<?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>0035-001X</journal-id>
<journal-title><![CDATA[Revista mexicana de física]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. mex. fis.]]></abbrev-journal-title>
<issn>0035-001X</issn>
<publisher>
<publisher-name><![CDATA[Sociedad Mexicana de Física]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0035-001X2010000100003</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Unfolding ray trace for plates and wedges]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Cardona-Nuñez]]></surname>
<given-names><![CDATA[O.]]></given-names>
</name>
<xref ref-type="aff" rid="A01"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Cornejo-Rodríguez]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<xref ref-type="aff" rid="A01"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[García-Flores]]></surname>
<given-names><![CDATA[P.C.]]></given-names>
</name>
<xref ref-type="aff" rid="A01"/>
</contrib>
</contrib-group>
<aff id="A01">
<institution><![CDATA[,Instituto Nacional de Astrofísica, Óptica y Electrónica  ]]></institution>
<addr-line><![CDATA[Puebla Pue.]]></addr-line>
<country>México</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>02</month>
<year>2010</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>02</month>
<year>2010</year>
</pub-date>
<volume>56</volume>
<numero>1</numero>
<fpage>14</fpage>
<lpage>20</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0035-001X2010000100003&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0035-001X2010000100003&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0035-001X2010000100003&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[We present a new procedure to obtain analytic expressions for tracing rays in plates and wedges used edgewise applying the unfolding method for ray tracing, to be able to analyze the behavior of these optical components for transporting light in optical systems. The plates and wedges are useful in transforming the shape and characteristics of light beams, and also for changing the focal ratio or aperture number of these beams. The analytic expressions derived are simple to use in any application.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Presentamos un nuevo procedimiento para obtener expresiones analíticas para trazar rayos en placas y cunas usadas de canto aplicando el método de desdoblamiento para trazar rayos, para analizar el comportamiento de las placas y cuñas para transportar luz en sistemas ópticos. Las placas y las cunas son útiles en transformar la forma y las característica de los haces de luz. Y también para cambiar la razón focal o número de abertura de esos haces. Las expresiones analíticas derivadas son sencillas de usar en cualquier aplicación.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Optical design]]></kwd>
<kwd lng="en"><![CDATA[ray trace]]></kwd>
<kwd lng="en"><![CDATA[plates]]></kwd>
<kwd lng="en"><![CDATA[wedges]]></kwd>
<kwd lng="es"><![CDATA[Diseño óptico]]></kwd>
<kwd lng="es"><![CDATA[trazo de rayos]]></kwd>
<kwd lng="es"><![CDATA[placas]]></kwd>
<kwd lng="es"><![CDATA[cuñas]]></kwd>
</kwd-group>
</article-meta>
</front><body><![CDATA[ <p align="justify"><font face="verdana" size="4">Investigaci&oacute;n</font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="center"><font face="verdana" size="4"><b>Unfolding ray trace for plates and wedges</b></font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="center"><font face="verdana" size="2"><b>O. Cardona&#150;Nu&ntilde;ez, A. Cornejo&#150;Rodr&iacute;guez, and P.C. Garc&iacute;a&#150;Flores</b></font></p>     <p align="center"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2"><i>Instituto Nacional de Astrof&iacute;sica, &Oacute;ptica y Electr&oacute;nica Apartado Postal 51 y 216, 72000 Puebla, Pue., M&eacute;xico.</i></font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2">Recibido el 13 de mayo de 2009    <br> Aceptado el 3 de diciembre de 2009</font></p>     ]]></body>
<body><![CDATA[<p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2"><b>Abstract</b></font></p>     <p align="justify"><font face="verdana" size="2">We present a new procedure to obtain analytic expressions for tracing rays in plates and wedges used edgewise applying the unfolding method for ray tracing, to be able to analyze the behavior of these optical components for transporting light in optical systems. The plates and wedges are useful in transforming the shape and characteristics of light beams, and also for changing the focal ratio or aperture number of these beams. The analytic expressions derived are simple to use in any application.</font></p>     <p align="justify"><font face="verdana" size="2"><b>Keywords: </b>Optical design; ray trace; plates; wedges.</font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2"><b>Resumen</b></font></p>     <p align="justify"><font face="verdana" size="2">Presentamos un nuevo procedimiento para obtener expresiones anal&iacute;ticas para trazar rayos en placas y cunas usadas de canto aplicando el m&eacute;todo de desdoblamiento para trazar rayos, para analizar el comportamiento de las placas y cu&ntilde;as para transportar luz en sistemas &oacute;pticos. Las placas y las cunas son &uacute;tiles en transformar la forma y las caracter&iacute;stica de los haces de luz. Y tambi&eacute;n para cambiar la raz&oacute;n focal o n&uacute;mero de abertura de esos haces. Las expresiones anal&iacute;ticas derivadas son sencillas de usar en cualquier aplicaci&oacute;n.</font></p>     <p align="justify"><font face="verdana" size="2"><b>Descriptores: </b>Dise&ntilde;o &oacute;ptico; trazo de rayos; placas; cu&ntilde;as.</font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2">PACS:42.15.Dp;42.15.Eq;42.15.&#150;i</font></p>     ]]></body>
<body><![CDATA[<p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2"><a href="/pdf/rmf/v56n1/v56n1a3.pdf" target="_blank">DESCARGAR ART&Iacute;CULO EN FORMATO PDF</a></font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2"><b>Acknowledgements</b></font></p>     <p align="justify"><font face="verdana" size="2">The authors greatly appreciate the technical assistance of Maria de los &Aacute;ngeles L&oacute;pez Castillo.</font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2"><b>References</b></font></p>     <!-- ref --><p align="justify"><font face="verdana" size="2">1. F.A.   Jenkins   and   H.E.   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