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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} }}}.}
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
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 Luneburg lens (original German Lüneburg lens) is a spherically symmetric gradient-index lens. A typical Luneburg lens's refractive index n decreases radially from the center to the outer surface. They can be made for use with electromagnetic radiation from visible light to radio waves .
A corrective lens can be used to correct myopia by imaging an object at infinity onto a virtual image at the patient's far point. According to the thin lens formula the required optical power P is P ≈ 1 ∞ − 1 F P = − 1 F P {\displaystyle P\approx {\frac {1}{\infty }}-{\frac {1}{{\mathit {F}}P}}=-{\frac {1}{{\mathit {F}}P}}} , [1]
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]
A ball lens is an optical lens in the shape of a sphere. Formally, it is a bi-convex spherical lens with the same radius of curvature on both sides, and diameter equal to twice the radius of curvature. The same optical laws may be applied to analyze its imaging characteristics as for other lenses. As a lens, a transparent sphere of any material ...