{"id":27754,"date":"2021-10-22T13:00:18","date_gmt":"2021-10-22T13:00:18","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=27754"},"modified":"2024-08-11T20:00:24","modified_gmt":"2024-08-11T20:00:24","slug":"lentes-delgadas-tudo-sobre-suas-propriedades-e-calculos","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/pt\/lentes-delgadas-tudo-sobre-suas-propriedades-e-calculos\/","title":{"rendered":"Lentes Delgadas: Tudo sobre suas propriedades e c\u00e1lculos"},"content":{"rendered":"<p><center><\/p>\n<h1>Lentes Delgadas: Tudo sobre suas propriedades e c\u00e1lculos<\/h1>\n<p><em><strong>Resumo:<\/strong><br \/>\nEsta aula introduz as lentes delgadas, explicando seus tipos (convergentes e divergentes), suas propriedades \u00f3pticas e a rela\u00e7\u00e3o objeto-imagem. M\u00e9todos gr\u00e1ficos s\u00e3o apresentados, e a equa\u00e7\u00e3o do fabricante de lentes \u00e9 deduzida para entender seu funcionamento. O objetivo \u00e9 fornecer uma compreens\u00e3o b\u00e1sica das lentes delgadas e sua aplica\u00e7\u00e3o em \u00f3ptica, complementada com exerc\u00edcios pr\u00e1ticos.<\/em><\/p>\n<p><strong>Objetivos de Aprendizagem:<\/strong><br \/>\nAo final desta aula, o aluno ser\u00e1 capaz de:<\/p>\n<ul style=\"text-align:left;\">\n<li><strong>Compreender<\/strong> as propriedades \u00f3pticas das lentes delgadas, incluindo a dist\u00e2ncia focal e os pontos focais.<\/li>\n<li><strong>Identificar<\/strong> os diferentes tipos de lentes delgadas, como lentes convergentes e divergentes, e suas aplica\u00e7\u00f5es.<\/li>\n<li><strong>Aplicar<\/strong> a rela\u00e7\u00e3o objeto-imagem para resolver problemas \u00f3pticos utilizando lentes delgadas.<\/li>\n<li><strong>Analisar<\/strong> como as superf\u00edcies esf\u00e9ricas nas lentes delgadas afetam a refra\u00e7\u00e3o da luz.<\/li>\n<li><strong>Explicar<\/strong> a equa\u00e7\u00e3o do fabricante de lentes e sua relev\u00e2ncia na fabrica\u00e7\u00e3o de lentes \u00f3pticas.<\/li>\n<li><strong>Utilizar<\/strong> m\u00e9todos gr\u00e1ficos para determinar as posi\u00e7\u00f5es de imagem e objeto em lentes delgadas.<\/li>\n<li><strong>Calcular<\/strong> a amplia\u00e7\u00e3o das imagens produzidas por lentes delgadas.<\/li>\n<li><strong>Deducir<\/strong> f\u00f3rmulas a partir da geometria das lentes delgadas para resolver problemas \u00f3pticos.<\/li>\n<\/ul>\n<p><strong>\u00cdNDICE DE CONTE\u00daDOS<\/strong><br \/>\n<a href=\"#1\">Introdu\u00e7\u00e3o<\/a><br \/>\n<a href=\"#2\">Tipos de Lentes<\/a><br \/>\n<a href=\"#3\">Propriedades das Lentes Delgadas<\/a><br \/>\n<a href=\"#4\">Equa\u00e7\u00e3o do Fabricante de Lentes<\/a><br \/>\n<a href=\"#5\">M\u00e9todos Gr\u00e1ficos para Lentes Delgadas<\/a><br \/>\n<a href=\"#6\">Exerc\u00edcios<\/a><br \/>\n<\/center><\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>Introdu\u00e7\u00e3o<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=QLn3Ml-Mrng&amp;t=137s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">As lentes delgadas,<\/span><\/strong><\/a> junto com os espelhos, s\u00e3o de longe os dispositivos \u00f3pticos mais utilizados. Estes s\u00e3o objetos transparentes cuja superf\u00edcie \u00e9 limitada por duas interfaces esf\u00e9ricas e s\u00e3o geralmente feitos de vidro ou pl\u00e1stico.<\/p>\n<p><center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogger.googleusercontent.com\/img\/a\/AVvXsEg7unooQ_wxtWDSCBGloGkESSCipu1eXSsKSP7GDD5Ml4X2pkxZrsCcf4QaDdMVlQyanvVs14N2JNyyDBQNMlFJeha_Ezta0ffo_0ayyQzEi__H1BKAa_2RCJJTunRomWHOozGV5S4eots7dpRsQStGG9qoiEK8rrtU2IihiEMmyS7mMVw1Vcb54KVI8g\" width=\"455\" height=\"366\" alt=\"Lente Delgada\" class=\"alignnone size-full lazyload\" \/><noscript><img decoding=\"async\" src=\"https:\/\/blogger.googleusercontent.com\/img\/a\/AVvXsEg7unooQ_wxtWDSCBGloGkESSCipu1eXSsKSP7GDD5Ml4X2pkxZrsCcf4QaDdMVlQyanvVs14N2JNyyDBQNMlFJeha_Ezta0ffo_0ayyQzEi__H1BKAa_2RCJJTunRomWHOozGV5S4eots7dpRsQStGG9qoiEK8rrtU2IihiEMmyS7mMVw1Vcb54KVI8g\" width=\"455\" height=\"366\" alt=\"Lente Delgada\" class=\"alignnone size-full lazyload\" \/><\/noscript><\/center><\/p>\n<p style=\"text-align: justify; color: #000000;\">Em uma lente delgada, a dist\u00e2ncia entre as superf\u00edcies refrativas \u00e9 pequena o suficiente para ser considerada desprez\u00edvel.<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/QLn3Ml-Mrng\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>Tipos de Lentes<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=QLn3Ml-Mrng&amp;t=321s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">As lentes, assim como os espelhos,<\/span><\/strong><\/a> s\u00e3o divididas em dois tipos: convergentes e divergentes.<\/p>\n<p><center><\/center><\/p>\n<figure style=\"width: 384px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"lazyload\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogger.googleusercontent.com\/img\/a\/AVvXsEh0PLkCTvVUlV2B0T4PY2ipA8hwHOyKg3FBZxKjH-x4K9hsI72_bZzkV97FwglcMi2YpndB7i-TSUjGnpcWmgQ-YD66EZlOuZkD8MaD6Bsvxzq8AO9IBUN3L_a2BJAEIoJEYv2wtaThEY1pUlL-OsQRMR8hfTc7_fxr9riBzH4WVsXf2goI6xxCmhKPsw\" width=\"384\" height=\"294\" alt=\"Lente Convergente\" \/><figcaption class=\"wp-caption-text\"><noscript><img decoding=\"async\" class=\"lazyload\" src=\"https:\/\/blogger.googleusercontent.com\/img\/a\/AVvXsEh0PLkCTvVUlV2B0T4PY2ipA8hwHOyKg3FBZxKjH-x4K9hsI72_bZzkV97FwglcMi2YpndB7i-TSUjGnpcWmgQ-YD66EZlOuZkD8MaD6Bsvxzq8AO9IBUN3L_a2BJAEIoJEYv2wtaThEY1pUlL-OsQRMR8hfTc7_fxr9riBzH4WVsXf2goI6xxCmhKPsw\" width=\"384\" height=\"294\" alt=\"Lente Convergente\" \/><\/noscript> Lente Delgada Convergente<\/figcaption><\/figure>\n<figure style=\"width: 386px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"lazyload\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogger.googleusercontent.com\/img\/a\/AVvXsEjhz-x8M2Gh8zkKs0GDC5NFDr4UbWieeumfLilpyTIu_-4OM8wChs-mRLAfkhA0YTYX99OEWvY0vpDrw5z9CjytxhKnUxy5SYrZwbIq59Hs-jvPLydnGFOt9SNMr_SGHycnNR6cLgXgeKNNqT3B0F8LxqoQrJemvYhvqjEfGsNMFAEW-V9DVxtosf_neg\" width=\"386\" height=\"211\" alt=\"Lente Divergente\" \/><figcaption class=\"wp-caption-text\"><noscript><img decoding=\"async\" class=\"lazyload\" src=\"https:\/\/blogger.googleusercontent.com\/img\/a\/AVvXsEjhz-x8M2Gh8zkKs0GDC5NFDr4UbWieeumfLilpyTIu_-4OM8wChs-mRLAfkhA0YTYX99OEWvY0vpDrw5z9CjytxhKnUxy5SYrZwbIq59Hs-jvPLydnGFOt9SNMr_SGHycnNR6cLgXgeKNNqT3B0F8LxqoQrJemvYhvqjEfGsNMFAEW-V9DVxtosf_neg\" width=\"386\" height=\"211\" alt=\"Lente Divergente\" \/><\/noscript> Lente Delgada Divergente<\/figcaption><\/figure>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify; color: #000000;\">Os pontos <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F_1<\/span><\/span> e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F_2<\/span><\/span> s\u00e3o os pontos focais e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u00e9 a <strong>dist\u00e2ncia focal.<\/strong> Em uma lente fina, as duas dist\u00e2ncias focais s\u00e3o iguais, por isso s\u00e3o representadas pela mesma letra.<\/p>\n<p style=\"text-align: justify; color: #000000;\">Em uma lente delgada, a dist\u00e2ncia entre as superf\u00edcies refrativas \u00e9 pequena o suficiente para ser considerada desprez\u00edvel.<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>Propriedades das Lentes Delgadas<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=QLn3Ml-Mrng&amp;t=497s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">Se fizermos geometria com uma lente convergente,<\/span><\/strong><\/a> veremos o seguinte:<\/p>\n<p><center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogger.googleusercontent.com\/img\/a\/AVvXsEiaZBBNwYEXZsxfDEdwRFW-ryUPjItussuFx6RZZWsRxR1kXu-wW_Ns5F2KUdG8anzCHUUToJLMQPgqtM57eO4UcUD8H78minimIOvD8yUM78Zr1ykd81o1O7PNqidqh3LfJGwl62dZQTfzI9EwH7sQttwlwipe6hVAZFb9KqBTbA2y7_ZMJ5IeNHD6QA\" width=\"637\" height=\"353\" alt=\"rela\u00e7\u00e3o objeto-imagem em lentes delgadas\" class=\"alignnone lazyload\" \/><noscript><img decoding=\"async\" src=\"https:\/\/blogger.googleusercontent.com\/img\/a\/AVvXsEiaZBBNwYEXZsxfDEdwRFW-ryUPjItussuFx6RZZWsRxR1kXu-wW_Ns5F2KUdG8anzCHUUToJLMQPgqtM57eO4UcUD8H78minimIOvD8yUM78Zr1ykd81o1O7PNqidqh3LfJGwl62dZQTfzI9EwH7sQttwlwipe6hVAZFb9KqBTbA2y7_ZMJ5IeNHD6QA\" width=\"637\" height=\"353\" alt=\"rela\u00e7\u00e3o objeto-imagem em lentes delgadas\" class=\"alignnone lazyload\" \/><\/noscript><\/center>&nbsp;<\/p>\n<p style=\"text-align: justify; color: #000000;\">Como os tri\u00e2ngulos pintados s\u00e3o semelhantes, os lados correspondentes ser\u00e3o proporcionais<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rlr}\n\n&amp;\\displaystyle \\frac{y}{s} = -\\frac{y^\\prime}{s^\\prime} &amp; \\\\ \\\\\n\n\\equiv &amp; \\displaystyle \\color{blue}{\\frac{y^\\prime}{y} = -\\frac{s^\\prime}{s}} &amp; (\\triangle)\n\n\\end{array}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">Da mesma forma,<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rlr}\n\n&amp; \\displaystyle  \\frac{y}{f} = -\\frac{y^\\prime}{s^\\prime-f} &amp;  \\\\ \\\\\n\n\\equiv &amp; \\displaystyle \\color{blue}{\\frac{y^\\prime}{y} = -\\frac{s^\\prime-f}{f}} &amp; (\\star)\n\n\\end{array}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">Ent\u00e3o, a partir de <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\triangle)<\/span><\/span> e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\star)<\/span><\/span> temos:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rlr}\n\n&amp;\\displaystyle-\\frac{s^\\prime}{s} = -\\frac{s^\\prime-f}{f} &amp;  \\\\ \\\\\n\n\\equiv \\displaystyle &amp; \\frac{s^\\prime}{s} = \\frac{s^\\prime-f}{f} = \\frac{s^\\prime}{f} - 1 = \\frac{s^\\prime}{f} - \\frac{s^\\prime}{s^\\prime} &amp; \\\\ \\\\\n\n{} \\equiv &amp; \\displaystyle \\frac{s^\\prime}{s}+ \\frac{s^\\prime}{s^\\prime} = \\frac{s^\\prime}{f} &amp; \\\\ \\\\\n\n\\equiv &amp; \\displaystyle \\color{blue}{\\frac{1}{s}+ \\frac{1}{s^\\prime} = \\frac{1}{f}} &amp;\n\n\\end{array}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">O que acabamos de ver \u00e9 o que chamamos de <strong>rela\u00e7\u00e3o objeto-imagem para lentes finas.<\/strong><\/p>\n<p style=\"text-align: justify; color: #000000;\" e=\"\" de=\"\" forma=\"\" an=\"\" loga=\"\" a=\"\" como=\"\" se=\"\" trabalha=\"\" com=\"\" espelhos=\"\" \u00e9=\"\" poss\u00edvel=\"\" definir=\"\" o=\"\" strong=\"\">fator de amplia\u00e7\u00e3o <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">m<\/span><\/span> atrav\u00e9s de<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\color{blue}{m=-\\frac{y^\\prime}{y}= - \\frac{s^\\prime}{s}}<\/span><\/span><\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h2>Equa\u00e7\u00e3o do Fabricante de Lentes<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=QLn3Ml-Mrng&amp;t=978s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">Uma lente fina, como sabemos, \u00e9 composta por duas interfaces esf\u00e9ricas<\/span><\/strong><\/a> que separam os meios pelos quais a luz viaja, e j\u00e1 estudamos o que acontece quando a luz cruza de um meio para outro, atravessando interfaces desse tipo. Portanto, para analisar lentes finas, bastar\u00e1 compor o que j\u00e1 revisamos para interfaces individuais.<\/p>\n<p style=\"text-align: justify; color: #000000;\">Em geral, uma lente fina tem a seguinte apar\u00eancia:<\/p>\n<p><center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogger.googleusercontent.com\/img\/a\/AVvXsEhygh_mFDH99yumaDNCW3XtO0TKGWDJc1uLRFPCb2Q6hKL0bJo6GOFpB03jeMFHAX9_4E06j2RwBD4R_SecOhKo35QojZkTGzCkUwgp_R9yY6k0gQ7qGROcDcVja6jegTnOUYD-Krhb6iiwHIXrNh90jcMwf4M_082mTqGQb56nQyElN42iO_pg0dy-DA\" width=\"704\" height=\"216\" class=\"alignnone lazyload\" alt=\"an\u00e1lise de lentes finas\" \/><noscript><img decoding=\"async\" src=\"https:\/\/blogger.googleusercontent.com\/img\/a\/AVvXsEhygh_mFDH99yumaDNCW3XtO0TKGWDJc1uLRFPCb2Q6hKL0bJo6GOFpB03jeMFHAX9_4E06j2RwBD4R_SecOhKo35QojZkTGzCkUwgp_R9yY6k0gQ7qGROcDcVja6jegTnOUYD-Krhb6iiwHIXrNh90jcMwf4M_082mTqGQb56nQyElN42iO_pg0dy-DA\" width=\"704\" height=\"216\" class=\"alignnone lazyload\" alt=\"an\u00e1lise de lentes finas\" \/><\/noscript><\/center><\/p>\n<p style=\"text-align: justify; color: #000000;\">Mas para simplificar, isso pode ser separado<\/p>\n<p><center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogger.googleusercontent.com\/img\/a\/AVvXsEi6FTZ9Y6F-hJUKjczKbnCeHFtXEpUg8us8DmK_OZCRVnwELmbBOKb_p4Zrf_s6h0cdlWJXQqRz4p2rAmVWQnJoLK7O5zRB97FdT_iATYs7Ny0CqWyyU4X0Ofh5BfB1KHNE7LYaOsG9YU-B1ocy4BGsWHlwfALeaStDYVK2UXxorT_ggCv80xGQ9zpG6A\" width=\"862\" height=\"317\" class=\"alignnone lazyload\" alt=\"separa\u00e7\u00e3o dos casos de lentes finas\" \/><noscript><img decoding=\"async\" src=\"https:\/\/blogger.googleusercontent.com\/img\/a\/AVvXsEi6FTZ9Y6F-hJUKjczKbnCeHFtXEpUg8us8DmK_OZCRVnwELmbBOKb_p4Zrf_s6h0cdlWJXQqRz4p2rAmVWQnJoLK7O5zRB97FdT_iATYs7Ny0CqWyyU4X0Ofh5BfB1KHNE7LYaOsG9YU-B1ocy4BGsWHlwfALeaStDYVK2UXxorT_ggCv80xGQ9zpG6A\" width=\"862\" height=\"317\" class=\"alignnone lazyload\" alt=\"separa\u00e7\u00e3o dos casos de lentes finas\" \/><\/noscript><\/center><\/p>\n<p style=\"text-align: justify; color: #000000;\">J\u00e1 que analisamos cada caso (aqui), podemos extrair as seguintes duas equa\u00e7\u00f5es:<\/p>\n<p style=\"text-align: justify; color: #000000;\"><strong>Para o lado a-b:<\/strong><\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{n_a}{s_a} + \\frac{n_b}{s_{ab}^\\prime} = \\frac{n_b - n_a}{R_c}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\"><strong>Para o lado b-c:<\/strong><\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{n_b}{s_{b}} + \\frac{n_c}{s_{bc}^\\prime} = \\frac{n_c - n_b}{R_a}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">Neste ponto, se fizermos <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_a = n_c = n_{ar}\\approx 1.0,<\/span><\/span> acontecer\u00e1 que <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">s_b = -s_{ab}^\\prime;<\/span><\/span> portanto, essas equa\u00e7\u00f5es s\u00e3o escritas da seguinte forma<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n\\displaystyle \\frac{1}{s_a} + \\frac{n_b}{s_{ab}^\\prime} &amp; \\displaystyle = \\frac{n_b - 1}{R_c} \\\\ \\\\\n\n\\displaystyle -\\frac{n_b}{s_{ab}^\\prime} + \\frac{1}{s_{bc}^\\prime} &amp; \\displaystyle= \\frac{1-n_b}{R_a}\n\n\\end{array}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">e somando-as, agora \u00e9 poss\u00edvel obter uma \u00fanica express\u00e3o:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n&amp;\\displaystyle \\frac{1}{s_a} + \\frac{1}{s_{bc}^\\prime} = \\frac{n_b-1}{R_c} + \\frac{1-n_b}{R_a} \\\\ \\\\\n\n\\equiv &amp; \\displaystyle \\frac{1}{s_a} + \\frac{1}{s_{bc}^\\prime} = (n_b -1) \\left( \\frac{1}{R_a} - \\frac{1}{R_c} \\right)\n\n\\end{array}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">Neste ponto, \u00e9 conveniente renomear as vari\u00e1veis em jogo; usaremos a seguinte troca de nomes<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{ll}\n\ns_a = s &amp; R_a = R_1 \\\\ \\\\\n\ns_{bc}^\\prime = s^\\prime &amp; R_c =R_2 \\\\ \\\\\n\nn_b =n &amp;\n\n\\end{array}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">de modo que obteremos uma vers\u00e3o mais \u00ablimpa\u00bb da equa\u00e7\u00e3o que originalmente hav\u00edamos obtido:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\displaystyle \\frac{1}{s} + \\frac{1}{s^\\prime} = (n -1) \\left( \\frac{1}{R_1} - \\frac{1}{R_2} \\right)\n\n<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">Finalmente, utilizando a rela\u00e7\u00e3o objeto-imagem para lentes finas que foi deduzida no in\u00edcio, obt\u00e9m-se:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\displaystyle \\color{blue}{\\frac{1}{f} = (n -1) \\left( \\frac{1}{R_1} - \\frac{1}{R_2} \\right)}\n\n<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">Isso \u00e9 o que chamamos de <strong>Equa\u00e7\u00e3o do Fabricante de Lentes.<\/strong><\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h2>M\u00e9todos Gr\u00e1ficos para Lentes Delgadas<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=QLn3Ml-Mrng&amp;t=1591s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">Uma ferramenta muito \u00fatil para corroborar<\/span><\/strong><\/a> ou encontrar sentido nos c\u00e1lculos que realizamos s\u00e3o os m\u00e9todos gr\u00e1ficos desenhados abaixo; tais m\u00e9todos s\u00e3o an\u00e1logos aos utilizados com espelhos.<\/p>\n<p><center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogger.googleusercontent.com\/img\/a\/AVvXsEia8CpQNx2bWAqtwRIZHNcwK3w2WnxMgWC98tv9VmH4-XfBmHvxDZJ7wpZJciDFfCIqIDSN3xp4of9XV9ppTy8PY9AJ1oUUoGo57kMZb5GZhl4aqYzvc8pfYwaKJ07GB2XDMlwBknnUNmB1k_5uXfhmpVjZXrISt2sj_KkqzDZQ0_U5crTzrv_3l_QyvA\" width=\"576\" height=\"489\" class=\"alignnone lazyload\" alt=\"m\u00e9todos gr\u00e1ficos para lentes delgadas convergente e divergente\" \/><noscript><img decoding=\"async\" src=\"https:\/\/blogger.googleusercontent.com\/img\/a\/AVvXsEia8CpQNx2bWAqtwRIZHNcwK3w2WnxMgWC98tv9VmH4-XfBmHvxDZJ7wpZJciDFfCIqIDSN3xp4of9XV9ppTy8PY9AJ1oUUoGo57kMZb5GZhl4aqYzvc8pfYwaKJ07GB2XDMlwBknnUNmB1k_5uXfhmpVjZXrISt2sj_KkqzDZQ0_U5crTzrv_3l_QyvA\" width=\"576\" height=\"489\" class=\"alignnone lazyload\" alt=\"m\u00e9todos gr\u00e1ficos para lentes delgadas convergente e divergente\" \/><\/noscript><\/center><\/p>\n<p style=\"text-align: justify; color: #000000;\">Estes m\u00e9todos fornecem diferentes resultados dependendo da posi\u00e7\u00e3o do objeto em frente \u00e0 lente.<\/p>\n<p><center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogger.googleusercontent.com\/img\/a\/AVvXsEggmEYClTymUmTSO0a8u5-I4jFIV9UFZNB_UC87-yD8ihh8WpKHcHtkQoyx23eCbfbbAFRh9BfsKVM-lsQDbug8KQKPZebKf6qKkXDeSPsSJCNxHE46VJqHO6A_LKxxdoAXLwk71TJMhLAMm6QRXy2-MqGjEOEHIGRMEgnMx1KFRc2g_s9y9D1O516kDw\" width=\"607\" height=\"685\" class=\"alignnone lazyload\" alt=\"m\u00e9todo gr\u00e1fico para lentes delgadas convergente\" \/><noscript><img decoding=\"async\" src=\"https:\/\/blogger.googleusercontent.com\/img\/a\/AVvXsEggmEYClTymUmTSO0a8u5-I4jFIV9UFZNB_UC87-yD8ihh8WpKHcHtkQoyx23eCbfbbAFRh9BfsKVM-lsQDbug8KQKPZebKf6qKkXDeSPsSJCNxHE46VJqHO6A_LKxxdoAXLwk71TJMhLAMm6QRXy2-MqGjEOEHIGRMEgnMx1KFRc2g_s9y9D1O516kDw\" width=\"607\" height=\"685\" class=\"alignnone lazyload\" alt=\"m\u00e9todo gr\u00e1fico para lentes delgadas convergente\" \/><\/noscript><\/center><\/p>\n<p><a name=\"6\"><\/a><\/p>\n<h2>Exerc\u00edcios:<\/h2>\n<ol style=\"text-align: justify; color: #000000;\">\n<li>Temos uma lente divergente e um feixe de raios paralelos que \u00abse abrem\u00bb ao passar por ela, de modo que suas proje\u00e7\u00f5es convergem para um ponto situado a 30[cm] do centro da lente. Se voc\u00ea deseja usar esta lente para obter uma imagem virtual de 1\/2 da altura de um determinado objeto:\n<ol>\n<li type=\"a\">Calcule onde tal objeto deve ser colocado.<\/li>\n<li type=\"a\">Fa\u00e7a um diagrama de raios para descrever a situa\u00e7\u00e3o.<\/li>\n<\/ol>\n<\/li>\n<li>Um objeto de 7[cm] de altura \u00e9 colocado a 13[cm] \u00e0 esquerda de uma lente convergente com dist\u00e2ncia focal de 5[cm]. Uma segunda lente convergente com dist\u00e2ncia focal de 2[cm] \u00e9 colocada a 30[cm] \u00e0 direita da primeira lente, compartilhando ambas o mesmo eixo \u00f3ptico. Encontre o tamanho e a posi\u00e7\u00e3o da imagem gerada pelas duas lentes combinadas.<\/li>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/tUQxvRPZo_A\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/center><\/p>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>Lentes Delgadas: Tudo sobre suas propriedades e c\u00e1lculos Resumo: Esta aula introduz as lentes delgadas, explicando seus tipos (convergentes e divergentes), suas propriedades \u00f3pticas e a rela\u00e7\u00e3o objeto-imagem. M\u00e9todos gr\u00e1ficos s\u00e3o apresentados, e a equa\u00e7\u00e3o do fabricante de lentes \u00e9 deduzida para entender seu funcionamento. O objetivo \u00e9 fornecer uma compreens\u00e3o b\u00e1sica das lentes delgadas [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":27751,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":209,"footnotes":""},"categories":[637,837],"tags":[],"class_list":["post-27754","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-fisica-pt","category-optica-geometrica-pt"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Lentes Delgadas: Tudo sobre suas propriedades e c\u00e1lculos - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Descubra as propriedades e c\u00e1lculos essenciais das lentes delgadas, incluindo tipos, rela\u00e7\u00e3o objeto-imagem, m\u00e9todos gr\u00e1ficos e a equa\u00e7\u00e3o do fabricante de lentes. 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