Lens (optics)
= Lens
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= Lenses
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= Optical lens
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= Lens
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An <optical lens> is a transparent element, or assembly of elements, that redirects a bundle of <light rays> to form images or change how the bundle spreads. In an ordinary glass <optical lens>, <refraction> at the surfaces provides the redirection: their changing <normal vectors> make <Snell's law> bend different <light rays> by different amounts. A converging <optical lens> brings incoming <light rays> parallel to its <optical axis> toward an <optical focus>; a diverging <optical lens> makes them spread as if from an <optical focus> on the incoming side. https://openstax.org/books/university-physics-volume-3/pages/2-4-thin-lenses[Ling, Sanny and Moebs, OpenStax University Physics Volume 3, §2.4: Thin lenses]{ref}.
For a usual glass <thin lens> in air, a form thicker at the centre than at the edges normally converges, with positive <focal length>; one thinner at the centre normally diverges. Shape alone is insufficient: the <refractive index> relative to the surroundings also matters, as the <lensmaker's equation> shows. An <aperture> selects which <light rays> pass; an <optical lens> also changes their directions. The distinction explains how an <optical camera> can gather <light> from one object point over many incoming directions and deliver it to one image location.
The beautiful simplification is that an entire bundle can be characterized by a <focal length>, and two constructed <light rays> can locate an image. The <thin lens> examples below turn that geometry into a prediction of image position, orientation and <transverse magnification>. A real <optical lens> retains <optical aberrations> and <diffraction>, so the construction is a useful leading model rather than an exact solution of <Maxwell's equations>.<MIT 2.71 and 2.710 Optics, Spring 2014 by Nicholas X. Fang/Lecture Notes on Geometrical Optics>[§H]{ref}
Early mathematical treatments include <Johannes Kepler>'s 1611 Dioptrice, whose title explicitly concerns vision through newly invented instruments using transparent glass, and René Descartes's 1637 La Dioptrique, whose seventh discourse discusses improving vision with shaped glass. These are landmarks in explaining and designing <optical instruments>, rather than dates for the invention of the <optical lens>. https://www.e-rara.ch/zut/content/titleinfo/120202[Kepler, Dioptrice, 1611, original edition digitized by ETH-Bibliothek]{ref}; https://classiques.uqam.ca/classiques/Descartes/dioptrique/dioptrique.html[Descartes, La Dioptrique, 1637, seventh discourse, UQAM text edition]{ref}.