Optics Study Guide

## (Formula Finder)

Contents

Focal Length
Prism
Prentices Rule
Prismatic Power
Back Vertex Power
Front Vertex Power
Oblique Total Power Or Total Power at a given meridian/degree (cyl @ whatever)
Snells Law - Critical Angle
Vertical Imbalance
Image Jump
True & Marked Power
Bifocal O.C. determination in Uncommon Size Segments (flat top); Bifocal B.T.S.
Circle of Least Confusion
Index of Thin Film Coatings
Decentration Caused by Vertical Imbalance (used in dissimilar segment solutions)
Pantoscopic Tilt / Martin's formula
Faceform / Parabolic Tilt
Vergence (lenses and mirrors) - telescopes, multiple lens systems, linear and angular magnification
Reading Field Size - Determining Field of View Through a Bifocal
Inset
Obliquely Crossed Cylinders
Spectacle Magnification (Iseikonic Lenses)
Illumination
Apparent Depth
Luminous Flux
Velocity of a Wave
Electromagnetic Spectrum
Boxing System and Frame Measurements
Convergence and Accommodation
Sagitta, Sag of a Lens, Thickness Difference
Notes - converting between metric and American, Slab Off
Bibliography

 F.L. = 1 / Diopter Diopter = 1 / F.L  (meters) Δ = Diopter /  Meters Diopters =  Δ *  Meters Meters = Diopters / Δ Δ = (Diopters * decentration (mm)) / 10 Diopters = (Δ * 10) / dec (mm) dec (mm) = (Δ * 10) / Diopters Radius of Curvature (mm) = 337.5 / (K Reading in Diopters K Reading in Diopters = 337.5 / (Radius of Curvature in mm) Radius of Curvature = (n - 1) / Diopters Diopters = (n - 1) / R Δ = deviation (cm) / distance away (Meters) Δ = a (n -1)     a = apical angle
 Back Vertex Power:  (Ocular surface toward lens stop) Dioptereffective power = Diopterfront + Diopterback + (ThicknessMeters * (Diopterfront)2) / n Front Vertex Power:  (Objective surface toward lens stop) Dioptereffective power = Diopterfront + Diopterback + (ThicknessMeters * (Diopterback)2) / n
 Total Power = Sphere Power + Cylinder Power * (sin(θd))2
 n1Sin(θ1) = n2Sin(θ2) Snells Law (modified): n = sin(θi) / sin(θr) Critical angle: sin(θcritical angle) = 1 / n1
 Vertical Imbalance = ((difference @ 90) * Reading Level) / 10
 Image Jump = (distance of segment to segment O.C. (mm) * Add Power) / 10
 (True Power / Marked Power) =  (n - 1) / 0.530
 Bifocal BTS: Bifocal BTS = (width / 2) + height Circle of Least Confusion: Circle of Least Confusion = 1 / (Spherical Equivalent) (It is the Sph. Eq. expressed in metric) Thin Film Coatings (i.e. A/R): nideal index of film = √(nindex of lens material)