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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. The image of a figure by a reflection is its mirror image in ...
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. Let the angle of refraction, measured in the same sense, be θ t, where the subscript t stands for transmitted (reserving r ...
In mathematics, reflection through the origin refers to the point reflection of Euclidean space R n across the origin of the Cartesian coordinate system. Reflection through the origin is an orthogonal transformation corresponding to scalar multiplication by − 1 {\displaystyle -1} , and can also be written as − I {\displaystyle -I} , where I ...
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 ...
The standard orientation, where the xy-plane is horizontal and the z-axis points up (and the x- and the y-axis form a positively oriented two-dimensional coordinate system in the xy-plane if observed from above the xy-plane) is called right-handed or positive. 3D Cartesian coordinate handedness. The name derives from the right-hand rule.
The most general form of this equation is = + + +, where n is the refractive index, λ is the wavelength, and A, B, C, etc., are coefficients that can be determined for a material by fitting the equation to measured refractive indices at known wavelengths.
In geometry, a glide reflection or transflection is a geometric transformation that consists of a reflection across a hyperplane and a translation ("glide") in a direction parallel to that hyperplane, combined into a single transformation. Because the distances between points are not changed under glide reflection, it is a motion or isometry.
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 ...