Formula sheet

Transposition

S' = S + C; C' = -C; axis' = axis rotated 90 (1..180)

S sphere, C cylinder, axis in degrees; 180 is written instead of 0

Example: -2.00 -1.50 x 180 transposes to -3.50 +1.50 x 090

Prentice's rule

P = c x F

P prism diopters, c decentration in centimeters, F power (D) in that meridian

Example: 3 mm on a +4.00 D lens: 0.3 x 4.00 = 1.20 prism diopters

Vertex compensation

F' = F / (1 - d x F), d = (vertex from - vertex to) / 1000

F original power (D), d distance moved in meters, positive toward the eye

Example: +10.00 D at 12 mm to the cornea: 10 / (1 - 0.012 x 10) = +11.36 D; -10.00 D gives -8.93 D

Meridian power

F(theta) = S + C x sin^2(theta - axis)

theta the meridian inspected, in degrees

Example: -2.00 -1.50 x 180 at 90 degrees: -2.00 + (-1.50 x 1) = -3.50 D

Minimum blank size

MBS = ED + 2 x decentration per lens + allowance

ED effective diameter (mm); decentration per lens = (A + DBL - patient PD) / 2

Example: ED 56, frame PD 70, patient PD 64, allowance 2: 56 + 2 x 3 + 2 = 64 mm

Vertical imbalance at reading

imbalance = |c x F90(OD) - c x F90(OS)|, c = drop in cm

F90 the vertical meridian power of each eye; drop commonly 10 mm below the OCs

Example: OD +1.00, OS -2.50 sph at 10 mm drop: |1.00 - (-2.50)| = 3.50 prism diopters

Spectacle magnification (power factor)

SM = 1 / (1 - d x F)

d vertex distance in meters; shape factor omitted in this approximation

Example: +10.00 D at 12 mm: 1 / 0.88 = 1.136, about 13.6 percent larger

Induced prism from OC height error

P = (error mm / 10) x F90

plain Prentice with the vertical meridian power of the affected eye

Example: 3 mm error on a +4.00 D vertical meridian: 0.3 x 4.00 = 1.20 prism diopters

Axis tolerance (ANSI Z80.1, as commonly published)

cyl 0.25 D or less: 14 deg; over 0.25 to 0.50: 7; over 0.50 to 0.75: 5; over 0.75 to 1.50: 3; over 1.50: 2

Verify the edition in force before applying tolerances to real work.