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) Dioptereffective power = Diopterfront + Diopterback + (ThicknessMeters * (Diopterfront)2) / n |
| Front Vertex Power: (Objective surface toward lens stop) Dioptereffective power = Diopterfront + Diopterback + (ThicknessMeters * (Diopterback)2) / n |
| Oblique Total Power: Total Power = Sphere Power + Cylinder Power * (sin(θd))2 |
| Snells Law: n1Sin(θ1) = n2Sin(θ2) |
|
| Snells Law (modified): n = sin(θi) / sin(θr) |
Critical angle: sin(θcritical angle) = 1 / n1 |
| 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): nideal index of film = √(nindex 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 = θimage subtended / θobject subtended |
| F = -2 / (radius of curvature) = -1 / f (mirrors) (concave mirrors are minus, convex mirrors are plus ) | power of telescope = angular magnification = f1 / f2 ( f1 being the objective lens) |
| magnification (#x) = (Diopter of Lens) / 4 (i.e. 2x, 3x, etc...) | Magnification in Multiple Lens Systems: Total Magnification = magfrom first lens * magfrom second lens * mag .... |
| To the left of mirrors and lenses U are negative | Image Size = (Object Size) * magnification Length of Telescope = f1 + f2 (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. |
|
| C2 = A2 + B2 + 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 = (Acyl + Bcyl - C) / 2 + (First Sphere) + (Second Sphere) |
| Spectacle Magnification Formula: |
|
| Magnification (M) = (Shape Factor) * (Power Factor) Shape Factor = 1 / (1 - ((c * D1) / n)) Power Factor = 1 / (1 - z Dv) |
D1 = front surface power (base curve) in diopters c = center thickness in meters n = index of refraction of lens z = vertex distance in meters Dv = back vertex power |
|
|
| % Magnification = (M - 1) * 100 | |
| Difference in Magnification = % M1 - % M2 | |
| Approximate shape factor change = (X * D1) / 15 Approximate power factor change = (z * Dv) / 10 |
X = change in center thickness in mm D1 = change in base curve Dv = back vertex power z = change in vertex distance in mm |
| Illumination: Illumination = (Candle Power) / Distance2 |
Apparent Depth: Apparent Depth = (Actual Depth) / nmedium |
| 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. yellow-green). |
| 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: | |
| D2 / L1 = U / (L1 + L2) | D2 = Diameter of object between point source and Shadow L1 = Length from point source to L1 L2 = Length from L1 to Umbra U = Umbra |
| Extended Source: | |
| D2 / L1 = (P + U) / (L1 + L2) D1 / L1 = P / L2 Total Shadow = 2P + U |
D1 = Diameter of light source D2 = Diameter of object between light source and Shadow L1 = Length from light source to L1 L2 = Length from L1 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 - √(R2 - (radius2)) | C.T. = center thickness (in mm) |
| C.T. = S1 + E.T. - S2 (for plus lenses) | E.T. = edge thickness (in mm) |
| E.T. = S2 + C.T. - S1 (for minus lenses) | S1 = front sagittal curve |
| S2 = 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." 3rd Ed. Charles C. Thomas - Publisher: Springfield, Illinois
Rubin, Melvin L. (1993). "Optics for Clinicians." 25th 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." 3rd Ed. Triad Publishing Company: Gainesville, Florida
Brooks, Clifford W., & Borish, Irvin M. (1996). "System for Ophthalmic Dispensing." 2nd Ed. Butterworth-Heinemann: Boston
Stoner, Ellen., Perkins, Patricia., & Ferguson, Roy. (2005). "Optical Formulas: Tutorial" 2nd Ed. Elsevier Butterworth-Heinemann: St. Louis, Missouri
Brooks, Clifford W. (2003). "Essentials of Ophthalmic Lens Finishing" 2nd Ed. Elsevier Butterworth-Heinemann: St. Louis, Missouri
Appler V. Thomas., Dennis, Raymond P., Muth, Eric P., & White, Debra R. (1999). "Management for Opticians." 2nd Ed. Butterworth-Heinemann: Boston
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