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)
 New Sphere = D(power @ 90) * (1 + (sin(θ))2 / 3) New Cylinder = D(power @ 90) * (tan(θ))2 Axis is always @ 180 New Sphere = D(power @ 180) * (1 + (sin(θ))2 / 3) New Cylinder = D(power @ 180) * (tan(θ))2 Axis is always @ 90
 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)
 (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
 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
 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)
 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 Flatter base curves decrease magnification Steeper base curves increase magnification Thinner lenses decrease magnification Thicker lenses increase magnification Higher vertex distances create more magnification Shorter vertex distances create less magnification Higher index yield less magnification Lower index yield more magnification % 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 = (Candle Power) / Distance2 Apparent Depth = (Actual Depth) / nmedium Luminous Flux = 4π(Candle Power) Velocity = Frequency * λ       ; λ = wavelength
 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
 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.

Notes

• Slab Off (bi-centric grinding) is always Base Up.  Reverse slab off is always Base Down
• With Vertical Imbalance the "problem" is always with the strongest lens in the 90th meridian
• Shortest BTS goes on the (most minus/ least plus)
• Average vertex distance is 13.75 mm
• Average center of rotation is 13.25 mm
• 1 meter = 100 centimeters = 1000 millimeters
• 1 inch equals 2.54 cm or 25.4 mm
• 1 cm equal 0.3937 inches
• The Snellen "E" has 5 minutes of arc and is 8.87 mm on the 20/20 line
• 2 degrees of pantoscopic tilt = 1mm decentered down
• 1 Diopter = the ability to converge light a meter away
• 1Δ Diopter = the ability to deviate light 1cm a meter away
• 1Δ Diopter = 0.3mm (approx.) of vertical Decentration which is always decentered in direction of prism apex (for multifocal lenses)
• 1 Diopter BC Change = 0.6mm (approx.) of vertex distance change
• Drop Ball Test: Dress Wear - 50" free fall of a ⅝" steel ball weighing 0.56oz on the convex surface of hardened lens
• Drop Ball Test: Z 87 Industrial Wear - 50" free fall of a 1" steel ball weighing 2.4oz on the convex surface of hardened lens & minimum 2.0 (applies to polycarbonate and trivex only) mm at thinnest point (3.0 mm minimum thickness was the previous Z 87 requirement - still is for glass and CR-39)
• ASTM (American Society for Testing and Materials) F803.88 is designated "sport" for frames - sport frames must be designated for specific sports.  As of this writing (9/15/2005) there is no frame designated for baseball.
• If pupil diameter is less than 2 mm, then diffraction will affect resolution

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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