Every point on a lens other than its optical center (OC) acts like a small prism. When a patient's pupil isn't lined up with the OC — because the PD was measured wrong, the frame sits crooked, or they're reading through the lower part of the lens — they look through that prism. Prentice's Rule tells you how much.
The formula
Δ = c × F
Δ = c × F = 0.4 cm × 3.00 D = 1.20Δ
- Δ = induced prism, in prism diopters
- c = decentration (distance from the OC), in centimeters
- F = lens power, in diopters (use the absolute value; the sign tells you the base direction)
Finding the base direction
A plus lens is thickest in the middle, like two prisms base-to-base, so the base points toward the optical center. A minus lens is thinnest in the middle, like two prisms apex-to-apex, so the base points away from the optical center.
| Where the OC is, relative to the pupil | Plus lens | Minus lens |
|---|---|---|
| OC is nasal (in) | Base in | Base out |
| OC is temporal (out) | Base out | Base in |
| OC is above (patient looks below it) | Base up | Base down |
| OC is below (patient looks above it) | Base down | Base up |
Worked examples
Example 1: the classic
A +4.00 D lens is decentered 5 mm. How much prism is induced?
5 mm = 0.5 cm → 0.5 × 4.00 = 2.00Δ
If the OC sits 5 mm nasal to the pupil, the plus lens gives 2.00Δ base in.
Example 2: a PD that's too wide
A patient with a 62 mm PD receives −5.00 D glasses with the optical centers 66 mm apart — each OC sits 2 mm temporal (out) to the pupil.
Each eye: 0.2 × 5.00 = 1.00Δ → total 2.00Δ
The lenses are minus and the OCs are out, so the base points away from them: base in in each eye. Horizontal prism in the same direction (base in in both eyes) adds up, for 2.00Δ base in in total.
Example 3: vertical imbalance at near
OD −3.00 D, OS −1.00 D. The patient reads through points 10 mm below both optical centers.
OD: 1.0 × 3.00 = 3.00Δ base down · OS: 1.0 × 1.00 = 1.00Δ base down
Vertically, what matters is the difference between the eyes. Both bases are down, so subtract: 3.00 − 1.00 = 2.00Δ of vertical imbalance. If the bases pointed in opposite directions (one up, one down), you would add them.
Common mistakes
- Leaving decentration in millimeters (answers ten times too big).
- Using the sphere power for a cylinder lens instead of the power in the meridian of decentration.
- Mixing up the base rule — say it out loud: plus toward, minus away.
- Adding vertical prism that should be subtracted (same direction in both eyes means subtract).
Frequently asked questions
What is Prentice's Rule?
Prentice's Rule says the prism induced at a point on a lens equals the distance from the optical center in centimeters multiplied by the lens power in diopters: Δ = c × F.
Do I use millimeters or centimeters in Prentice's Rule?
Centimeters. Decentration is usually measured in millimeters, so divide by 10 first — 5 mm becomes 0.5 cm. Forgetting this makes the answer ten times too large.
Which way does the base point?
For a plus lens, the base points toward the optical center. For a minus lens, the base points away from the optical center.
Does Prentice's Rule work for cylinder lenses?
Yes, if you use the lens power in the meridian of the decentration. For decentration along a principal meridian, use the power cross. Oblique cylinder axes need a more involved calculation.