{"id":34552,"date":"2021-10-22T13:00:22","date_gmt":"2021-10-22T13:00:22","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=34552"},"modified":"2025-09-08T06:02:30","modified_gmt":"2025-09-08T06:02:30","slug":"lens-tenues-omnia-de-proprietatibus-et-calculis-earum","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/la\/lens-tenues-omnia-de-proprietatibus-et-calculis-earum\/","title":{"rendered":"Lens tenues: Omnia de proprietatibus et calculis earum"},"content":{"rendered":"<p><center><\/p>\n<h1>Lens tenuis: Omnia de proprietatibus eius et calculis<\/h1>\n<p><em><strong>Summarium:<\/strong><br \/>\nHaec lectio lens tenues introducit, explicans earum genera (convergentes et divergentes), proprietates opticas atque relationem obiecti-imaginis. Methodi graphici proponuntur et aequatio fabricantium lentium deducitur ad intellectum functionis earum. Propositum est comprehensionem fundamentalem lentium tenuium earumque applicationem in optica praebere, exercitiis practicis completam.<\/em><\/p>\n<p><strong>Proposita Discendi:<\/strong><br \/>\nhoc cursu absoluto discipulus poterit:<\/p>\n<ul style=\"text-align:left;\">\n<li><strong>Intelligere<\/strong> proprietates opticas lentium tenuium, inter distantiam focalem et puncta focalia.<\/li>\n<li><strong>Identificare<\/strong> varia genera lentium tenuium, ut lentes convergentes et divergentes, earumque applicationes.<\/li>\n<li><strong>Applicare<\/strong> relationem obiecti-imaginis ad problemata optica solvenda utens lentibus tenuibus.<\/li>\n<li><strong>Analyzare<\/strong> quomodo superficies sphaericae in lentibus tenuibus refractionem luminis afficiant.<\/li>\n<li><strong>Explicare<\/strong> aequationem fabricantium lentium eiusque momentum in confectione lentium opticorum.<\/li>\n<li><strong>Uti<\/strong> methodis graphicis ad determinandas positiones imaginis et obiecti in lentibus tenuibus.<\/li>\n<li><strong>Computare<\/strong> magnificationem imaginum a lentibus tenuibus productarum.<\/li>\n<li><strong>Deducere<\/strong> formulas ex geometria lentium tenuium ad problemata optica solvenda.<\/li>\n<\/ul>\n<p><strong>INDEX CONTENTORUM<\/strong><br \/>\n<a href=\"#1\">Introductio<\/a><br \/>\n<a href=\"#2\">Genera lentium<\/a><br \/>\n<a href=\"#3\">Proprietates lentium tenuium<\/a><br \/>\n<a href=\"#4\">Aequatio fabricantium lentium<\/a><br \/>\n<a href=\"#5\">Methodi graphici pro lentibus tenuibus<\/a><br \/>\n<a href=\"#6\">Exercitia<\/a><br \/>\n<\/center><br \/>\n<a name=\"1\"><\/a><\/p>\n<h2>Introductio<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=QLn3Ml-Mrng&amp;t=137s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">Lentes tenues,<\/span><\/strong><\/a> una cum speculis, sunt longe frequentissime adhibita instrumenta optica. Haec sunt corpora transparens quorum superficies duabus interfaciebus sphaericis terminatur et plerumque ex vitro vel plastico fiunt.<\/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=\"Lens tenuis\" 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=\"Lens tenuis\" class=\"alignnone size-full lazyload\" \/><\/noscript><\/center><\/p>\n<p style=\"text-align: justify;\">In lente tenui, distantia inter superficies refractivas tam exigua est ut neglegenda habeatur.<\/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>Genera lentium<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=QLn3Ml-Mrng&amp;t=321s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">Lentes, sicut et specula,<\/span><\/strong><\/a> in duas species dividuntur: convergentes et divergentes.<\/p>\n<p><center><\/center><br \/>\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=\"Lens 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=\"Lens Convergente\" \/><\/noscript> Lens tenuis Convergens<\/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=\"Lens 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=\"Lens Divergente\" \/><\/noscript> Lens tenuis Divergens<\/figcaption><\/figure>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\">Puncta <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F_1<\/span><\/span> et <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F_2<\/span><\/span> sunt puncta focalia et <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> est <strong>distantia focalis.<\/strong> In lente tenui, duae longitudines focales aequales sunt, ideo utraque eadem littera repraesentatur.<\/p>\n<p style=\"text-align: justify;\">In lente tenui, distantia inter superficies refractivas tam exigua est ut neglegenda habeatur.<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>Proprietates lentium tenuium<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=QLn3Ml-Mrng&amp;t=497s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">Si geometriam cum lente<\/span><\/strong><\/a> convergente facimus, sequentia videbimus:<\/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=\"relatio obiecti-imaginis in lentibus tenuibus\" class=\"alignnone lazyload\" \/><noscript><img decoding=\"async\" src=\"https:\/\/blogger.googleusercontent.com\/img\/a\/AVvXsEiaZBBNwYEXZsxfDEdwRFW-ryUPjItussuFx6RZZWsRxR1kXu-wW_Ns5F2KUdG8anzCHUUToJLMQPgqtM57eO4UcUD8H78minimIOvD8yUM78Zr1ykd81o1O7PNqidqh3LfJGwl62dZQTfzI9EwH7sQttwlwipe6hVAZFb9KqBTbA2y7_ZMJ5IeNHD6QA\" width=\"637\" height=\"353\" alt=\"relatio obiecti-imaginis in lentibus tenuibus\" class=\"alignnone lazyload\" \/><\/noscript><\/center>&nbsp;<\/p>\n<p style=\"text-align: justify;\">Cum triangula depicta similia sint, erit ut latera correspondentia proportionalia sint<\/p>\n<p style=\"text-align: center;\"><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;\">Similiter<\/p>\n<p style=\"text-align: center;\"><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;\">Deinde, ex <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\triangle)<\/span><\/span> et <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\star)<\/span><\/span> habetur:<\/p>\n<p style=\"text-align: center;\"><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;\">Hoc ultimum est quod appellamus <strong>relationem obiecti-imaginis pro lentibus tenuibus.<\/strong><\/p>\n<p style=\"text-align: justify;\">Simili modo ac in speculis laboratur, fieri potest definire <strong>factor magnificationis<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">m<\/span><\/span> per<\/p>\n<p style=\"text-align: center;\"><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>Aequatio fabricantium lentium<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=QLn3Ml-Mrng&amp;t=978s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">Lens tenuis, ut scimus, ex duabus interfaciebus sphaericis constat<\/span><\/strong><\/a> quae media distinguunt per quae lux propagatur, et iam perspeximus quid accidat cum lux e medio in aliud medium per huiusmodi interfacies transeat. Itaque, ad lentes tenues perpendendas sufficiet componere quod iam de singulis interfaciebus consideravimus.<\/p>\n<p style=\"text-align: justify;\">In universum, lens tenuis hanc speciem habet:<\/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=\"analysis lens tenuis\" \/><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=\"analysis lens tenuis\" \/><\/noscript><\/center><\/p>\n<p style=\"text-align: justify;\">Sed ad maiorem simplicitatem, hoc separari potest<\/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=\"separatio in casibus lentium tenuium\" \/><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=\"separatio in casibus lentium tenuium\" \/><\/noscript><\/center><\/p>\n<p style=\"text-align: justify;\">Cum unumquodque casum iam perscrutati simus (hic), possumus sequentia duo aequationes deducere:<\/p>\n<p style=\"text-align: justify;\"><strong>Pro latere a-b:<\/strong><\/p>\n<p style=\"text-align: center;\"><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;\"><strong>Pro latere b-c:<\/strong><\/p>\n<p style=\"text-align: center;\"><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;\">Hoc loco, si ponimus <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_a = n_c = n_{aer}\\approx 1.0,<\/span><\/span> eveniet <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">s_b = -s_{ab}^\\prime;<\/span><\/span> itaque hae aequationes ita scribuntur<\/p>\n<p style=\"text-align: center;\"><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;\">et eas addendo, nunc fieri potest unam expressionem obtinere:<\/p>\n<p style=\"text-align: center;\"><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;\">Hoc loco expedit variabiles mutare; adhibebimus hanc substitutionem<\/p>\n<p style=\"text-align: center;\"><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;\">ita ut versionem magis \u00abpuram\u00bb aequationis quam initio invenimus obtineamus:<\/p>\n<p style=\"text-align: center;\"><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;\">Denique, utens relatione obiecti-imaginis pro lentibus tenuibus initio deducta, obtinetur:<\/p>\n<p style=\"text-align: center;\"><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;\">Hoc est quod appellamus <strong>Aequationem Fabricantium Lentium.<\/strong><\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h2>Methodi graphici pro lentibus tenuibus<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=QLn3Ml-Mrng&amp;t=1591s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">Instrumentum valde utile ad confirmandum<\/span><\/strong><\/a> vel ad sensum inveniendum calculorum quos fecimus sunt methodi graphici infra depicti; tales methodi analogi sunt iis qui cum speculis adhibentur.<\/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=\"methodi graphici pro lentibus tenuibus convergentibus et divergentibus\" \/><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=\"methodi graphici pro lentibus tenuibus convergentibus et divergentibus\" \/><\/noscript><\/center><\/p>\n<p style=\"text-align: justify;\">Hi methodi diversos exitus praebent secundum situm obiecti coram 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=\"methodus graphicus pro lente tenui 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=\"methodus graphicus pro lente tenui convergente\" \/><\/noscript><\/center><br \/>\n<a name=\"6\"><\/a><\/p>\n<h2>Exercitia:<\/h2>\n<ol style=\"text-align: justify;\">\n<li>Habemus lentem divergentem et fasciculum radiorum parallelorum qui \u00abaperitur\u00bb transeundo per eam ita ut projectiones eius ad punctum 30[cm] a centro lentis situm confluant. Si haec lens adhiberi velit ad imaginem virtualem obtinendam cuius altitudo est dimidia altitudinis cuiusdam obiecti:\n<ol>\n<li type=\"a\">Computa locum ubi tale obiectum poni debeat.<\/li>\n<li type=\"a\">Fac diagramma radiorum ad describendam condicionem.<\/li>\n<\/ol>\n<\/li>\n<li>Obiectum 7[cm] altitudinis ponitur 13[cm] ad sinistram lentis convergentis longitudinis focalis 5[cm]. Secunda lens convergens longitudinis focalis 2[cm] ponitur 30[cm] ad dextram primae lentis, eundem axem opticorum communicantes. Inveni magnitudinem et situm imaginis a duabus lentibus coniunctis generatae.<\/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>Lens tenuis: Omnia de proprietatibus eius et calculis Summarium: Haec lectio lens tenues introducit, explicans earum genera (convergentes et divergentes), proprietates opticas atque relationem obiecti-imaginis. Methodi graphici proponuntur et aequatio fabricantium lentium deducitur ad intellectum functionis earum. Propositum est comprehensionem fundamentalem lentium tenuium earumque applicationem in optica praebere, exercitiis practicis completam. Proposita Discendi: hoc cursu [&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":2,"footnotes":""},"categories":[1280,1250],"tags":[],"class_list":["post-34552","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 v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Lens tenues: Omnia de proprietatibus et calculis earum - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Explora proprietates et calculos essentiales lentium tenuium, inter genera, relationem obiecti-imaginis, methodos graphicos atque aequationem fabricantium lentium. 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