formulasearchengine - User contributions [en]

Mahler's 3/2 problem

2013-06-09T02:27:11Z

171.64.38.21: Flatto et. al have not solved Mahler's problem, see first page of their paper.

{{unreferenced|date=April 2013}}
In algebraic geometry, a '''complex algebraic variety''' is an [[algebraic variety]] (in the scheme sense or otherwise) over the field of [[complex number]]s. [[Algebraic geometry and analytic geometry#Chow.27s theorem|Chow's theorem]] states that a projective analytic variety; i.e., a closed analytic subvariety of the [[complex projective space]] <math>\mathbb{C}\mathbf{P}^n</math> is an algebraic variety; it is usually simply referred to as a [[projective variety]]. Not every complex analytic variety is algebraic, though.

[[Category:Algebraic varieties]]

{{geometry-stub}}

Formal scheme

2012-10-22T23:45:16Z

171.64.38.40: /* Morphisms between formal schemes */

{{Refimprove|date=February 2013}}

'''Field flattener lens''' is a type of [[Lens (optics)|lens]] used in modern [[binoculars|binocular]] designs (e.g. [[Canon (company)|Canon]] 10 x 42 L IS WP, 18 x 50 IS All Weather and [[Swarovski Optik|Swarovski]] EL 8.5 x 42, EL 10 x 42) and in astronomic [[Optical telescope|telescopes]].

Field flattener lenses in binoculars improve edge sharpness and lower the distortion.

Field flattener lenses counteract the [[Petzval field curvature]] of an optical system. In other words, the function of a field flattener lens is to counter the field-angle dependence of the focal length of a system.

The object in designing a field flattening lens is to create a lens that shifts the focal points of the Petzval surface to lie in the same plane. Consider inserting a pane of glass in a focusing beam. Due to refraction, the focal point of the beam is shifted by <math>\delta_{x}</math> dependent on the thickness of the glass. Thus we have a thickness as a function of focal shift: <math>t(\delta_{x})=(\frac{n}{n-1})\delta_{x}</math>.

<math>\delta_{x}(y)</math> is given by the radius of curvature of the Petzval surface, <math>R_{p}</math>. It can be shown, then, that the radius of curvature for the lens that would flatten out the field is given by <math>R_{f}=(\frac{n-1}{n})R_{p}.</math> <ref name=Geary>{{cite book|last=Geary|first=Joseph|title=Introduction to Lens Design with Practical ZEMAX Examples|year=2002|publisher=Willmann-Bell|isbn=0943396751}}</ref>

== See also ==
* [[Petzval field curvature]]

==References==

{{Reflist}}

{{DEFAULTSORT:Field Flattener Lens}}
[[Category:Lenses]]

{{optics-stub}}

Dold–Thom theorem

2012-03-30T00:02:07Z

171.64.38.43:

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