Optics Study Guide
Contents
Focal Length: F.L. = 1 / Diopter 
Diopter = 1 / F.L (meters) 

Prism: Δ = Diopter / Meters 
Diopters = Δ * Meters 
Meters = Diopters / Δ 
Prentices Rule: Δ = (Diopters * decentration (mm)) / 10 
Diopters = (Δ * 10) / dec (mm) 
dec (mm) = (Δ * 10) / Diopters 
Radius of Curvature (Contact Lens): Radius of Curvature (mm) = 337.5 / (K Reading in Diopters 
K Reading in Diopters = 337.5 / (Radius of Curvature in mm) 

Radius of Curvature: Radius of Curvature = (n  1) / Diopters 
Diopters = (n  1) / R 

Prismatic Power: Δ = deviation (cm) / distance away (Meters) 
Δ = a (n 1) a = apical angle 
Back Vertex Power: (Ocular surface toward lens stop) Diopter_{effective power} = Diopter_{front} + Diopter_{back} + (Thickness_{Meters} * (Diopter_{front})^{2}) / n 
Front Vertex Power: (Objective surface toward lens stop) Diopter_{effective power} = Diopter_{front} + Diopter_{back} + (Thickness_{Meters} * (Diopter_{back})^{2}) / n 
Oblique Total Power: Total Power = Sphere Power + Cylinder Power * (sin(θ_{d}))^{2} 
Snells Law: n_{1}Sin(θ_{1}) = n_{2}Sin(θ_{2}) 

Snells Law (modified): n = sin(θ_{i}) / sin(θ_{r}) 
Critical angle: sin(θ_{critical angle}) = 1 / n_{1} 
Vertical Imbalance: Vertical Imbalance = ((difference @ 90) * Reading Level) / 10 
Image Jump: Image Jump = (distance of segment to segment O.C. (mm) * Add Power) / 10 
True Power & Marked Power: (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): n_{ideal index of film} = √(n_{index of lens material}) 
Decentration Caused by VI (used for dissimilar segment solutions of VI): decentration(mm) = (Δ* 10) / Add (average of adds if dissimilar) 
Pantoscopic Tilt: New Sphere = D_{(power @ 90)} * (1 + (sin(θ))^{2} / 3) 
New Cylinder = D_{(power @ 90)} * (tan(θ))^{2} 
Axis is always @ 180 
Face Form Tilt: New Sphere = D_{(power @ 180)} * (1 + (sin(θ))^{2} / 3) 
New Cylinder = D_{(power @ 180)} * (tan(θ))^{2} 
Axis is always @ 90 
Vergence: V = U + F 

V = 100 / v vergence of image (to the right of the lens/mirror in diopters)  v = 100 / V distance to the right (left for mirror) where the image forms (cm) 
U = 100 / u vergence of object (to the left of the lens/mirror in diopters)  u = 100 / U distance to the left where the object is (cm) 
F = 100 / f diopter value of lens or mirror  f = 100 / F focal point of lens or mirror (cm) 
linear magnification = v / u (mirrors) linear magnification = v / u (lenses) 
angular magnification = θ_{image subtended} / θ_{object subtended} 
F = 2 / (radius of curvature) = 1 / f (mirrors) (concave mirrors are minus, convex mirrors are plus )  power of telescope = angular magnification = f_{1} / f_{2} ( f_{1} being the objective lens) 
magnification (#x) = (Diopter of Lens) / 4 (i.e. 2x, 3x, etc...)  Magnification in Multiple Lens Systems: Total Magnification = mag_{from first lens} * mag_{from second lens} * mag .... 
To the left of mirrors and lenses U are negative  Image Size = (Object Size) * magnification Length of Telescope = f_{1} + f_{2} (Objective Lens + Eyepiece) 
Reading Field Size: (MQ / AB) = (MC / AC) 
MQ = (MC * AB) / AC 
MQ = Width or height through segment  MC = Distance from fixation point to center of rotation 
AB = Segment diameter  pupil size  AC = Distance from segment to center of rotation (vertex distance + center of rotation 
Inset: Gerstman Inset = 0.75 * (dioptric demand) 

Lebensohn Inset = (Binocular Distance PD in mm) / (Reading distance in inches + 1) reading distance usually equals add 
Creates some base in prism to assist in convergence 
Approximation Inset Formula = (Monocular PD in mm) / (working distance in inches) + (distance Rx in 180th meridian) / 20  Takes into account the distance Rx 
Obliquely Crossed Cylinders: Put Rx in to plus cylinder form with strongest cylinder on top. 

C^{2} = A^{2} + B^{2} + 2AB cos(2a)  C = Resultant Cylinder power A = Power of strongest cylinder B = Power of other cylinder a = difference between 
sin (2a') = (B / C) * sin (2a) Solve for a' New Axis = a' is added to the strongest cylinder axis 
The axis must be between both meridians and the strongest axis will have more influence. If the Rx is arranged in order simply add a' to whatever A axis is. 
New Sphere = (A_{cyl} + B_{cyl}  C) / 2 + (First Sphere) + (Second Sphere) 
Spectacle Magnification Formula: 

Magnification (M) = (Shape Factor) * (Power Factor) Shape Factor = 1 / (1  ((c * D_{1}) / n)) Power Factor = 1 / (1  z D_{v}) 
D_{1} = front surface power (base curve) in diopters c = center thickness in meters n = index of refraction of lens z = vertex distance in meters D_{v} = back vertex power 


% Magnification = (M  1) * 100  
Difference in Magnification = % M_{1}  % M_{2}  
Approximate shape factor change = (X * D_{1}) / 15 Approximate power factor change = (z * D_{v}) / 10 
X = change in center thickness in mm D_{1} = change in base curve D_{v} = back vertex power z = change in vertex distance in mm 
Illumination: Illumination = (Candle Power) / Distance^{2} 
Apparent Depth: Apparent Depth = (Actual Depth) / n_{medium} 
Luminous Flux: Luminous Flux = 4π(Candle Power) 
Velocity of a Wave: Velocity = Frequency * λ ; λ = wavelength 
Electromagnetic Spectrum: 
mμ (millimicrons) = nm (nanometers)  
Type of Light  Wavelength  Sources  Effects on Eyes 
Short UV  14 mμ  310 mμ  Sunlight @ high altitude. Snow sand, and water reflections, mercury arc lamps, UV lamps  Absorbed by the cornea and conjunctiva. Causes Conjunctivitis and Keratitis 
Long UV  310 mμ  380 mμ  Intense sunlight, fluorescent bulbs, UV and mercury arc lamps  Solar Retinitis, may cause cataracts and play a role in Age Related Macular Degeneration 
Visible Spectrum Violet Indigo Blue Green Yellow Orange Red 
380 mμ  435 mμ 435 mμ  450 mμ 450 mμ  500 mμ 500 mμ  570 mμ 570 mμ  590 mμ 590 mμ  620 mμ 620 mμ  780 mμ 
Sunlight and artificial light sources as well.  Ooooh pretty colors. 570 mμ is the most sensitive wavelength to the eye (i.e. yellowgreen). 
Short Infra Red  780 mμ  1500 mμ  Direct sunlight, Molten glass and metal, Mercury and Infrared Lamps  Short exposure to Infra Red rays are harmful to the retina (e.g. Solar Eclipse) 
Long Infra Red  1500 mμ and longer  Direct sunlight, Molten glass and metal, Mercury and Infrared Lamps 
May cause Keratitis or Conjunctivitis 
Shadows: Umbra & Penumbra 

Point Source:  
D_{2} / L_{1} = U / (L_{1} + L_{2})  D_{2} = Diameter of object between point source and Shadow_{} L_{1} = Length from point source to L_{1} L_{2} = Length from L_{1} to Umbra U = Umbra 
Extended Source:  
D_{2} / L_{1} = (P + U) / (L_{1} + L_{2}) D_{1} / L_{1} = P / L_{2} Total Shadow = 2P + U 
D_{1} = Diameter of light source D_{2} = Diameter of object between light source and Shadow_{} L_{1} = Length from light source to L_{1} L_{2} = Length from L_{1} to Umbra U = Umbra P = Penumbra 
Boxing System & Frame Measurements: 
A = horizontal boxing width B = vertical boxing length ED = Effective Diameter = 2 * longest radius DBL = Distance between lenses MBS = Minimum Blank Size 
Frame PD = A + DBL  
Set Minus = Pattern A  Machine Standard  
MBS = 2 * decentration + ED + (2) (Optional/Manual)  
Edger Setting = Frame A  Set Minus  
Machine Standards: 36.5 Shuron; 37.1 AO 
Convergence & Accommodation: AC = Accommodation (in use; Diopters) * distance PD (cm) 
AC = accommodative convergence (measured in Δ diopters) A = accommodation BI = Base In BO = Base Out 
AC / A = ratio of accommodative convergence for every diopter of accommodation  Adding plus increases convergence (less accommodation) Adding minus decreases convergence (more accommodation) Adding BI Δ decreases convergence (moves image away) Adding BO Δ increases convergence (moves image closer) 
Sagitta, the Sag of a Lens & Thickness Difference Prism: 

Sagitta = R  √(R^{2}  (radius^{2}))  C.T. = center thickness (in mm) 
C.T. = S_{1} + E.T.  S_{2 } (for plus lenses)  E.T. = edge thickness (in mm) 
E.T. = S_{2} + C.T.  S_{1} (for minus lenses)  S_{1} = front sagittal curve 
S_{2} = back sagittal curve  
Sag of a Lens = ((radius)^{2} * Diopters) / (2000 * (n 1))  ← an approximate formula 
C.T. = Sag + E.T.  
E.T. = Sag + C.T.  
Thickness Difference = ((diameter of lens) * prism) / (100 (n  1))  ← this would be added to the final amount calculated for sagitta or sag of a lens. 
Note: It is entirely possible that there may be mistakes so please verify. I do not warrant this info in any way shape or form. As far as I can tell the information is correct and will change it accordingly upon verification of information
Bibliography and Information in order of Importance.
Thomas, Brian A. A.B.O.M. In house publications from Raritan Valley Community College to whom I owe much in terms of my education.
Velardi, Thomas O.D. In house publication from Raritan Valley Community College another great teacher from my days at school.
Stimson, Russell L. (1979). "Ophthalmic Dispensing." 3^{rd} Ed. Charles C. Thomas  Publisher: Springfield, Illinois
Rubin, Melvin L. (1993). "Optics for Clinicians." 25^{th} Anniversary Ed. Triad Publishing Company: Gainesville, Florida
Milder, Benjamin., & Rubin, Melvin L. (2004). "The Fine Art of Prescribing Glasses: Without Making a Spectacle of Yourself." 3^{rd} Ed. Triad Publishing Company: Gainesville, Florida
Brooks, Clifford W., & Borish, Irvin M. (1996). "System for Ophthalmic Dispensing." 2^{nd} Ed. ButterworthHeinemann: Boston
Stoner, Ellen., Perkins, Patricia., & Ferguson, Roy. (2005). "Optical Formulas: Tutorial" 2^{nd} Ed. Elsevier ButterworthHeinemann: St. Louis, Missouri
Brooks, Clifford W. (2003). "Essentials of Ophthalmic Lens Finishing" 2^{nd} Ed. Elsevier ButterworthHeinemann: St. Louis, Missouri
Appler V. Thomas., Dennis, Raymond P., Muth, Eric P., & White, Debra R. (1999). "Management for Opticians." 2^{nd} Ed. ButterworthHeinemann: Boston
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