Prentice's Rule: Induced Prism With Worked Examples
Last updated: October 2026
Short answer: Prentice's rule calculates the prism induced when looking through a point away from a lens's optical centre: prism (Δ) = decentration (cm) × lens power (D). For a plus lens, the induced prism is base towards the optical centre; for a minus lens, base away from it. It explains symptoms from decentred glasses and vertical imbalance in anisometropia.
The formula
P = c × F where P = prism dioptres, c = decentration in centimetres, F = lens power in dioptres
Direction of the prism
- Plus lens: behaves like two prisms base to base. The induced prism is base towards the optical centre.
- Minus lens: behaves like two prisms apex to apex. The induced prism is base away from the optical centre.
Worked examples
| Situation | Calculation | Result |
|---|---|---|
| +4.00 D lens, looking 5 mm (0.5 cm) nasal to the optical centre | 0.5 × 4 | 2Δ base out (towards the optical centre, which lies temporal to the visual axis) |
| −6.00 D lens, looking 3 mm (0.3 cm) below the optical centre | 0.3 × 6 | 1.8Δ base down (away from the optical centre) |
| Anisometropia: R −1.00 D, L −4.00 D, reading 1 cm below the optical centres | R: 1 × 1 = 1Δ base down; L: 1 × 4 = 4Δ base down | Net vertical imbalance 3Δ, which can cause reading discomfort or diplopia |
Clinical uses
- Wrong pupillary distance (PD): decentred optical centres induce horizontal prism, especially in high prescriptions.
- Vertical imbalance in anisometropia: when reading through the lower part of the lenses, the two eyes receive different vertical prism. Small vertical prism differences (around 1Δ or more) can cause symptoms.
- Managing vertical imbalance: lowering the reading segment's optical centre, separate reading glasses, contact lenses, or a slab-off (bicentric grinding), usually on the more minus (or less plus) lens.
- Prescribing prism by decentration: small amounts of prism can be created by deliberately decentring a lens, if the power is high enough.
Frequently asked questions
What is Prentice's rule?
A formula for the prism induced by looking through a lens away from its optical centre: prism dioptres equal the decentration in centimetres multiplied by the lens power in dioptres.
What is the base direction of induced prism in a minus lens?
Base away from the optical centre. In a plus lens, it is base towards the optical centre.
How is vertical imbalance in anisometropia treated?
Options include separate reading glasses, contact lenses, adjusting the optical centres, or a slab-off (bicentric grinding) on the more minus lens.
Related: formulas in ophthalmology, vertex distance and eyeglass lens guide.
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