{"id":34522,"date":"2021-09-18T13:00:17","date_gmt":"2021-09-18T13:00:17","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=34522"},"modified":"2025-09-08T05:32:46","modified_gmt":"2025-09-08T05:32:46","slug":"refractio-lucis-et-lex-snellii","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/la\/refractio-lucis-et-lex-snellii\/","title":{"rendered":"Refractio Lucis et Lex Snellii"},"content":{"rendered":"<p><center><\/p>\n<h1>Refractio Lucis et Lex Snellii<\/h1>\n<p><em><strong>Summarium:<\/strong><br \/>\nIn hac lectione explorabitur refractio lucis per analysin Legis Snellii. Explicabitur notio indicis refractionis, derivabitur Lex Snellii utens principio Fermat, et investigabitur quomodo haec lex sinat calculare trajectoriam radiorum lucis transeuntium inter diversa media. Praeterea tractabuntur phaenomena reflexionis et reflexionis totalis, his notionibus adhibitis in serie exercitationum practicorum. Propositum est intelligere et applicare Legem Snellii in problematibus opticis.<\/em><\/p>\n<p><strong>Proposita Discendi<\/strong><\/p>\n<ol style=\"text-align:left\">\n<li><strong>Intellegere<\/strong> notionem indicis refractionis eiusque relationem cum velocitate lucis in diversis mediis.<\/li>\n<li><strong>Applicare<\/strong> principium Fermat ad intellegendum quomodo lux sequatur trajectoriam quae minuit tempus itineris inter duo puncta.<\/li>\n<li><strong>Demonstrari<\/strong> Legem Snellii ex principio Fermat, ad determinandam trajectoriam radii lucis transeuntis per diversa media.<\/li>\n<li><strong>Computare<\/strong> angulos incidentiae et refractionis utens Lege Snellii in condicionibus cum diversis indicibus refractionis.<\/li>\n<li><strong>Intellegere<\/strong> notionem reflexionis totalis internae eiusque nexum cum angulo critico et indicibus refractionis.<\/li>\n<li><strong>Determinare<\/strong> angulum criticum pro reflexione totali interna in superficie inter duo media.<\/li>\n<\/ol>\n<p><strong>INDEX CONTENTORUM<\/strong><br \/>\n<a href=\"#1\"><strong>Index refractionis<\/strong><\/a><br \/>\n<a href=\"#2\">Principium Fermat<\/a><br \/>\n<a href=\"#3\">Lex Snellii de refractione lucis<\/a><br \/>\n<a href=\"#4\"><strong>Refractio, reflexio et reflexio totalis lucis<\/strong><\/a><br \/>\n<a href=\"#5\"><strong>Exercitia<\/strong><\/a><\/p>\n<p><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/LxhWbErujpo\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><br \/>\n<a name=\"1\"><\/a><\/p>\n<h2>Index refractionis<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=LxhWbErujpo&amp;t=186s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">Definitor index refractionis<\/span><\/strong><\/a> medii ut ratio inter velocitatem lucis in vacuo et velocitatem lucis in eodem medio. Haec est quantitas sine dimensione et plerumque repraesentatur per litteram <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_k:<\/span><\/span><\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_k=\\displaystyle \\frac{c}{c_k}<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">Ubi <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">c<\/span><\/span> est velocitas lucis in vacuo et <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">c_k<\/span><\/span> est velocitas lucis in medio <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">Cum lux semper tardius moveatur in quolibet medio quam in vacuo, habetur quod index refractionis semper maior vel aequalis est 1.<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h3>Principium Fermat<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=LxhWbErujpo&amp;t=397s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">Velocitas lucis pendet<\/span><\/strong><\/a> ex medio in quo iter facit. Quanto maiorem indicem refractionis medium habet, tanto minor erit velocitas lucis in eo; et ad hoc refertur principium Fermat:<\/p>\n<p style=\"text-align: center; background-color: #80ff80;\">Cum lux iter facit ab uno puncto ad alterum, sequitur trajectoriam quae minuit tempus itineris.<\/p>\n<p style=\"text-align: justify;\">Hoc principium valet etiam cum lux per diversa media transit.<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h3>Lex Snellii de refractione lucis<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=LxhWbErujpo&amp;t=608s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">Ex principiis a Fermat constitutis<\/span><\/strong><\/a> possibile est formare problema optimizationis quod sinet investigare trajectoriam quam radius lucis sequatur transeundo per diversa media. Hoc est quod tandem ad Legem Snellii perducit, cuius expositionem et demonstrationem infra videbimus.<\/p>\n<p style=\"text-align: justify;\">Ponamus radium egredi ex puncto A et advenire ad punctum B transeundo per superficiem quae separat duo media cum indicibus refractionis <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_1<\/span><\/span> et <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_2<\/span><\/span> respective. Propositum nostrum erit invenire relationem quae nobis permittat computare trajectoriam radii lucis sequendo principium Fermat de minimo tempore itineris; ad hoc componitur sequens schema:<\/p>\n<p><center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-1CdoEOp5SHc\/YUDNPnQyOxI\/AAAAAAAAFjE\/RG-kYgV4KKwAE3QwiM9nB3cA-OOXesONQCLcBGAsYHQ\/s0\/n1n2leydeSnell.PNG\" width=\"875\" height=\"518\" alt=\"Lex Snellii\" class=\"alignnone size-full lazyload\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-1CdoEOp5SHc\/YUDNPnQyOxI\/AAAAAAAAFjE\/RG-kYgV4KKwAE3QwiM9nB3cA-OOXesONQCLcBGAsYHQ\/s0\/n1n2leydeSnell.PNG\" width=\"875\" height=\"518\" alt=\"Lex Snellii\" class=\"alignnone size-full lazyload\" \/><\/noscript><\/center><\/p>\n<p style=\"text-align: justify;\">Ratiocinatio incipit ex analysi formae temporis itineris radii lucis. Habemus:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}{Tempus\\,Itineris} &amp; =\\displaystyle \\frac{{Distantia}}{{Celeritas}} \\\\ \\\\ &amp; \\displaystyle =\\frac{{Distantia\\,in\\,medio\\,1}}{{Celeritas\\,in\\,medio\\,1}} + \\frac{{Distantia\\,in\\,medio\\,2}}{{Celeritas\\,in\\,medio\\,2}}\\\\ \\\\&amp; =\\displaystyle \\frac{\\sqrt{a^2 + x^2}}{c_1} + \\frac{\\sqrt{b^2 + (d-x)^2}}{c_2}\\end{array}<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">His positis, manentibus fixis punctis A et B, tempus itineris determinatur per punctum <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x<\/span><\/span> ubi radius interfaciem inter media attingit. Hoc modo definiri potest functio temporis <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">t(x)<\/span><\/span> per<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">t(x) = \\displaystyle \\frac{1}{c_1}\\sqrt{a^2 + x^2} + \\frac{1}{c_2}\\sqrt{b^2 + (d-x)^2}<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">Nunc, cum principium Fermat statuat lucem sequi trajectoriam quae minuit tempus itineris, possibile est ex hoc invenire <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x<\/span><\/span> quod minuit functionem <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">t(x).<\/span><\/span> Agitur de problemate optimizationis.<\/p>\n<p style=\"text-align: justify;\">Derivando <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">t<\/span><\/span> respectu <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x<\/span><\/span> habetur:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\begin{array}{rl}\\dfrac{dt}{dx} &amp;\\displaystyle = \\frac{1}{c_1}\\frac{d}{dx}\\sqrt{a^2 + x^2} + \\frac{1}{c_2}\\frac{d}{dx}\\sqrt{b^2+(d-x)^2}\\\\ \\\\ &amp;\\displaystyle = \\frac{1}{c_1} \\frac{2x}{2\\sqrt{a^2 + x^2}} + \\frac{1}{c_2}\\frac{2(d-x)(-1)}{2\\sqrt{b^2+(d-x)^2}} \\\\ \\\\ &amp;\\displaystyle = \\frac{1}{c_1} \\frac{x}{\\sqrt{a^2 + x^2}} - \\frac{1}{c_2}\\frac{(d-x)}{\\sqrt{b^2+(d-x)^2}} \\end{array}<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">Iam animadvertamus quod:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\\sin(\\theta_1) &amp;\\displaystyle =\\frac{x}{\\sqrt{a^2 + x^2}}\\\\ \\\\ \\sin(\\theta_2) &amp;\\displaystyle = \\frac{(d-x)}{\\sqrt{b^2+(d-x)^2}} \\\\ \\\\ c_1 &amp; \\displaystyle = \\frac{c}{n_1} \\\\ \\\\ c_2 &amp; \\displaystyle = \\frac{c}{n_2} \\end{array} <\/span><\/span><\/p>\n<p style=\"text-align: justify;\">Itaque, substitutis his in derivata temporis, habetur:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{dt}{dx} = \\frac{n_1}{c} \\sin(\\theta_1) - \\frac{n_2}{c}\\sin(\\theta_2)<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">Denique, si punctum <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x<\/span><\/span> minuit functionem <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">t(x),<\/span><\/span> tunc derivata annihilatur et habetur:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\color{blue}{n_1 \\sin(\\theta_1) = n_2 \\sin(\\theta_2)}<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">Haec est Lex Snellii pro refractione radii lucis transeuntis inter duo media et nobis ostendit relationem quae intercedit inter angulum incidentiae <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\theta_1<\/span><\/span> et angulum refractum <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\theta_2.<\/span><\/span><\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>Refractio, reflexio et reflexio totalis lucis<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=LxhWbErujpo&amp;t=1614s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">Vidimus quod cum lux<\/span> <\/strong><\/a>de uno medio ad aliud transeat, refringitur; sed generatim fit compositio inter refractionem et reflexionem, et secundum indices refractionis atque angulum incidentiae radii lucis, refractio evanescere potest ita ut sola reflexio remaneat.<\/p>\n<p style=\"text-align: justify;\">Ponamus radium lucis incidere ex materiali <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a<\/span><\/span> in aliud <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b<\/span><\/span> cum indicibus refractionis <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_a<\/span><\/span> et <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_b<\/span><\/span> respective. Si <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_a \\gt n_b,<\/span><\/span> ex Lege Snellii habebitur<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\sin(\\theta_b) = \\frac{n_a}{n_b}\\sin(\\theta_a)<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">Cum <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_a\/n_b \\gt 1,<\/span><\/span> evenit ut <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\sin(\\theta_b) \\gt \\sin(\\theta_a),<\/span><\/span> quod significat radium refractum a norma discedere. Hoc significat existere aliquod <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\theta_a\\lt 90^o<\/span><\/span> pro quo <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\sin(\\theta_b)=1<\/span><\/span> et, proinde, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\theta_b=90^o,<\/span><\/span> ut ostenditur in sequenti figura.<\/p>\n<p style=\"text-align: justify;\">Angulus incidentiae qui efficit ut radius refringatur per superficiem appellatur angulus criticus et satisfacit relationi<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\sin(\\theta_{critico}) = \\frac{n_b}{n_a}<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">Quod aequivalet dicere:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\theta_{critico} = \\arcsin\\left( \\frac{n_b}{n_a} \\right)<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">Si <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\theta_a \\gt \\theta_{critico},<\/span><\/span> tunc fit reflexio totalis.<\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h2>Exercitia:<\/h2>\n<ol style=\"text-align: justify;\">\n<li>Consideretur radius lucis transeuns ex aqua in vitrum ut ostenditur in sequenti figura:<br \/>\n<center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-98FbTK-_FZo\/YT-61nYxRnI\/AAAAAAAAFiM\/JbBsuAnS6IA8aB-4hvroeZ1qDF2ebxQUwCLcBGAsYHQ\/s0\/n1n2snell.PNG\" width=\"442\" height=\"321\" alt=\"radius lucis transeuns ex aqua in vitrum\" class=\"alignnone size-full lazyload\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-98FbTK-_FZo\/YT-61nYxRnI\/AAAAAAAAFiM\/JbBsuAnS6IA8aB-4hvroeZ1qDF2ebxQUwCLcBGAsYHQ\/s0\/n1n2snell.PNG\" width=\"442\" height=\"321\" alt=\"radius lucis transeuns ex aqua in vitrum\" class=\"alignnone size-full lazyload\" \/><\/noscript><\/center><br \/>\nIndex refractionis aquae est <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_1 = 1,33,<\/span><\/span> et vitri est <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_2=1,52.<\/span><\/span> Si radius lucis transeuns ex aqua in vitrum incidit in superficiem quae utrumque medium separat cum angulo inclinationis <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\theta_1 = 60^o<\/span><\/span> respectu normae, quo angulo <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\theta_2<\/span><\/span> egreditur radius refractus? <span class=\"collapseomatic \" id=\"id69e03a056e16a\"  tabindex=\"0\" title=\"SOLUTIO\"    >SOLUTIO<\/span><div id=\"target-id69e03a056e16a\" class=\"collapseomatic_content \">\nUtendo Lege Snellii habetur:<\/p>\n<table>\n<tbody>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(1)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_1 \\sin(\\theta_1) = n_2 \\sin(\\theta_2)<\/span><\/span><\/td>\n<td>; Lex Snellii<\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\equiv <\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\sin(\\theta_2) = \\frac{n_1}{n_2}\\sin(\\theta_1)<\/span><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\equiv <\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\theta_2 = \\arcsin\\left(\\frac{n_1}{n_2}\\sin(\\theta_1)\\right)<\/span><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(2)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_1=1,33<\/span><\/span><\/td>\n<td>; Index refractionis aquae<\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(3)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_2=1,52<\/span><\/span><\/td>\n<td>; Index refractionis vitri<\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(4)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\theta_1=60^o<\/span><\/span><\/td>\n<td>; Angulus incidentiae in superficie radii lucis<\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(5)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\theta_2 = \\arcsin\\left(\\frac{1,33}{1,52}\\sin(60^o)\\right) \\approx 49,268^o<\/span><\/span><\/td>\n<td>; Ex (1,2,3,4), Angulus refractionis<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div><a href=\"https:\/\/www.youtube.com\/watch?v=LxhWbErujpo&amp;t=1363s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\"><\/span><\/strong><\/a><\/li>\n<li>Tria liquida separata per duas superficies habent hos indices refractionis: <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_1=1,33,<\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_2=1,41<\/span><\/span> et <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_3=1,68,<\/span><\/span>, et disponuntur ut ostenditur in sequenti figura:<center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-AAZlxjqC4s4\/YUAdiGNMSQI\/AAAAAAAAFiU\/mOE-xMfybOoxenNH2O8sufjpTuzH6-WIwCLcBGAsYHQ\/s0\/n1n2n3snell.PNG\" width=\"443\" height=\"430\" alt=\"Lex Snellii applicata tribus mediis\" class=\"alignnone size-full lazyload\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-AAZlxjqC4s4\/YUAdiGNMSQI\/AAAAAAAAFiU\/mOE-xMfybOoxenNH2O8sufjpTuzH6-WIwCLcBGAsYHQ\/s0\/n1n2n3snell.PNG\" width=\"443\" height=\"430\" alt=\"Lex Snellii applicata tribus mediis\" class=\"alignnone size-full lazyload\" \/><\/noscript><\/center>Si radius qui transit ex medio cum indice <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_1<\/span><\/span> in medium <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_2<\/span><\/span> incidat in superficiem cum angulo <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\theta_1=70^o<\/span><\/span>, quo angulo refringetur cum transeat in medium cum indice <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_3<\/span><\/span>?<br \/>\n<span class=\"collapseomatic \" id=\"id69e03a056ea5b\"  tabindex=\"0\" title=\"SOLUTIO\"    >SOLUTIO<\/span><div id=\"target-id69e03a056ea5b\" class=\"collapseomatic_content \">\nSimiliter ac in exercitio priore, habetur sequens ratiocinatio:<\/p>\n<table>\n<tbody>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(1)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_1 \\sin(\\theta_1) = n_2 \\sin(\\theta_2) <\/span><\/span><\/td>\n<td>; Lex Snellii pro transitu a medio n1 ad n2<\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(2)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_2 \\sin(\\theta_2) = n_3 \\sin(\\theta_3) <\/span><\/span><\/td>\n<td>; Lex Snellii pro transitu a medio n2 ad n3<\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(3)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_1 \\sin(\\theta_1) = n_3 \\sin(\\theta_3) <\/span><\/span><\/td>\n<td>; Ex (1,2)<\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\equiv<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\sin(\\theta_3) = \\frac{n_1}{n_3}\\sin(\\theta_1) <\/span><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\equiv<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\theta_3 = \\arcsin\\left(\\frac{n_1}{n_3}\\sin(\\theta_1)\\right) <\/span><\/span><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Denique, substitutis valoribus, habetur:<\/p>\n<p><center><br \/>\n<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\theta_3= \\arcsin\\left(\\frac{1,33}{1,68}\\sin(70^o)\\right) \\approx 48,0667^o <\/span><\/span><\/center><br \/>\nAnimadvertendum est hoc ratiocinium ostendere nos posse computationes facere solum sumendo media initii et exitus radii, medio intermedio omnino neglecto.<br \/>\n<\/div>\n<a href=\"https:\/\/www.youtube.com\/watch?v=LxhWbErujpo&amp;t=1417s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\"><\/span><\/strong><\/a><\/li>\n<li>Ex imo piscinae iacitur radius lucis versus superficiem aeris et aquae. Determinandus est angulus incidentiae ut fiat reflexio totalis.<center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-GiDk_G3uybI\/YUDhONr0MaI\/AAAAAAAAFjM\/aSGUOspZeCsm7Cz7DG4r-JrCr03QhYyBgCLcBGAsYHQ\/s0\/%25C3%25A1ngulocr%25C3%25ADtico.PNG\" width=\"588\" height=\"358\" alt=\"radius lucis incidens in angulo critico\" class=\"alignnone size-full lazyload\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-GiDk_G3uybI\/YUDhONr0MaI\/AAAAAAAAFjM\/aSGUOspZeCsm7Cz7DG4r-JrCr03QhYyBgCLcBGAsYHQ\/s0\/%25C3%25A1ngulocr%25C3%25ADtico.PNG\" width=\"588\" height=\"358\" alt=\"radius lucis incidens in angulo critico\" class=\"alignnone size-full lazyload\" \/><\/noscript><\/center><br \/>\n<span class=\"collapseomatic \" id=\"id69e03a056ee01\"  tabindex=\"0\" title=\"SOLUTIO\"    >SOLUTIO<\/span><div id=\"target-id69e03a056ee01\" class=\"collapseomatic_content \">\nAngulus criticus datur per:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\theta_{critico}= \\arcsin\\left(\\frac{1,00}{1,33}\\right) \\approx 48,7535^o<\/span><\/span><\/p>\n<\/div><a href=\"https:\/\/www.youtube.com\/watch?v=LxhWbErujpo&amp;t=1869s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\"><\/span><\/strong><\/a><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>Refractio Lucis et Lex Snellii Summarium: In hac lectione explorabitur refractio lucis per analysin Legis Snellii. Explicabitur notio indicis refractionis, derivabitur Lex Snellii utens principio Fermat, et investigabitur quomodo haec lex sinat calculare trajectoriam radiorum lucis transeuntium inter diversa media. Praeterea tractabuntur phaenomena reflexionis et reflexionis totalis, his notionibus adhibitis in serie exercitationum practicorum. Propositum [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":27682,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":24,"footnotes":""},"categories":[1280,1250],"tags":[],"class_list":["post-34522","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-optica-geometrica-la","category-physica"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Refractio Lucis et Lex Snellii - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Refractio et Lex Snellii explicatae: disce quomodo lux mutet directionem transeundo inter media, computa angulos incidentiae et refractionis, et solve exercitationes practicas.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"http:\/\/toposuranos.com\/material\/la\/refractio-lucis-et-lex-snellii\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Refractio Lucis et Lex Snellii\" \/>\n<meta property=\"og:description\" content=\"Refractio et Lex Snellii explicatae: disce quomodo lux mutet directionem transeundo inter media, computa angulos incidentiae et refractionis, et solve exercitationes practicas.\" \/>\n<meta property=\"og:url\" content=\"http:\/\/toposuranos.com\/material\/la\/refractio-lucis-et-lex-snellii\/\" \/>\n<meta property=\"og:site_name\" content=\"toposuranos.com\/material\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/groups\/toposuranos\" \/>\n<meta property=\"article:published_time\" content=\"2021-09-18T13:00:17+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-09-08T05:32:46+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/08\/leydesnell.jpg\" \/>\n<meta name=\"author\" content=\"giorgio.reveco\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:title\" content=\"Refractio Lucis et Lex Snellii\" \/>\n<meta name=\"twitter:description\" content=\"Refractio et Lex Snellii explicatae: disce quomodo lux mutet directionem transeundo inter media, computa angulos incidentiae et refractionis, et solve exercitationes practicas.\" \/>\n<meta name=\"twitter:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/08\/leydesnell.jpg\" \/>\n<meta name=\"twitter:creator\" content=\"@topuranos\" \/>\n<meta name=\"twitter:site\" content=\"@topuranos\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"giorgio.reveco\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tiempo de lectura\" \/>\n\t<meta name=\"twitter:data2\" content=\"6 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"http:\/\/toposuranos.com\/material\/la\/refractio-lucis-et-lex-snellii\/#article\",\"isPartOf\":{\"@id\":\"http:\/\/toposuranos.com\/material\/la\/refractio-lucis-et-lex-snellii\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"Refractio Lucis et Lex Snellii\",\"datePublished\":\"2021-09-18T13:00:17+00:00\",\"dateModified\":\"2025-09-08T05:32:46+00:00\",\"mainEntityOfPage\":{\"@id\":\"http:\/\/toposuranos.com\/material\/la\/refractio-lucis-et-lex-snellii\/\"},\"wordCount\":1304,\"commentCount\":0,\"publisher\":{\"@id\":\"http:\/\/toposuranos.com\/material\/#organization\"},\"image\":{\"@id\":\"http:\/\/toposuranos.com\/material\/la\/refractio-lucis-et-lex-snellii\/#primaryimage\"},\"thumbnailUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/08\/leydesnell.jpg\",\"articleSection\":[\"Optica Geometrica\",\"Physica\"],\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"http:\/\/toposuranos.com\/material\/la\/refractio-lucis-et-lex-snellii\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"http:\/\/toposuranos.com\/material\/la\/refractio-lucis-et-lex-snellii\/\",\"url\":\"http:\/\/toposuranos.com\/material\/la\/refractio-lucis-et-lex-snellii\/\",\"name\":\"Refractio Lucis et Lex Snellii - toposuranos.com\/material\",\"isPartOf\":{\"@id\":\"http:\/\/toposuranos.com\/material\/#website\"},\"primaryImageOfPage\":{\"@id\":\"http:\/\/toposuranos.com\/material\/la\/refractio-lucis-et-lex-snellii\/#primaryimage\"},\"image\":{\"@id\":\"http:\/\/toposuranos.com\/material\/la\/refractio-lucis-et-lex-snellii\/#primaryimage\"},\"thumbnailUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/08\/leydesnell.jpg\",\"datePublished\":\"2021-09-18T13:00:17+00:00\",\"dateModified\":\"2025-09-08T05:32:46+00:00\",\"description\":\"Refractio et Lex Snellii explicatae: disce quomodo lux mutet directionem transeundo inter media, computa angulos incidentiae et refractionis, et solve exercitationes practicas.\",\"breadcrumb\":{\"@id\":\"http:\/\/toposuranos.com\/material\/la\/refractio-lucis-et-lex-snellii\/#breadcrumb\"},\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"http:\/\/toposuranos.com\/material\/la\/refractio-lucis-et-lex-snellii\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"http:\/\/toposuranos.com\/material\/la\/refractio-lucis-et-lex-snellii\/#primaryimage\",\"url\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/08\/leydesnell.jpg\",\"contentUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/08\/leydesnell.jpg\",\"width\":1024,\"height\":346},{\"@type\":\"BreadcrumbList\",\"@id\":\"http:\/\/toposuranos.com\/material\/la\/refractio-lucis-et-lex-snellii\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Portada\",\"item\":\"https:\/\/toposuranos.com\/material\/es\/cursos-de-matematica-y-fisica\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Refractio Lucis et Lex Snellii\"}]},{\"@type\":\"WebSite\",\"@id\":\"http:\/\/toposuranos.com\/material\/#website\",\"url\":\"http:\/\/toposuranos.com\/material\/\",\"name\":\"toposuranos.com\/material\",\"description\":\"\",\"publisher\":{\"@id\":\"http:\/\/toposuranos.com\/material\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"http:\/\/toposuranos.com\/material\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"es\"},{\"@type\":\"Organization\",\"@id\":\"http:\/\/toposuranos.com\/material\/#organization\",\"name\":\"toposuranos.com\/material\",\"url\":\"http:\/\/toposuranos.com\/material\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"http:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/\",\"url\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png\",\"contentUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png\",\"width\":2400,\"height\":2059,\"caption\":\"toposuranos.com\/material\"},\"image\":{\"@id\":\"http:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.facebook.com\/groups\/toposuranos\",\"https:\/\/x.com\/topuranos\",\"https:\/\/www.youtube.com\/channel\/UC16yDm12cPcrwsE0fAM7X1g\",\"https:\/\/www.linkedin.com\/company\/69429190\"]},{\"@type\":\"Person\",\"@id\":\"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1\",\"name\":\"giorgio.reveco\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"http:\/\/toposuranos.com\/material\/#\/schema\/person\/image\/\",\"url\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg\",\"contentUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg\",\"caption\":\"giorgio.reveco\"},\"description\":\"Soy Licenciado en F\u00edsica, Magister en Ingenier\u00eda Industrial y Docente Universitario. Me dedico a desmitificar la f\u00edsica y las matem\u00e1ticas. Mi objetivo es hacer que estos campos sean f\u00e1cilmente comprensibles para todos, proporcionando las herramientas para explorar no solo el mundo que nos rodea, sino tambi\u00e9n las profundidades de nuestra propia existencia y el orden natural que nos conecta con el cosmos.\",\"sameAs\":[\"http:\/\/toposuranos.com\/material\"],\"url\":\"http:\/\/toposuranos.com\/material\/author\/giorgio-reveco\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Refractio Lucis et Lex Snellii - toposuranos.com\/material","description":"Refractio et Lex Snellii explicatae: disce quomodo lux mutet directionem transeundo inter media, computa angulos incidentiae et refractionis, et solve exercitationes practicas.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"http:\/\/toposuranos.com\/material\/la\/refractio-lucis-et-lex-snellii\/","og_locale":"es_ES","og_type":"article","og_title":"Refractio Lucis et Lex Snellii","og_description":"Refractio et Lex Snellii explicatae: disce quomodo lux mutet directionem transeundo inter media, computa angulos incidentiae et refractionis, et solve exercitationes practicas.","og_url":"http:\/\/toposuranos.com\/material\/la\/refractio-lucis-et-lex-snellii\/","og_site_name":"toposuranos.com\/material","article_publisher":"https:\/\/www.facebook.com\/groups\/toposuranos","article_published_time":"2021-09-18T13:00:17+00:00","article_modified_time":"2025-09-08T05:32:46+00:00","og_image":[{"url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/08\/leydesnell.jpg","type":"","width":"","height":""}],"author":"giorgio.reveco","twitter_card":"summary_large_image","twitter_title":"Refractio Lucis et Lex Snellii","twitter_description":"Refractio et Lex Snellii explicatae: disce quomodo lux mutet directionem transeundo inter media, computa angulos incidentiae et refractionis, et solve exercitationes practicas.","twitter_image":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/08\/leydesnell.jpg","twitter_creator":"@topuranos","twitter_site":"@topuranos","twitter_misc":{"Escrito por":"giorgio.reveco","Tiempo de lectura":"6 minutos"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"http:\/\/toposuranos.com\/material\/la\/refractio-lucis-et-lex-snellii\/#article","isPartOf":{"@id":"http:\/\/toposuranos.com\/material\/la\/refractio-lucis-et-lex-snellii\/"},"author":{"name":"giorgio.reveco","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1"},"headline":"Refractio Lucis et Lex Snellii","datePublished":"2021-09-18T13:00:17+00:00","dateModified":"2025-09-08T05:32:46+00:00","mainEntityOfPage":{"@id":"http:\/\/toposuranos.com\/material\/la\/refractio-lucis-et-lex-snellii\/"},"wordCount":1304,"commentCount":0,"publisher":{"@id":"http:\/\/toposuranos.com\/material\/#organization"},"image":{"@id":"http:\/\/toposuranos.com\/material\/la\/refractio-lucis-et-lex-snellii\/#primaryimage"},"thumbnailUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/08\/leydesnell.jpg","articleSection":["Optica Geometrica","Physica"],"inLanguage":"es","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["http:\/\/toposuranos.com\/material\/la\/refractio-lucis-et-lex-snellii\/#respond"]}]},{"@type":"WebPage","@id":"http:\/\/toposuranos.com\/material\/la\/refractio-lucis-et-lex-snellii\/","url":"http:\/\/toposuranos.com\/material\/la\/refractio-lucis-et-lex-snellii\/","name":"Refractio Lucis et Lex Snellii - toposuranos.com\/material","isPartOf":{"@id":"http:\/\/toposuranos.com\/material\/#website"},"primaryImageOfPage":{"@id":"http:\/\/toposuranos.com\/material\/la\/refractio-lucis-et-lex-snellii\/#primaryimage"},"image":{"@id":"http:\/\/toposuranos.com\/material\/la\/refractio-lucis-et-lex-snellii\/#primaryimage"},"thumbnailUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/08\/leydesnell.jpg","datePublished":"2021-09-18T13:00:17+00:00","dateModified":"2025-09-08T05:32:46+00:00","description":"Refractio et Lex Snellii explicatae: disce quomodo lux mutet directionem transeundo inter media, computa angulos incidentiae et refractionis, et solve exercitationes practicas.","breadcrumb":{"@id":"http:\/\/toposuranos.com\/material\/la\/refractio-lucis-et-lex-snellii\/#breadcrumb"},"inLanguage":"es","potentialAction":[{"@type":"ReadAction","target":["http:\/\/toposuranos.com\/material\/la\/refractio-lucis-et-lex-snellii\/"]}]},{"@type":"ImageObject","inLanguage":"es","@id":"http:\/\/toposuranos.com\/material\/la\/refractio-lucis-et-lex-snellii\/#primaryimage","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/08\/leydesnell.jpg","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/08\/leydesnell.jpg","width":1024,"height":346},{"@type":"BreadcrumbList","@id":"http:\/\/toposuranos.com\/material\/la\/refractio-lucis-et-lex-snellii\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Portada","item":"https:\/\/toposuranos.com\/material\/es\/cursos-de-matematica-y-fisica\/"},{"@type":"ListItem","position":2,"name":"Refractio Lucis et Lex Snellii"}]},{"@type":"WebSite","@id":"http:\/\/toposuranos.com\/material\/#website","url":"http:\/\/toposuranos.com\/material\/","name":"toposuranos.com\/material","description":"","publisher":{"@id":"http:\/\/toposuranos.com\/material\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"http:\/\/toposuranos.com\/material\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"es"},{"@type":"Organization","@id":"http:\/\/toposuranos.com\/material\/#organization","name":"toposuranos.com\/material","url":"http:\/\/toposuranos.com\/material\/","logo":{"@type":"ImageObject","inLanguage":"es","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png","width":2400,"height":2059,"caption":"toposuranos.com\/material"},"image":{"@id":"http:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/groups\/toposuranos","https:\/\/x.com\/topuranos","https:\/\/www.youtube.com\/channel\/UC16yDm12cPcrwsE0fAM7X1g","https:\/\/www.linkedin.com\/company\/69429190"]},{"@type":"Person","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1","name":"giorgio.reveco","image":{"@type":"ImageObject","inLanguage":"es","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/person\/image\/","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg","caption":"giorgio.reveco"},"description":"Soy Licenciado en F\u00edsica, Magister en Ingenier\u00eda Industrial y Docente Universitario. Me dedico a desmitificar la f\u00edsica y las matem\u00e1ticas. Mi objetivo es hacer que estos campos sean f\u00e1cilmente comprensibles para todos, proporcionando las herramientas para explorar no solo el mundo que nos rodea, sino tambi\u00e9n las profundidades de nuestra propia existencia y el orden natural que nos conecta con el cosmos.","sameAs":["http:\/\/toposuranos.com\/material"],"url":"http:\/\/toposuranos.com\/material\/author\/giorgio-reveco\/"}]}},"_links":{"self":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/34522","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/comments?post=34522"}],"version-history":[{"count":0,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/34522\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media\/27682"}],"wp:attachment":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media?parent=34522"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/categories?post=34522"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/tags?post=34522"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}