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In 1815, Brewster experimented with higher-quality materials and showed that this angle was a function of the refractive index, defining Brewster's law. Brewster's angle is often referred to as the "polarizing angle", because light that reflects from a surface at this angle is entirely polarized perpendicular to the plane of incidence ("s ...
Snell's law (also known as the Snell–Descartes law, the ibn-Sahl law, [1] and the law of refraction) is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water, glass, or air.
The haversine formula determines the great-circle distance between two points on a sphere given their longitudes and latitudes.Important in navigation, it is a special case of a more general formula in spherical trigonometry, the law of haversines, that relates the sides and angles of spherical triangles.
This phenomenon, known as total internal reflection, occurs at incidence angles for which Snell's law predicts that the sine of the angle of refraction would exceed unity (whereas in fact sin θ ≤ 1 for all real θ). For glass with n = 1.5 surrounded by air, the critical angle is approximately 42°.
The angles of proper spherical triangles are (by convention) less than π, so that < + + < (Todhunter, [1] Art.22,32). In particular, the sum of the angles of a spherical triangle is strictly greater than the sum of the angles of a triangle defined on the Euclidean plane, which is always exactly π radians.
When dealing with a beam that is nearly parallel to a surface, it is sometimes more useful to refer to the angle between the beam and the surface tangent, rather than that between the beam and the surface normal. The 90-degree complement to the angle of incidence is called the grazing angle or glancing angle. Incidence at small grazing angles ...
ω (omega) is the angle in the chain C α − C' − N − C α, φ (phi) is the angle in the chain C' − N − C α − C' ψ (psi) is the angle in the chain N − C α − C' − N (called φ′ by Ramachandran) The figure at right illustrates the location of each of these angles (but it does not show correctly the way they are defined). [8]
It is even possible to obtain a result slightly greater than one for the cosine of an angle. The third formula shown is the result of solving for a in the quadratic equation a 2 − 2ab cos γ + b 2 − c 2 = 0. This equation can have 2, 1, or 0 positive solutions corresponding to the number of possible triangles given the data.