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Optical Formulas Tutorial

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Table of Contents

Section I: Math Review Signed Numbers Calculators Significance and Precision Rounding Conversions Sine, Cosine, Tangent Scientific Notation Section II: Theory of Light Properties of waves Wave formula Diffraction Properties of Rays Vergence Illumination Absorption, reflection, refraction Law of reflection Laws of refraction Index of refraction Snell's law Critical angle Apparent Depth Apparent Thickness Lateral Displacement Dispersion and Abbe number Section III: Lenses Refraction through a lens Focal length formula Diopters Lens surfaces Lens types Radius of curvature Surface power formula Nominal power formula The lensmaker's equation Cylinders, compound lenses Lens Meridians Optical cross Flat transposition Cross cylinder transposition Hand neutralization Prescription notation Circle of least confusion Refractive errors Types of Ametropias Regular Astigmatisms With and Against the Rule Astigmatism Power in oblique meridians Vertex distance and effective power Effective power Compensated power Back and Front Vertex Power Section IV: Prisms Prism definitions Dispersion of Light by a Prism Object Displacement by a Prism Prism Power Segment Styles Section V: Surfacing and Finishing Lens and frame measurements Boxing System Datum System Frame Center Distance Decentration Effective Diameter Segment Height and Drop Segment Inset and Total Inset Minimum blank size Base curves Toric Transposition Refractive Power Formula Sagittal depth and lens thickness Prism thickness Section VI: Advanced Lens Formulas Martin's formula for lens tilt Spectacle Magnification Angular Magnification Thompson's formula for obliquely crossed cylinders Fresnel's equation for reflection Anti-reflective coatings Transmission through absorptive lenses Polarizing filters Section VII: Image Formation Image size and placement: mirrors Image size and placement: thin lenses Principal planes Image size and placement: thick lenses Nodal points Diagram of the human eye Appendices 1. Basic Glossary 2. ANSI Standards: Z80.1-1999 3. Optical Symbols and Formulas 4. Trigonometric Tables 5. Oblique Meridian (sine-squared method) table 6. References 7. Answer Key

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