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The equation of a line can be given in vector form: = + Here a is the position of a point on the line, and n is a unit vector in the direction of the line. Then as scalar t varies, x gives the locus of the line. The distance of an arbitrary point p to this line is given by
The OPD can be calculated from the following equation: O P D = d 1 n 1 − d 2 n 2 {\displaystyle \mathrm {OPD} =d_{1}n_{1}-d_{2}n_{2}} where d 1 and d 2 are the distances of the ray passing through medium 1 or 2, n 1 is the greater refractive index (e.g., glass) and n 2 is the smaller refractive index (e.g., air).
A tactical light mounted to the bottom rail of a rifle Tactical light and a target in a low-light environment. A tactical light or weapon light is a flashlight used in conjunction with a firearm to aid low-light target identification, allowing the user to simultaneously aim a weapon and illuminate the target. Tactical lights can be handheld or ...
Kirchhoff's integral theorem, sometimes referred to as the Fresnel–Kirchhoff integral theorem, [3] uses Green's second identity to derive the solution of the homogeneous scalar wave equation at an arbitrary spatial position P in terms of the solution of the wave equation and its first order derivative at all points on an arbitrary closed surface as the boundary of some volume including P.
Given n lines L and a point P(L) on each line, find the locus of points Q such that the lengths of the line segments QP(L) satisfy certain conditions. For example, when n = 4, given the lines a, b, c, and d and a point A on a, B on b, and so on, find the locus of points Q such that the product QA*QB equals the product QC*QD.
Distance from the origin O to the line E calculated with the Hesse normal form. Normal vector in red, line in green, point O shown in blue. In analytic geometry, the Hesse normal form (named after Otto Hesse) is an equation used to describe a line in the Euclidean plane, a plane in Euclidean space, or a hyperplane in higher dimensions.
Rayleigh distance in optics is the axial distance from a radiating aperture to a point at which the path difference between the axial ray and an edge ray is λ / 4. An approximation of the Rayleigh Distance is Z = D 2 2 λ {\displaystyle Z={\frac {D^{2}}{2\lambda }}} , in which Z is the Rayleigh distance, D is the aperture of radiation, λ the ...
The last term, proportional to the second derivative of the unit direction vector ′, is sensitive to charge motion perpendicular to the line of sight. It can be shown that the electric field generated by this term is proportional to a t / r ′ {\displaystyle a_{t}/r'} , where a t {\displaystyle a_{t}} is the transverse acceleration in the ...
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