<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>1794-1237</journal-id>
<journal-title><![CDATA[Revista EIA]]></journal-title>
<abbrev-journal-title><![CDATA[Rev.EIA.Esc.Ing.Antioq]]></abbrev-journal-title>
<issn>1794-1237</issn>
<publisher>
<publisher-name><![CDATA[Escuela de ingenieria de Antioquia]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1794-12372018000100087</article-id>
<article-id pub-id-type="doi">10.24050/reia.v15i29.1129</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[DISEÑO GEOMÉTRICO DE UN PROPAGADOR DE RAYOS ÓPTICOS SOBRE UN SISTEMA ACOPLADO DE LENTES]]></article-title>
<article-title xml:lang="en"><![CDATA[GEOMETRICAL DESIGN OF AN OPTICAL RAY PROPAGATOR OVER A LENS-COUPLED SYSTEM]]></article-title>
<article-title xml:lang="pt"><![CDATA[DESENHO GEOMÉTRICO DE UM RAIOS ÓPTICOS PROPAGATOR EM UM SISTEMA DE LENTES ACOPLADAS]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Madrigal-Argáez]]></surname>
<given-names><![CDATA[Jairo]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Usma]]></surname>
<given-names><![CDATA[Jorge I.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Pérez]]></surname>
<given-names><![CDATA[John A.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,ITM Institución Universitaria Facultad de Artes y Humanidades ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
</aff>
<aff id="Af2">
<institution><![CDATA[,ITM Institución Universitaria Facultad de Ciencias Exactas y Aplicadas ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
</aff>
<aff id="Af3">
<institution><![CDATA[,ITM Institución Universitaria Facultad de Ciencias Exactas y Aplicadas ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2018</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2018</year>
</pub-date>
<volume>15</volume>
<numero>29</numero>
<fpage>87</fpage>
<lpage>95</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S1794-12372018000100087&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S1794-12372018000100087&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S1794-12372018000100087&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[RESUMEN Se presenta un esquema modular computacional para cálculo analítico y trazado geométrico de vectores los cuales al cruzarse satisfacen la ley de Snell. Este esquema es extendido a un sistema modular de lentes acoplados, dando lugar a un sistema óptico compuesto de conjuntos de lentes incrustados sobre el eje óptico. Las lentes son parametrizadas por un índice de refracción homogéneo asociado a una región de puntos cartesianos acotados por dos radios de curvatura separados y la pupila de entrada; en tanto que la refracción (en las superficies de la lente) es calculada como la interceptación de dos vectores geométricos bajo el régimen de la ley de Snell.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[ABSTRACT In this paper a computational modular scheme to calculate and draw a set of vectors which satisfy the Snell Law is presented. This scheme can be extended to build a modular coupled lenses system, so a compound optical system containing inlayed lenses over an optical axis can be admitted. The lenses are parametrized by a homogeneous refractive index which is associated to a Cartesian Coordinates System in which a region is limited by two separated radii of curvature and an entrance pupil while the refraction over the lens surface is calculated as the interception between two geometric vectors under Snell Law regime.]]></p></abstract>
<abstract abstract-type="short" xml:lang="pt"><p><![CDATA[RESUMO Apresenta-se um esquema modular computacional para o cálculo analítico e traçado geométrico de vetores os quais ao se cruzarem satisfazem a lei de Snell. Esse esquema e estendido a um sistema modular de lentes acopladas, dando lugar a um sistema óptico composto por conjuntos de lentes incorporados sobre o eixo óptico. As lentes são parametrizadas por um índice de refração homogêneo associado a uma região de pontos cartesianos dimensionais por dois rádios de curvatura separado e a pupila de entrada; em quanto a refração (nas superfícies da lente) e calculada como a intercepção dos vetores geométricos embaixo do regime da lei de Snell.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Lente geométrica]]></kwd>
<kwd lng="es"><![CDATA[Sistema modular de lentes]]></kwd>
<kwd lng="es"><![CDATA[Ley de Snell]]></kwd>
<kwd lng="es"><![CDATA[Óptica geométrica]]></kwd>
<kwd lng="en"><![CDATA[Geometric lens]]></kwd>
<kwd lng="en"><![CDATA[Modular lenses system]]></kwd>
<kwd lng="en"><![CDATA[Snell law]]></kwd>
<kwd lng="en"><![CDATA[Geometrical optics]]></kwd>
<kwd lng="pt"><![CDATA[Lente geométrica]]></kwd>
<kwd lng="pt"><![CDATA[Sistema de lentes modular]]></kwd>
<kwd lng="pt"><![CDATA[Lei de Snell]]></kwd>
<kwd lng="pt"><![CDATA[Óptica geométrica]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Gómez González]]></surname>
<given-names><![CDATA[E]]></given-names>
</name>
</person-group>
<source><![CDATA[Guía Básica de Conceptos de Óptica Geometrica]]></source>
<year>2012</year>
</nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Halrach]]></surname>
<given-names><![CDATA[K]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Matrix representation of gaussian optics]]></article-title>
<source><![CDATA[American Journal of Physics]]></source>
<year>1964</year>
</nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hetch]]></surname>
<given-names><![CDATA[E]]></given-names>
</name>
</person-group>
<source><![CDATA[Óptica]]></source>
<year>2005</year>
<edition>5</edition>
</nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hugh D. Young]]></surname>
<given-names><![CDATA[R. A. F]]></given-names>
</name>
</person-group>
<source><![CDATA[Física universitaria, con física moderna]]></source>
<year>2009</year>
<edition>Decimosegunda</edition>
<publisher-loc><![CDATA[México ]]></publisher-loc>
<publisher-name><![CDATA[AddisonWesley]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lehmann]]></surname>
<given-names><![CDATA[C]]></given-names>
</name>
</person-group>
<source><![CDATA[Geometría Analítica]]></source>
<year>1989</year>
<edition>Decimatercera</edition>
<publisher-loc><![CDATA[México ]]></publisher-loc>
<publisher-name><![CDATA[Limusa, S. A. de C. V]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Mortenson]]></surname>
<given-names><![CDATA[M]]></given-names>
</name>
</person-group>
<source><![CDATA[Mathematics for Computer Graphics]]></source>
<year>1999</year>
<edition>Second</edition>
<publisher-name><![CDATA[Industrial press,Inc]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Sagrario Millán]]></surname>
<given-names><![CDATA[M. y. o]]></given-names>
</name>
</person-group>
<source><![CDATA[Óptica Geométrica]]></source>
<year>2004</year>
<publisher-loc><![CDATA[Barcelona ]]></publisher-loc>
<publisher-name><![CDATA[Ariel]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Serrano]]></surname>
<given-names><![CDATA[A. C. R. y. G. U]]></given-names>
</name>
</person-group>
<source><![CDATA[ÓPTICA GEOME&#769;TRICA Resumen de Conceptos y Fórmulas]]></source>
<year>2005</year>
<publisher-loc><![CDATA[Puebla(Tonanzintla ) ]]></publisher-loc>
<publisher-name><![CDATA[Instituto Nacional de Astrofísica, Óptica y Electrónica]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Thompson]]></surname>
<given-names><![CDATA[D. M. a. B. J]]></given-names>
</name>
</person-group>
<source><![CDATA[Stravroudis, O. &#8220;Basic Ray Optics,&#8221;]]></source>
<year>2001</year>
<publisher-loc><![CDATA[New York ]]></publisher-loc>
<publisher-name><![CDATA[Handbook of Optical Engineering, Optical Eng]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Wolf]]></surname>
<given-names><![CDATA[M. B. &amp;. E]]></given-names>
</name>
</person-group>
<source><![CDATA[Principles of Optics]]></source>
<year>1970</year>
<edition>4</edition>
<publisher-name><![CDATA[Pergamon Press]]></publisher-name>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
