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The numerical aperture with respect to a point P depends on the half-angle, θ1, of the maximum cone of light that can enter or exit the lens and the ambient index of refraction. As a pencil of light goes through a flat plane of glass, its half-angle changes to θ2. Due to Snell's law, the numerical aperture remains the same: NA = n1 sin θ1 ...
Ray transfer matrix analysis (also known as ABCD matrix analysis) is a mathematical form for performing ray tracing calculations in sufficiently simple problems which can be solved considering only paraxial rays. Each optical element (surface, interface, mirror, or beam travel) is described by a 2×2 ray transfer matrix which operates on a ...
The focal point F and focal length f of a positive (convex) lens, a negative (concave) lens, a concave mirror, and a convex mirror. The focal length of an optical system is a measure of how strongly the system converges or diverges light; it is the inverse of the system's optical power. A positive focal length indicates that a system converges ...
For optics in the visual range, the amount of dispersion of a lens material is often quantified by the Abbe number: V = n y e l l o w − 1 n b l u e − n r e d . {\displaystyle V={\frac {n_{\mathrm {yellow} }-1}{n_{\mathrm {blue} }-n_{\mathrm {red} }}}.}
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.
An imaging system may have many individual components, including one or more lenses, and/or recording and display components. Each of these contributes (given suitable design, and adequate alignment) to the optical resolution of the system; the environment in which the imaging is done often is a further important factor.
A dioptre ( British spelling) or diopter ( American spelling ), symbol dpt, is a unit of measurement with dimension of reciprocal length, equivalent to one reciprocal metre, 1 dpt = 1 m−1. It is normally used to express the optical power of a lens or curved mirror, which is a physical quantity equal to the reciprocal of the focal length ...
Here we assumed the lens is a collection of point masses at angular coordinates and distances =. Use sinh − 1 1 / x = ln ( 1 / x + 1 / x 2 + 1 ) ≈ − ln ( x / 2 ) {\displaystyle \sinh ^{-1}1/x=\ln(1/x+{\sqrt {1/x^{2}+1}})\approx -\ln(x/2)} for very small x we find
In optics, optical power (also referred to as dioptric power, refractive power, focusing power, or convergence power) is the degree to which a lens, mirror, or other optical system converges or diverges light. It is equal to the reciprocal of the focal length of the device: P = 1/f. [1]
Beam divergence. In electromagnetics, especially in optics, beam divergence is an angular measure of the increase in beam diameter or radius with distance from the optical aperture or antenna aperture from which the beam emerges. The term is relevant only in the "far field", away from any focus of the beam. Practically speaking, however, the ...