Related Experiment Video

Updated: May 13, 2026

Evanescent Field Based Photoacoustics: Optical Property Evaluation at Surfaces
10:21

Evanescent Field Based Photoacoustics: Optical Property Evaluation at Surfaces

Published on: July 26, 2016

Exact ray tracing formulas based on a nontrigonometric alternative to Snell's law

Hassan A Elagha1

  • 1High Institute of Optics Technology, El-Nozha, Heliopolis, Cairo 17361, Egypt. Hassanelagha@gmail.com

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|March 5, 2013
PubMed

More Related Videos

Interfacial Molecular-level Structures of Polymers and Biomacromolecules Revealed via Sum Frequency Generation Vibrational Spectroscopy09:43

Interfacial Molecular-level Structures of Polymers and Biomacromolecules Revealed via Sum Frequency Generation Vibrational Spectroscopy

Published on: August 13, 2019

Recombination Dynamics in Thin-film Photovoltaic Materials via Time-resolved Microwave Conductivity11:30

Recombination Dynamics in Thin-film Photovoltaic Materials via Time-resolved Microwave Conductivity

Published on: March 6, 2017

Related Concept Videos

The Law of Sines01:29

The Law of Sines

Solving oblique triangles—those without right angles—relies on specific trigonometric relationships, most notably the Law of Sines. This is because, unlike right triangles, where the Pythagorean theorem can be used to relate side lengths, oblique triangles lack a 90-degree angle and therefore require a different approach. The Pythagorean theorem is only valid for right-angled triangles, making it unsuitable for solving non-right triangles. In such cases, the Law of Sines becomes essential, as...
Trigonometric Identities II01:28

Trigonometric Identities II

Double-angle and half-angle trigonometric identities are derived from the fundamental sum and difference formulas and serve as essential tools for simplifying expressions, solving equations, and evaluating integrals. These identities reduce the complexity of trigonometric functions by relating functions of a multiple or fractional angle to functions of a single angle. Their applications extend across mathematics, physics, and engineering, particularly in Fourier analysis, wave mechanics, and...
Trigonometric Equations01:30

Trigonometric Equations

Trigonometric equations involve one or more trigonometric functions and arise frequently in mathematical modeling. These equations may be either identities, which are valid for all values of the variable, or conditional equations, which hold true only for specific values. The process of solving trigonometric equations typically involves both algebraic techniques and the use of fundamental properties of trigonometric functions.Some trigonometric equations resemble standard algebraic forms and...
Trigonometric Identities I01:27

Trigonometric Identities I

Trigonometric identities are equations that relate trigonometric functions and hold for all angles within their domains. A fundamental identity among these is the Pythagorean identity, which arises directly from the geometry of the unit circle. For any angle θ, a point on the unit circle has coordinates (cos⁡ θ, sin ⁡θ), and since the radius of the circle is one, the Pythagorean Theorem gives:This identity serves as the basis for deriving additional identities. Dividing the Pythagorean identity...
Trigonometry of Right Triangles01:29

Trigonometry of Right Triangles

In a right triangle, trigonometric functions establish specific ratios that describe the relationship between the lengths of the triangle's sides and its acute angles. These relationships are foundational in understanding the structure of right-angled geometry. The sine function quantifies the proportion of the side opposite a given angle compared to the triangle's hypotenuse. In contrast, the cosine function expresses how the side adjacent to the angle relates to the hypotenuse in terms of...
The Law of Cosines01:15

The Law of Cosines

The Law of Cosines is a fundamental result in trigonometry that relates the lengths of the sides of a triangle to the cosine of one of its angles. It serves as a generalization of the Pythagorean Theorem, enabling calculations in non-right triangles where the simple relationships of right-angled geometry no longer apply. The formula is especially useful in scenarios where direct measurement of one side or angle is not feasible, such as in surveying, navigation, and engineering applications.For...