# Dispensing Optics > Dispensing optics for Optometry exams: transposition, lens materials and Abbe numbers, Prentice's rule decentration, boxing system and PD measurement. - Canonical URL: https://prepelephant.com/topics/allied/optometry/dispensing-optics-basics - Exam / course: Allied Health · Subject: Optometry - Publisher: PrepElephant (https://prepelephant.com) — Prepared and reviewed by the PrepElephant Academic Review Team - First published: 2026-10-02 - Last updated: 2026-10-02 - How to cite: "Dispensing Optics", PrepElephant, https://prepelephant.com/topics/allied/optometry/dispensing-optics-basics ## Direct answer Take any prescription written in plus cylinder to the bench and it must first be transposed — algebraic sum of sphere and cylinder, cylinder sign reversed, axis rotated 90 degrees — before edging, prism calculation or lens form selection makes sense. Dispensing then balances four decisions: lens material (index and impact resistance against weight, where a low Abbe number means coloured fringes), frame geometry in the boxing system, centration on the pupil using Prentice's rule to control unwanted prism, and coatings from anti-reflection to photochromic. A beautifully refracted eye in a badly dispensed pair is a failed prescription — the patient sees the errors, not the refraction. ## What you must remember - Transposition, three steps: new sphere = algebraic sum of sphere and cylinder; new cylinder = cylinder with sign changed; new axis = old axis ± 90 degrees. Example: +2.00 DS/+1.00 DC × 90 becomes +3.00 DS/−1.00 DC × 180. - Materials: crown glass (n 1.523, Abbe about 59, heavy but scratch-resistant); CR-39 plastic (n about 1.50, light, cheap); polycarbonate (n 1.586, impact-resistant, Abbe about 30); Trivex (n 1.53, impact-resistant, better Abbe); high-index 1.60–1.74 for strong prescriptions. - Abbe number: lower means more lateral chromatic aberration — the polycarbonate wearer's colour fringes are physics, not imagination. - Prentice's rule: prismatic effect (prism dioptres) = decentration in centimetres × lens power in dioptres; prescribed prism is created by deliberate decentration, unwanted prism by careless centration. - Boxing system: A (horizontal box width), B (vertical height), DBL (distance between lenses); frame PD = A + DBL; decentration per eye = (frame PD − patient PD) / 2. - PD: measure monocularly (pupillometer) for progressives and prism; near PD is roughly 2–3 mm less than distance. - Progressive addition lenses: the fitting cross sits at pupil centre, measured as monocular PDs and fitting heights; corridor length trades reading width against intermediate utility. - Children and monocular patients receive polycarbonate or Trivex as standard — impact resistance is a safety obligation, not an upgrade. - Beyond about ±4.00 D, vertex distance changes effective power: a −8.00 D spectacle prescription converts to roughly −7.25 D in a contact lens. ## A dispense that Prentice would audit A young man chooses a large frame for his −6.00 DS prescription; his distance PD is 58 mm. The frame boxes out at A = 54, DBL = 18, so frame PD = 72 mm. Decentration needed per eye: (72 − 58)/2 = 7 mm inward. If the laboratory edged without decentring, each optical centre would sit 7 mm temporal to its pupil, and Prentice's rule prices the mistake: 0.7 cm × 6.00 D = 4.2 prism dioptres per eye of unwanted base-out prism, forcing compensating convergence. The wearer reports eye strain within minutes, and the cause is arithmetic, not the prescription. The professional dispense reorders the decisions: choose a smaller frame, or specify the 7 mm inward decentration per eye. Material follows power: at −6.00 D, a 1.67 high-index lens with anti-reflection coating thins the edge and strips weight. The lens that reaches this face is the product of as many measurements as the refraction itself. ## Where students slip Transposition heads the list: the axis moves exactly 90 degrees, and forgetting the algebraic-sum sphere loses the mark. Prentice's rule comes second, usually with millimetres left unconverted to centimetres (0.7 × 6 = 4.2, not 7 × 6 = 42). Base-direction reasoning is the third trap: a minus lens decentred nasally induces base-in prism — prism base always points towards the lens periphery — and examiners like the direction question. Fourth, the Abbe defence: listing polycarbonate's impact resistance without its chromatic cost loses the pairing. And near PD: forgetting to subtract 2–3 mm for reading spectacles pushes segment centres outward and rekindles the very asthenopia the prescription meant to cure. PAL fitting-cross measurement, not pupil-margin guessing, is the standard for progressives. ## Frequently asked questions ### What are the three steps of transposition? Sum sphere and cylinder algebraically for the new sphere, reverse the cylinder's sign, and rotate the axis 90 degrees — converting between plus and minus cylinder forms of the same lens. ### State Prentice's rule and its use. Prismatic power in prism dioptres equals decentration in centimetres times lens power in dioptres (P = c × F); it creates prescribed prism by decentring and audits unwanted prism from poor centration. ### Which lens material is standard for children? Polycarbonate or Trivex — high impact resistance is mandatory for children's and safety eyewear, accepting the lower Abbe number. ### What does a low Abbe number mean for the wearer? Greater lateral chromatic aberration — colour fringes off-centre, classically with polycarbonate (Abbe about 30) against crown glass or Trivex. ### How is decentration calculated in the boxing system? Frame PD = boxed width A + DBL; the difference between frame PD and the patient's PD, divided by two, gives the decentration required per eye. ### How does near PD differ from distance PD? Near PD is about 2–3 mm less because the eyes converge for near; reading spectacles are centred on it.