{"id":27764,"date":"2021-10-22T13:00:57","date_gmt":"2021-10-22T13:00:57","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=27764"},"modified":"2024-08-11T20:24:47","modified_gmt":"2024-08-11T20:24:47","slug":"lentilles-minces-tout-sur-leurs-proprietes-et-calculs","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/fr\/lentilles-minces-tout-sur-leurs-proprietes-et-calculs\/","title":{"rendered":"Lentilles minces : Tout sur leurs propri\u00e9t\u00e9s et calculs"},"content":{"rendered":"<p><center><\/p>\n<h1>Lentilles minces : Tout sur leurs propri\u00e9t\u00e9s et calculs<\/h1>\n<p><em><strong>R\u00e9sum\u00e9 :<\/strong><br \/>\nCe cours introduit les lentilles minces, en expliquant leurs types (convergentes et divergentes), leurs propri\u00e9t\u00e9s optiques et la relation objet-image. Les m\u00e9thodes graphiques sont pr\u00e9sent\u00e9es, et l&#8217;\u00e9quation du fabricant de lentilles est d\u00e9duite pour comprendre leur fonctionnement. L&#8217;objectif est de fournir une compr\u00e9hension de base des lentilles minces et de leur application en optique, compl\u00e9t\u00e9e par des exercices pratiques.<\/em><\/p>\n<p><strong>Objectifs d&#8217;apprentissage :<\/strong><br \/>\n\u00c0 la fin de ce cours, l&#8217;\u00e9tudiant sera capable de :<\/p>\n<ul style=\"text-align:left;\">\n<li><strong>Comprendre<\/strong> les propri\u00e9t\u00e9s optiques des lentilles minces, y compris la distance focale et les points focaux.<\/li>\n<li><strong>Identifier<\/strong> les diff\u00e9rents types de lentilles minces, telles que les lentilles convergentes et divergentes, et leurs applications.<\/li>\n<li><strong>Appliquer<\/strong> la relation objet-image pour r\u00e9soudre des probl\u00e8mes optiques en utilisant des lentilles minces.<\/li>\n<li><strong>Analyser<\/strong> comment les surfaces sph\u00e9riques des lentilles minces affectent la r\u00e9fraction de la lumi\u00e8re.<\/li>\n<li><strong>Expliquer<\/strong> l&#8217;\u00e9quation du fabricant de lentilles et son importance dans la fabrication des lentilles optiques.<\/li>\n<li><strong>Utiliser<\/strong> des m\u00e9thodes graphiques pour d\u00e9terminer les positions des images et des objets dans les lentilles minces.<\/li>\n<li><strong>Calculer<\/strong> l&#8217;agrandissement des images produites par des lentilles minces.<\/li>\n<li><strong>D\u00e9river<\/strong> des formules \u00e0 partir de la g\u00e9om\u00e9trie des lentilles minces pour r\u00e9soudre des probl\u00e8mes optiques.<\/li>\n<\/ul>\n<p><strong>Table des mati\u00e8res<\/strong><br \/>\n<a href=\"#1\">Introduction<\/a><br \/>\n<a href=\"#2\">Types de lentilles<\/a><br \/>\n<a href=\"#3\">Propri\u00e9t\u00e9s des lentilles minces<\/a><br \/>\n<a href=\"#4\">\u00c9quation du fabricant de lentilles<\/a><br \/>\n<a href=\"#5\">M\u00e9thodes graphiques pour les lentilles minces<\/a><br \/>\n<a href=\"#6\">Exercices<\/a><br \/>\n<\/center><\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>Introduction<\/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;\">Les lentilles minces,<\/span><\/strong><\/a> avec les miroirs, sont de loin les dispositifs optiques les plus utilis\u00e9s. Ce sont des objets transparents dont la surface est limit\u00e9e par deux interfaces sph\u00e9riques, g\u00e9n\u00e9ralement fabriqu\u00e9s en verre ou en plastique.<\/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=\"Lentille mince\" 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=\"Lentille mince\" class=\"alignnone size-full lazyload\" \/><\/noscript><\/center><\/p>\n<p style=\"text-align: justify; color: #000000;\">Dans une lentille mince, la distance entre les surfaces r\u00e9fractantes est suffisamment petite pour \u00eatre consid\u00e9r\u00e9e comme n\u00e9gligeable.<\/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>Types de lentilles<\/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;\">Les lentilles, comme les miroirs,<\/span><\/strong><\/a> se divisent en deux types : convergentes et 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=\"Lentille 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=\"Lentille convergente\" \/><\/noscript> Lentille mince 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=\"Lentille 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=\"Lentille divergente\" \/><\/noscript> Lentille mince divergente<\/figcaption><\/figure>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify; color: #000000;\">Les points <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> sont les points focaux, et <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> est la <strong>distance focale.<\/strong> Dans une lentille mince, les deux distances focales sont \u00e9gales, c&#8217;est pourquoi elles sont repr\u00e9sent\u00e9es par la m\u00eame lettre.<\/p>\n<p style=\"text-align: justify; color: #000000;\">Dans une lentille mince, la distance entre les surfaces r\u00e9fractantes est suffisamment petite pour \u00eatre consid\u00e9r\u00e9e comme n\u00e9gligeable.<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>Propri\u00e9t\u00e9s des lentilles minces<\/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;\">Si nous faisons de la g\u00e9om\u00e9trie avec une lentille convergente,<\/span><\/strong><\/a> nous verrons ce qui suit :<\/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=\"Relation objet-image dans les lentilles minces\" class=\"alignnone lazyload\" \/><noscript><img decoding=\"async\" src=\"https:\/\/blogger.googleusercontent.com\/img\/a\/AVvXsEiaZBBNwYEXZsxfDEdwRFW-ryUPjItussuFx6RZZWsRxR1kXu-wW_Ns5F2KUdG8anzCHUUToJLMQPgqtM57eO4UcUD8H78minimIOvD8yUM78Zr1ykd81o1O7PNqidqh3LfJGwl62dZQTfzI9EwH7sQttwlwipe6hVAZFb9KqBTbA2y7_ZMJ5IeNHD6QA\" width=\"637\" height=\"353\" alt=\"Relation objet-image dans les lentilles minces\" class=\"alignnone lazyload\" \/><\/noscript><\/center>&nbsp;<\/p>\n<p style=\"text-align: justify; color: #000000;\">Comme les triangles trac\u00e9s sont similaires, les c\u00f4t\u00e9s correspondants seront proportionnels<\/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;\">De m\u00eame,<\/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;\">Puis, \u00e0 partir de <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>, on obtient :<\/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;\">Ce dernier est ce que nous appelons la <strong>relation objet-image pour les lentilles minces.<\/strong><\/p>\n<p style=\"text-align: justify; color: #000000;\" et=\"\" de=\"\" mani\u00e8re=\"\" analogue=\"\" \u00e0=\"\" celle=\"\" que=\"\" nous=\"\" utilisons=\"\" pour=\"\" les=\"\" miroirs,=\"\" il=\"\" est=\"\" possible=\"\" de=\"\" d\u00e9finir=\"\" le=\"\" strong=\"\">facteur de grossissement <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">m<\/span><\/span> par<\/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>\u00c9quation du fabricant de lentilles<\/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;\">Une lentille mince, comme nous le savons, est compos\u00e9e de deux interfaces sph\u00e9riques<\/span><\/strong><\/a> qui s\u00e9parent les milieux \u00e0 travers lesquels la lumi\u00e8re voyage, et nous avons d\u00e9j\u00e0 \u00e9tudi\u00e9 ce qui se passe lorsque la lumi\u00e8re passe d&#8217;un milieu \u00e0 un autre en traversant ces interfaces. Ainsi, pour analyser les lentilles minces, il suffit de combiner ce que nous avons d\u00e9j\u00e0 \u00e9tudi\u00e9 pour les interfaces individuelles.<\/p>\n<p style=\"text-align: justify; color: #000000;\">En g\u00e9n\u00e9ral, une lentille mince a l&#8217;apparence suivante :<\/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=\"Analyse de la lentille mince\" \/><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=\"Analyse de la lentille mince\" \/><\/noscript><\/center><\/p>\n<p style=\"text-align: justify; color: #000000;\">Mais pour simplifier, cela peut \u00eatre s\u00e9par\u00e9<\/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=\"S\u00e9paration des cas de lentilles minces\" \/><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=\"S\u00e9paration des cas de lentilles minces\" \/><\/noscript><\/center><\/p>\n<p style=\"text-align: justify; color: #000000;\">Puisque chaque cas a d\u00e9j\u00e0 \u00e9t\u00e9 analys\u00e9 (ici), nous pouvons en extraire les deux \u00e9quations suivantes :<\/p>\n<p style=\"text-align: justify; color: #000000;\"><strong>Pour le c\u00f4t\u00e9 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>Pour le c\u00f4t\u00e9 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;\">\u00c0 ce stade, si nous faisons <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_a = n_c = n_{air}\\approx 1.0,<\/span><\/span> il se trouve que <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">s_b = -s_{ab}^\\prime;<\/span><\/span> par cons\u00e9quent, ces \u00e9quations sont \u00e9crites de la mani\u00e8re suivante<\/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;\">et en les additionnant, il est maintenant possible d&#8217;obtenir une seule expression :<\/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;\">\u00c0 ce stade, il est pratique de renommer les variables en jeu ; nous utiliserons la d\u00e9nomination suivante :<\/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;\">ainsi, nous obtiendrons une version plus \u00abpropre\u00bb de l&#8217;\u00e9quation que nous avions initialement obtenue :<\/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;\">Enfin, en utilisant la relation objet-image pour les lentilles minces d\u00e9duite au d\u00e9but, on obtient :<\/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;\">C&#8217;est ce que nous appelons l&#8217;<strong>\u00e9quation du fabricant de lentilles.<\/strong><\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h2>M\u00e9thodes graphiques pour les lentilles minces<\/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;\">Un outil tr\u00e8s utile pour v\u00e9rifier<\/span><\/strong><\/a> ou comprendre les calculs que nous effectuons sont les m\u00e9thodes graphiques illustr\u00e9es ci-dessous ; ces m\u00e9thodes sont analogues \u00e0 celles utilis\u00e9es avec les miroirs.<\/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\u00e9thodes graphiques pour les lentilles minces convergentes et divergentes\" \/><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\u00e9thodes graphiques pour les lentilles minces convergentes et divergentes\" \/><\/noscript><\/center><\/p>\n<p style=\"text-align: justify; color: #000000;\">Ces m\u00e9thodes donnent des r\u00e9sultats diff\u00e9rents selon la position de l&#8217;objet devant la lentille.<\/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\u00e9thode graphique pour les lentilles minces convergentes\" \/><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\u00e9thode graphique pour les lentilles minces convergentes\" \/><\/noscript><\/center><\/p>\n<p><a name=\"6\"><\/a><\/p>\n<h2>Exercices :<\/h2>\n<ol style=\"text-align: justify; color: #000000;\">\n<li>On dispose d&#8217;une lentille divergente et d&#8217;un faisceau de rayons parall\u00e8les qui se \u00abdiverge\u00bb en passant \u00e0 travers elle de mani\u00e8re \u00e0 ce que leurs projections convergent en un point situ\u00e9 \u00e0 30[cm] du centre de la lentille. Si vous souhaitez utiliser cette lentille pour obtenir une image virtuelle d&#8217;une hauteur \u00e9gale \u00e0 la moiti\u00e9 de celle d&#8217;un certain objet :\n<ol>\n<li type=\"a\">Calculez o\u00f9 doit se trouver cet objet.<\/li>\n<li type=\"a\">Faites un diagramme des rayons pour d\u00e9crire la situation.<\/li>\n<\/ol>\n<\/li>\n<li>Un objet de 7[cm] de hauteur est plac\u00e9 \u00e0 13[cm] \u00e0 gauche d&#8217;une lentille convergente de distance focale de 5[cm]. Une deuxi\u00e8me lentille convergente de distance focale de 2[cm] est plac\u00e9e \u00e0 30[cm] \u00e0 droite de la premi\u00e8re lentille, partageant les deux le m\u00eame axe optique. Trouvez la taille et la position de l&#8217;image form\u00e9e par les deux lentilles combin\u00e9es.<\/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>Lentilles minces : Tout sur leurs propri\u00e9t\u00e9s et calculs R\u00e9sum\u00e9 : Ce cours introduit les lentilles minces, en expliquant leurs types (convergentes et divergentes), leurs propri\u00e9t\u00e9s optiques et la relation objet-image. Les m\u00e9thodes graphiques sont pr\u00e9sent\u00e9es, et l&#8217;\u00e9quation du fabricant de lentilles est d\u00e9duite pour comprendre leur fonctionnement. L&#8217;objectif est de fournir une compr\u00e9hension de [&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":26,"footnotes":""},"categories":[847,647],"tags":[],"class_list":["post-27764","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-optique-geometrique","category-physique"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Lentilles minces : Tout sur leurs propri\u00e9t\u00e9s et calculs - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"D\u00e9couvrez les propri\u00e9t\u00e9s essentielles et les calculs des lentilles minces, y compris les types, la relation objet-image, les m\u00e9thodes graphiques et l&#039;\u00e9quation du fabricant de lentilles. 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