A Millimetre Is Not a Formality: Pupillary-Distance Tolerance by Lens Power, from Prentice's Rule

Pupillary distance is the cheapest measurement in dispensing and one of the most consequential, because a lens centred away from the pupil acts as a prism. By Prentice's rule, prism equals decentration in centimetres times lens power, and this paper converts that rule into a tolerance table for low-cost dispensing, where pupillary distance is often estimated or taken from a ready-made pair's fixed geometry. Against a stated binocular comfort bound of 0.67 prism dioptres, the largest permissible total pupillary-distance error falls from 6.7 mm at 1 D to 1.68 mm at 4 D and 0.84 mm at 8 D. A single fixed rule follows: measure pupillary distance to the nearest millimetre whenever the stronger lens exceeds about 3 D, because at higher powers the customary 2 mm estimation error already exceeds the bound. This study is simulated, not measured.