ABO Exam
Core Formulas

The essential mathematical backbone of optical dispensing. Master these to pass the ABO exam.

Lens Power & Focus

Focal Length (f)

f = 1 / D

Relationship between power and focus distance.

Diopter (D)

D = 1 / f (meters)

Calculated in meters.

Lensmaker's Formula

D = (n - 1) / r

Basic lens design principle.

Prism & Prentice's Rule

Prentice's Rule

P = (h * D) / 10

Calculates induced prism from decentration (h in mm).

Resultant Prism

R = sqrt(V² + H²)

Combining vertical and horizontal prism components.

Slab-off Prism

Prism = (F1 - F2) * dist

Calculated at the reading level to correct vertical imbalance.

Advanced Optics

Vertex Compensation

Dc = D / (1 - dD)

Adjusting power for changes in vertex distance (d in meters).

Min. Blank Size (MBS)

MBS = ED + 2(dec) + 2mm

Determining the smallest lens blank required.

Martin's Formula (Tilt)

New Power = D(1 + 1/3 sin²θ)

Calculates power change induced by lens tilt.

Geometric Principles

Snell's Law

n1 * sin(θ1) = n2 * sin(θ2)

Fundamental law of refraction between two media.

Index of Refraction

n = c / v

Ratio of speed of light in vacuum to speed in medium.

Surface Power

Ps = (n2 - n1) / r

Power of a single refracting surface (r in meters).

Transposition

Follow these three steps:

  1. 1

    Sum the Sphere and Cylinder power to get the new Sphere.

  2. 2

    Change the sign of the Cylinder power (+ to - or - to +).

  3. 3

    Change the Axis by 90 degrees (must stay between 0-180).

Master these for the exam.

Memorization is just the first step. Head over to Opterio for interactive practice questions using these formulas.

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