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A reflection through an axis. In mathematics, a reflection (also spelled reflexion) [1] is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as the set of fixed points; this set is called the axis (in dimension 2) or plane (in dimension 3) of reflection.
Then the xz plane is the interface, and the y axis is normal to the interface (see diagram). Let i and j (in bold roman type) be the unit vectors in the x and y directions, respectively. Let the plane of incidence be the xy plane (the plane of the page), with the angle of incidence θ i measured from j towards i.
In mathematics, a reflection formula or reflection relation for a function f is a relationship between f(a − x) and f(x). It is a special case of a functional equation . It is common in mathematical literature to use the term "functional equation" for what are specifically reflection formulae.
A rotation in the plane can be formed by composing a pair of reflections. First reflect a point P to its image P′ on the other side of line L 1. Then reflect P′ to its image P′′ on the other side of line L 2. If lines L 1 and L 2 make an angle θ with one another, then points P and P′′ will make an angle 2θ around point O, the ...
When a < 0 the graph is reflected in the x-axis as well as being stretched vertically. The constant b translates the graph horizontally left b units when b > 0, or right when b < 0. The constant c translates the graph vertically up c units when c > 0 or down when c < 0. The asymptotes of a truncus are found at x = -b (for the vertical asymptote ...
In the complex reflection coefficient plane the Smith chart occupies a circle of unity radius centred at the origin. In cartesian coordinates therefore the circle would pass through the points (+1,0) and (−1,0) on the x-axis and the points (0,+1) and (0,−1) on the y-axis.
Specular reflection, or regular reflection, is the mirror-like reflection of waves, such as light, from a surface. [ 1 ] The law of reflection states that a reflected ray of light emerges from the reflecting surface at the same angle to the surface normal as the incident ray, but on the opposing side of the surface normal in the plane formed by ...
In Euclidean geometry, the inversion of a point X with respect to a point P is a point X* such that P is the midpoint of the line segment with endpoints X and X*. In other words, the vector from X to P is the same as the vector from P to X*. The formula for the inversion in P is x* = 2p − x. where p, x and x* are the position vectors of P, X ...