Introduction Light Refraction Tank Analogy Last Update: October 20,2024 This post provides a useful analogy for the bending and slowing of light rays when light is refracted from a lower refractive medium (e.g. air) to a higher refractive medium (e.g. glass or water). Also see my posts: Snell’s Law. Refractive Geometric Optics and Understand Your […]
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Menu (linked Index) Wave Superposition Last Update: October 20, 2024 Introduction Electromagnetic Wave Superposition Why Light Slows Down Introduction Electromagnetic waves produced by different sources will combine in a process called superposition. In this post, we’ll describe basic wave superposition and why light slows down when entering a medium with a higher refractive index. Also
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Menu (linked Index) Vision Correction Last Update: Feb 5, 2025 Introduction Anatomy of the Eye Near Sightedness and Far Sightedness A Normal Eye with Perfect Vision Far Sightedness and Its Correction Presbyopia Near Sightedness and its Correction Astigmatism Eye Glass / Contact Prescription Refractive Vision Error Corrective Procedures for Near Sightedness, Far Sightedness, Presbyopia, and
Menu (linked Index) Cataract Surgery : From Darkness, Light Last Update: February 9, 2025 Introduction What are Cataracts? Couching for Cataracts History of Cataract Surgical Procedures Characteristics of a Modern Cataract Surgery Pre-Cataract Surgery Homework A Modern Cataract Procedure Conclusion Also refer to my post: Understand Your Eyes where you can link to other eye and optics
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Menu (linked Index) Cataract Tabulated History Last Update: January 21, 2025 Introduction Cataract Historical Timeline Cataract References Introduction In this post I’ve created a (roughly) chronological tabulated history of cataract procedures and surgery developments through the ages. The first table is the historical listing, including a reference source number. The second table provided can then
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Menu (linked Index) Geometry and Trigonometry Rules Last Update: October 20, 2024 Introduction Similar Triangles Exterior and Interior Angles of Triangles Law of Cosines and Sines Right Triangle Trigonometric Functions Small Angle Approximations Radius of Curvature Normal (Perpendicular) Line to Circle Surface Introduction This post summarizes some useful geometric and trigonometric functions and rules. Return
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Exploring Euler’s Formula Exploring Euler’s Formula Last Update: December 18, 2024 Euler’s Identity It all started for me when I came across the formula below. It’s called Euler’s Identity. If you are a mathematician, you are getting pretty excited right now just seeing this equation. Kind of like a sportscaster’s reaction when you talk about
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Menu (linked Index) Unit Circle and Definitions of Radian and π Last Update: June 9, 2025 Introduction Properties of a Circle The Unit Circle and The Radian Conclusion Introduction In this post we’ll review some of the important mathematical formulas and properties derived from the circle. You probably know that the constant pi = π
Menu (linked Index) Number Classifications Last Update: November 25, 2024 Introduction Number Classification Organization Chart Number Classification Description Number Classification – Venn Chart – High Level Number Classification – Venn Chart – Real Numbers Number Classification – Venn Chart – Full Chart Introduction Understanding the various number types (classifications) is critical to gaining a deeper
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Menu (linked Index) Euler’s Formula Derivation Last Update: December 12, 2024 Introduction The Derivative Derivative Rules Derivatives of Useful Functions Taylor and Maclaurin Power Series Euler Formula Derivation Summary of the Derivation Conclusion Appendix 1 – Graphical meaning of (x-a) Appendix 2 – Full Derivation of Taylor and Maclaurin Power Series Appendix 3 – Unit
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