD error). Rx −4.00 DS OU. Patient PD 62 mm; the finished glasses measure 66 mm. How much prism, and which direction[4]?
- Each lens is off by 2 mm (half of 66 − 62).
- P = 0.2 cm × 4.00 = 0.8Δ per eye[4].
- Direction: centers too wide, minus lens → base in.
- Total horizontal prism for the pair: 0.8 + 0.8 = 1.6Δ base in. Both eyes see base-in prism, and the two effects add (next section).
Worked example 2 (NAO's vertical point). Find the prismatic effect 4 mm below the optical center of a +2.50 DS lens. P = 0.4 × 2.50 = 1.00Δ base up, because the eye is below the center of a plus lens[4].
Worked example 3 (the same error, two powers). A frame is made with each OC 3 mm too far out.
- For +1.00 DS OU: 0.3 × 1.00 = 0.3Δ base out per eye.
- For +6.00 DS OU: 0.3 × 6.00 = 1.8Δ base out per eye.
This is why NAO warns never to accept or reject a job on the millimeters alone: the same PD error that is harmless in a weak lens is a real problem in a strong one[6].
Worked example 4 (sphero-cylinder). OD −2.00 −2.00 × 180, OC 3 mm too far in. Horizontal decentration needs the power in the horizontal (180) meridian. The axis is 180, so the 180 meridian carries the sphere alone: −2.00. P = 0.3 × 2.00 = 0.6Δ. OCs too narrow with a minus lens → base out. The trap is to use −4.00 (the total in the vertical meridian) for a horizontal problem.
Rearranging Prentice's rule
The rule works backward as easily as forward[4]:
- How far to decenter? c (mm) = P ÷ F × 10. To get 1.6Δ from a 4.00 D lens: 1.6 ÷ 4.00 × 10 = 4 mm.
- What power produces it? F = P ÷ c (mm) × 10. If 4 mm of decentration gives 1.6Δ, the lens is 1.6 ÷ 4 × 10 = 4.00 D.
Decentration can produce prescribed prism only if the lens has enough power; a plano lens has no power to decenter, so its prism has to be ground[4].
Compounding and cancelling between the two eyes
When both eyes look through prism, the effects either add (compound) or subtract (cancel), depending on the directions[5]:
| Right eye | Left eye | Net effect on the pair |
|---|---|---|
| Base in | Base out | Cancel (subtract) |
| Base in | Base in | Compound (add) |
| Base out | Base out | Compound (add) |
| Base up | Base up | Cancel (subtract) |
| Base down | Base down | Cancel (subtract) |
| Base up | Base down | Compound (add) |
Horizontal: same named direction in both eyes adds. Vertical: same direction in both eyes cancels, opposite directions add. The vertical rule surprises people, so think of it physically: if both images move up by the same amount, the eyes simply look up a little together; only a difference between the eyes forces them apart.
Prism notation and resultant prism
Prescribed prism is written with a base direction (BU, BD, BI, BO) or as an amount at a base meridian on the 360° protractor[5]. When you face the patient or read the glasses in a lensmeter with the temples away from you, 0° is always on the right side of each lens[5]. So for the right eye, base in is toward 0° and base out toward 180°; for the left eye, base in is toward 180° and base out toward 0°.
When a lens carries both a vertical and a horizontal component, they combine into one resultant prism:
R = √(V² + H²), and the base meridian angle from the horizontal is a = tan⁻¹(V ÷ H)[5].
Worked example (NAO's numbers). OD 1.5Δ BU and 2Δ BI[5].
- R = √(1.5² + 2²) = √(2.25 + 4) = √6.25 = 2.5Δ[5].
- Angle: tan⁻¹(1.5 ÷ 2) = tan⁻¹(0.75) ≈ 36.9°, about 37°.
- The right eye's base-in direction is the 0° side and base up is 90°, so the base lies at about 037: 2.5Δ base 037. NAO writes the right eye as "Pl 2.5 @ 037" and the matching left-eye prescription, base down and in, as "@ 217"[5].
Splitting prescribed prism
A prescriber sometimes orders all the prism in one eye, which makes that lens much thicker and heavier. With the prescriber's agreement, the dispenser can split it: half in each eye, keeping the original direction in the prescribed eye and putting the other half in the compounding direction in the fellow eye[5].
- Vertical: OD 10Δ BU, OS none → OD 5Δ BU, OS 5Δ BD[5]. (Up and down in opposite eyes compound, so the total is still 10.)
- Horizontal: OS 4Δ BI, OD none → 2Δ BI in each eye[5]. (Base in plus base in compounds.)
The trap: splitting a vertical prism as "5 BU and 5 BU" — those cancel, leaving the patient with no vertical correction at all.
Prism and eye deviations
Prism moves the image toward its apex, so the eye turns toward the apex[2]. To help an eye that deviates, the prism's apex points the way the eye already turns — which puts the base on the opposite side. For an "eso" deviation (eye turned in), the base is placed out; for an "exo" deviation, the base goes in[5]. Yoked prism is the opposite idea: prism whose bases point the same way in space before both eyes (for example, base in before one eye and base out before the other), so the effects cancel between the eyes and both images shift together. It is used for purposes such as prism thinning and patients who misperceive their position in space, and it is always ordered in both lenses[5].
I.14.2 Vertical imbalance
Why the reading level matters
When a bifocal wearer reads, the eyes drop below the distance optical centers; NAO puts the normal reading excursion at about 8 to 10 mm[4]. If the two lenses have different powers in the vertical (90°) meridian, each eye meets a different amount of vertical prism. The difference is vertical imbalance, and it depends on two things: the vertical-meridian powers and the distance from the optical center to the reading level[4]. Because the eyes tolerate vertical differences poorly, even a modest imbalance can cause vertical diplopia[4]; ANSI Z80.1's vertical imbalance tolerance is tighter than the horizontal one (Chapter 5)[7].
Worked example (NAO's average-math problem)
OD −1.00 DS, OS +1.75 DS, add +2.00, reading depth 12 mm[6].
- OD: 1.2 cm × 1.00 = 1.2Δ base down (below the center of a minus lens)[6].
- OS: 1.2 cm × 1.75 = 2.1Δ base up (below the center of a plus lens)[6].
- Base down in one eye and base up in the other compound: 1.2 + 2.1 = 3.3Δ of vertical imbalance at the reading level[6].
Worked example with cylinder (NAO's reading-level problem)
OD −0.25 +3.00 × 180, OS −1.00 +1.00 × 090, add +1.50 OU, reading level 10 mm[4].
- OD, vertical meridian: the axis is 180, so the full cylinder is in the 90 meridian: −0.25 + 3.00 = +2.75.
- OS, vertical meridian: the axis is 090, so the 90 meridian carries the sphere only: −1.00.
- Distance powers alone: OD 1.0 × 2.75 = 2.75Δ BU; OS 1.0 × 1.00 = 1.00Δ BD. Up and down compound: 3.75Δ.
- NAO works the same problem by adding the +1.50 add to both lenses first (+4.25 and +0.50, both base up), which gives 4.25 − 0.50 = 3.75Δ[4]. The answer is the same because an equal add in both lenses adds equal prism to both eyes, which cancels. What creates imbalance is the difference in the vertical-meridian powers.
Shortcut. Imbalance at the reading level = (difference in vertical-meridian distance powers) × (reading depth in cm). In the example: (+2.75 − (−1.00)) × 1.0 = 3.75Δ.
What to do about it
NAO lists the options[4]:
| Method | What it is | NAO's working range |
|---|---|---|
| Separate single-vision reading glasses | OCs placed where the patient reads | Can handle imbalances over 5Δ, but inconvenient |
| Fresnel press-on prism | Temporary prism on the segment | A useful trial before slab-off |
| Prism segments | Prism ground into the segment | Rarely used; slow to process |
| Compensated ("R") segments | Segment OCs placed 4–10 mm below the seg top | About 1.5Δ or less |
| Dissimilar segments | Different seg styles or sizes in each eye | About 1.5Δ |
| Bicentric grinding (slab-off) | Prism added to the lower part of one lens | Most common; up to 5Δ |
Which lens gets the slab-off? Reason it out from the base-direction table. Looking down through the reading level, the more minus (or less plus) lens produces the relatively greater base-down effect — in the first example above, the −1.00 lens gave 1.2Δ base down against the +1.75 lens's 2.1Δ base up. To cancel the difference, the slab-off adds prism that opposes it: base-up prism in the reading area of the more minus (least plus) lens in the vertical meridian.
Imbalance is only worth correcting when both eyes see well enough to fuse. NAO's example: a patient correctable to 20/25 in one eye but only 20/200 in the other gains nothing from a slab-off[4].
Sources cited in this excerpt
- ABO-NCLE Basic Exam Handbook July 2026 (Candidate Handbook, NOCE and CLRE). American Board of Opticianry & National Contact Lens Examiners (ABO-NCLE), 2026-07. https://drive.google.com/file/d/1EjE8GtE_jfLiGeA2x3zAPOroAOtF-T3a/view?usp=sharing
- Prisms (StatPearls; PubMed abstract, PMID 35593813). StatPearls Publishing, via PubMed (National Library of Medicine), 2023 Jun 11. https://pubmed.ncbi.nlm.nih.gov/35593813/
- Optical Dilemmas and Solutions (continuing education course). National Academy of Opticianry, 2018. https://www.nao.org/wp-content/uploads/2020/04/Optical-Dilemmas-and-Solutions.pdf
- How to Use Prentice's Rule and Finding the Power of a Lens in Any Meridian (continuing education course). National Academy of Opticianry, 2025. https://www.nao.org/wp-content/uploads/2026/02/How-to-Use-Prentices-Rule-and-Finding-the-Power-of-a-Lens-in-Any-Meridian.pdf
- Not Your Basic Prism: Splitting Prism, Compounding Prism, Prism Notation, Resulting and Resolving Prism (continuing education course). National Academy of Opticianry, 2025. https://www.nao.org/wp-content/uploads/2025/10/Not-Your-Basic-Prism-Online.pdf
- Average Math for the Above Average Dispenser (continuing education course). National Academy of Opticianry, 2008. http://www.nao.org/wp-content/uploads/2013/12/Average-Math-for-the-Above-Average-Dispenser-pdf.pdf
- Quick Reference Guide - ANSI Z80.1-2015 (tolerance summary). The Vision Council (Secretariat, Accredited Standards Committee Z80), 2016-01-25. https://thevisioncouncil.org/sites/default/files/ANSI%20Z80%201-2015_Quick%20Reference%20v2.pdf