“reflection”的概念、定义、翻译、参考文献-科学参考

reflection

Physics

The return of all or part of a beam of particles or waves when it encounters the boundary between two media. The laws of reflection state: (1) that the incident ray, the reflected ray, and the normal to the reflecting interface at the point of incidence are all in the same plane; (2) that the angle of incidence equals the angle of reflection. See also mirror; reflectance; total internal reflection.

Mathematics

Let l be a line in the plane. Then the mirror-image of a point P is the point P′ such that PP′ is perpendicular to l and l cuts PP′ at its midpoint.

Reflection in l

Reflection in the line l is the transformation of the plane that maps each point P to its mirror-image P′. Suppose that the line l passes through the origin O and makes an angle α‎ with the x-axis. If P has polar coordinates (r,θ‎), its mirror-image P′ has polar coordinates (r,2α‎ − θ‎). In terms of Cartesian coordinates, reflection in the line l maps P with coordinates (x,y) to P′ with coordinates (x′,y′), where

$\begin{array}{l} x' = x cos 2 α + y sin 2 α, \\ y' = x sin 2 α - y cos 2 α . \end{array}$

In 3-dimensional space, an orthogonal matrix with determinant –1 and trace 1 represents a reflection in a plane containing the origin.

In higher dimensions, in ℝⁿ, reflection in the hyperplane with equation r∙n = c is given by

$r \mapsto r + 2 (\frac{c - r \cdot n}{n \cdot n}) n .$

If c = 0, this is represented by an orthogonal matrix. In general, reflections are isometries.

Geology and Earth Sciences

The rebounding of an object or wave (light, heat, sound, seismic, etc.) from a surface; the object or wave so reflected. In geophysics, a signal reflected from a reflector according to Snell’s law. A seismic reflection occurs as a result of a contrast in acoustic impedances; an electromagnetic reflection occurs because of a contrast in electrical and dielectrical properties.

单词	reflection
释义	reflection Physics The return of all or part of a beam of particles or waves when it encounters the boundary between two media. The laws of reflection state: (1) that the incident ray, the reflected ray, and the normal to the reflecting interface at the point of incidence are all in the same plane; (2) that the angle of incidence equals the angle of reflection. See also mirror; reflectance; total internal reflection. Mathematics Let l be a line in the plane. Then the mirror-image of a point P is the point P′ such that PP′ is perpendicular to l and l cuts PP′ at its midpoint. Reflection in l Reflection in the line l is the transformation of the plane that maps each point P to its mirror-image P′. Suppose that the line l passes through the origin O and makes an angle α‎ with the x-axis. If P has polar coordinates (r,θ‎), its mirror-image P′ has polar coordinates (r,2α‎ − θ‎). In terms of Cartesian coordinates, reflection in the line l maps P with coordinates (x,y) to P′ with coordinates (x′,y′), where $\begin{array}{l} x' = x cos 2 α + y sin 2 α, \\ y' = x sin 2 α - y cos 2 α . \end{array}$ In 3-dimensional space, an orthogonal matrix with determinant –1 and trace 1 represents a reflection in a plane containing the origin. In higher dimensions, in ℝⁿ, reflection in the hyperplane with equation r∙n = c is given by $r \mapsto r + 2 (\frac{c - r \cdot n}{n \cdot n}) n .$ If c = 0, this is represented by an orthogonal matrix. In general, reflections are isometries. Geology and Earth Sciences The rebounding of an object or wave (light, heat, sound, seismic, etc.) from a surface; the object or wave so reflected. In geophysics, a signal reflected from a reflector according to Snell’s law. A seismic reflection occurs as a result of a contrast in acoustic impedances; an electromagnetic reflection occurs because of a contrast in electrical and dielectrical properties.
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