Search results
Results from the WOW.Com Content Network
Fourier. v. t. e. In trigonometry, the law of tangents or tangent rule[1] is a statement about the relationship between the tangents of two angles of a triangle and the lengths of the opposing sides. In Figure 1, a, b, and c are the lengths of the three sides of the triangle, and α, β, and γ are the angles opposite those three respective sides.
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°.
Snell's law. Refraction of light at the interface between two media of different refractive indices, with n 2 > n 1. Since the velocity is lower in the second medium (v 2 < v 1), the angle of refraction θ 2 is less than the angle of incidence θ 1; that is, the ray in the higher-index medium is closer to the normal.
If we seek the required value of x, we find that the angles α and β satisfy Snell's law. Fermat's principle, also known as the principle of least time, is the link between ray optics and wave optics. Fermat's principle states that the path taken by a ray between two given points is the path that can be traveled in the least time.
Refractive index. In optics, the refractive index (or refraction index) of an optical medium is the ratio of the apparent speed of light in the medium to the speed in air or vacuum. The refractive index determines how much the path of light is bent, or refracted, when entering a material. This is described by Snell's law of refraction, n1 sin ...
Since it bisects the angle ∠FPT, this proves the tangent bisection property. The logic of the last paragraph can be applied to modify the above proof of the reflective property. It effectively proves the line BE to be the tangent to the parabola at E if the angles α are equal. The reflective property follows as shown previously.
Light passing through a Fresnel rhomb undergoes two total internal reflections at the same carefully chosen angle of incidence. After one such reflection, the p component is advanced by 1/8 of a cycle (45°; π/4 radians) relative to the s component. With two such reflections, a relative phase shift of 1/4 of a cycle (90°; π/2) is obtained. [6]
Solution of triangles (Latin: solutio triangulorum) is the main trigonometric problem of finding the characteristics of a triangle (angles and lengths of sides), when some of these are known. The triangle can be located on a plane or on a sphere. Applications requiring triangle solutions include geodesy, astronomy, construction, and navigation.