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Visulization of flux through differential area and solid angle. As always ^ is the unit normal to the incident surface A, = ^, and ^ is a unit vector in the direction of incident flux on the area element, θ is the angle between them.
Angles involved in a thin gravitational lens system. As shown in the diagram on the right, the difference between the unlensed angular position and the observed position is this deflection angle, reduced by a ratio of distances, described as the lens equation
Distances in the thin lens equation. For a lens of negligible thickness, and focal length f, the distances from the lens to an object, S 1, and from the lens to its image, S 2, are related by the thin lens formula: + =.
For a source right behind the lens, θ S = 0, the lens equation for a point mass gives a characteristic value for θ 1 that is called the Einstein angle, denoted θ E. When θ E is expressed in radians, and the lensing source is sufficiently far away, the Einstein Radius, denoted R E, is given by =. [2]
For a single lens surrounded by a medium of refractive index n = 1, the locations of the principal points H and H ′ with respect to the respective lens vertices are given by the formulas = ′ = (), where f is the focal length of the lens, d is its thickness, and r 1 and r 2 are the radii of curvature of its surfaces. Positive signs indicate ...
Magnetic lens. Electron optics is a mathematical framework for the calculation of electron trajectories in the presence of electromagnetic fields.The term optics is used because magnetic and electrostatic lenses act upon a charged particle beam similarly to optical lenses upon a light beam.
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.
For a thin lens or a curved mirror, + =, where u is the distance from the object to the center of the lens or mirror, v is the distance from the lens or mirror to the image, and f is the focal length of the lens or mirror.