{"id":27752,"date":"2021-10-22T13:00:32","date_gmt":"2021-10-22T13:00:32","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=27752"},"modified":"2024-08-11T19:56:08","modified_gmt":"2024-08-11T19:56:08","slug":"thin-lenses-everything-about-their-properties-and-calculations","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/en\/thin-lenses-everything-about-their-properties-and-calculations\/","title":{"rendered":"Thin Lenses: Everything About Their Properties and Calculations"},"content":{"rendered":"<p><center><\/p>\n<h1>Thin Lenses: Everything About Their Properties and Calculations<\/h1>\n<p><em><strong>Summary:<\/strong><br \/>\nThis class introduces thin lenses, explaining their types (convergent and divergent), their optical properties, and the object-image relationship. Graphical methods are presented, and the lens maker&#8217;s equation is derived to understand their functioning. The aim is to provide a basic understanding of thin lenses and their application in optics, complemented with practical exercises.<\/em><\/p>\n<p><strong>Learning Objectives:<\/strong><br \/>\nBy the end of this class, the student will be able to:<\/p>\n<ul style=\"text-align:left;\">\n<li><strong>Understand<\/strong> the optical properties of thin lenses, including focal length and focal points.<\/li>\n<li><strong>Identify<\/strong> different types of thin lenses, such as convergent and divergent lenses, and their applications.<\/li>\n<li><strong>Apply<\/strong> the object-image relationship to solve optical problems using thin lenses.<\/li>\n<li><strong>Analyze<\/strong> how spherical surfaces in thin lenses affect light refraction.<\/li>\n<li><strong>Explain<\/strong> the lens maker&#8217;s equation and its relevance in the manufacturing of optical lenses.<\/li>\n<li><strong>Use<\/strong> graphical methods to determine the positions of image and object in thin lenses.<\/li>\n<li><strong>Calculate<\/strong> the magnification of images produced by thin lenses.<\/li>\n<li><strong>Deduce<\/strong> formulas from the geometry of thin lenses to solve optical problems.<\/li>\n<\/ul>\n<p><strong>TABLE OF CONTENTS<\/strong><br \/>\n<a href=\"#1\">Introduction<\/a><br \/>\n<a href=\"#2\">Types of Lenses<\/a><br \/>\n<a href=\"#3\">Properties of Thin Lenses<\/a><br \/>\n<a href=\"#4\">Lens Maker&#8217;s Equation<\/a><br \/>\n<a href=\"#5\">Graphical Methods for Thin Lenses<\/a><br \/>\n<a href=\"#6\">Exercises<\/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;\">Thin lenses,<\/span><\/strong><\/a> along with mirrors, are by far the most widely used optical devices. These are transparent objects whose surface is bounded by two spherical interfaces and are generally made of glass or plastic.<\/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=\"Thin Lens\" 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=\"Thin Lens\" class=\"alignnone size-full lazyload\" \/><\/noscript><\/center><\/p>\n<p style=\"text-align: justify; color: #000000;\">In a thin lens, the distance between the refractive surfaces is small enough to be considered negligible.<\/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 of Lenses<\/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;\">Lenses, like mirrors,<\/span><\/strong><\/a> are divided into two types: convergent and divergent.<\/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=\"Convergent Lens\" \/><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=\"Convergent Lens\" \/><\/noscript> Thin Convergent Lens<\/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=\"Divergent Lens\" \/><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=\"Divergent Lens\" \/><\/noscript> Thin Divergent Lens<\/figcaption><\/figure>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify; color: #000000;\">The points <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F_1<\/span><\/span> and <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F_2<\/span><\/span> are the focal points, and <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> is the <strong>focal length.<\/strong> In a thin lens, the two focal lengths are equal, so they are represented by the same letter.<\/p>\n<p style=\"text-align: justify; color: #000000;\">In a thin lens, the distance between the refractive surfaces is small enough to be considered negligible.<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>Properties of Thin Lenses<\/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;\">If we do geometry with a convergent lens,<\/span><\/strong><\/a> we will see the following:<\/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=\"object-image relationship in thin lenses\" class=\"alignnone lazyload\" \/><noscript><img decoding=\"async\" src=\"https:\/\/blogger.googleusercontent.com\/img\/a\/AVvXsEiaZBBNwYEXZsxfDEdwRFW-ryUPjItussuFx6RZZWsRxR1kXu-wW_Ns5F2KUdG8anzCHUUToJLMQPgqtM57eO4UcUD8H78minimIOvD8yUM78Zr1ykd81o1O7PNqidqh3LfJGwl62dZQTfzI9EwH7sQttwlwipe6hVAZFb9KqBTbA2y7_ZMJ5IeNHD6QA\" width=\"637\" height=\"353\" alt=\"object-image relationship in thin lenses\" class=\"alignnone lazyload\" \/><\/noscript><\/center>&nbsp;<\/p>\n<p style=\"text-align: justify; color: #000000;\">Since the painted triangles are similar, the corresponding sides will be proportional<\/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;\">Similarly,<\/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;\">Then, from <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\triangle)<\/span><\/span> and <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\star)<\/span><\/span> we have:<\/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;\">The above is what we call the <strong>object-image relationship for thin lenses.<\/strong><\/p>\n<p style=\"text-align: justify; color: #000000;\" y=\"\" de=\"\" forma=\"\" an=\"\" loga=\"\" a=\"\" como=\"\" se=\"\" trabaja=\"\" con=\"\" espejos=\"\" es=\"\" posible=\"\" definir=\"\" el=\"\" strong=\"\">magnification factor <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">m<\/span><\/span> through<\/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>Lens Maker&#8217;s Equation<\/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;\">A thin lens, as we know, is composed of two spherical interfaces<\/span><\/strong><\/a> that separate mediums through which light travels, and we have already studied what happens when light crosses from one medium to another across interfaces of this style. Therefore, to analyze thin lenses, we will suffice to compose what we have already reviewed for individual interfaces.<\/p>\n<p style=\"text-align: justify; color: #000000;\">In general, a thin lens has the following appearance:<\/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=\"thin lens analysis\" \/><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=\"thin lens analysis\" \/><\/noscript><\/center><\/p>\n<p style=\"text-align: justify; color: #000000;\">But for simplicity, this can be separated<\/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=\"separation of thin lens cases\" \/><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=\"separation of thin lens cases\" \/><\/noscript><\/center><\/p>\n<p style=\"text-align: justify; color: #000000;\">Since we have already analyzed each case (here), we can extract the following two equations:<\/p>\n<p style=\"text-align: justify; color: #000000;\"><strong>For side 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>For side 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;\">At this point, if we set <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_a = n_c = n_{air}\\approx 1.0,<\/span><\/span> it will occur that <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">s_b = -s_{ab}^\\prime;<\/span><\/span> therefore, these equations are written as follows<\/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;\">and by summing them, it is now possible to obtain a single 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;\">At this point, it is convenient to rename the variables involved; we will use the following renaming<\/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;\">so that we obtain a cleaner version of the equation we originally derived:<\/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;\">Finally, using the object-image relationship for thin lenses derived at the beginning, we get:<\/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;\">This is what we call the <strong>Lens Maker&#8217;s Equation.<\/strong><\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h2>Graphical Methods for Thin Lenses<\/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;\">A very useful tool for corroborating<\/span><\/strong><\/a> or making sense of the calculations we perform are the graphical methods drawn below; such methods are analogous to those used with mirrors.<\/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=\"graphical methods for convergent and divergent thin lenses\" \/><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=\"graphical methods for convergent and divergent thin lenses\" \/><\/noscript><\/center><\/p>\n<p style=\"text-align: justify; color: #000000;\">These methods provide different results depending on the object&#8217;s position in front of the lens.<\/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=\"graphical method for convergent thin lenses\" \/><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=\"graphical method for convergent thin lenses\" \/><\/noscript><\/center><\/p>\n<p><a name=\"6\"><\/a><\/p>\n<h2>Exercises:<\/h2>\n<ol style=\"text-align: justify; color: #000000;\">\n<li>A divergent lens and a parallel beam of rays \u00abopen up\u00bb as they pass through it so that their projections converge to a point located 30[cm] from the center of the lens. If you want to use this lens to obtain a virtual image 1\/2 the height of a certain object:\n<ol>\n<li type=\"a\">Calculate where such an object must be placed.<\/li>\n<li type=\"a\">Make a ray diagram to describe the situation.<\/li>\n<\/ol>\n<\/li>\n<li>An object 7[cm] high is placed 13[cm] to the left of a convergent lens with a focal length of 5[cm]. A second convergent lens with a focal length of 2[cm] is placed 30[cm] to the right of the first lens, sharing the same optical axis. Find the size and position of the image generated by the two combined lenses.<\/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>Thin Lenses: Everything About Their Properties and Calculations Summary: This class introduces thin lenses, explaining their types (convergent and divergent), their optical properties, and the object-image relationship. Graphical methods are presented, and the lens maker&#8217;s equation is derived to understand their functioning. The aim is to provide a basic understanding of thin lenses and their [&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":16,"footnotes":""},"categories":[835,635],"tags":[],"class_list":["post-27752","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-geometrical-optics","category-physics"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Thin Lenses: Everything About Their Properties and Calculations - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Discover the essential properties and calculations of thin lenses, including types, object-image relationship, graphical methods, and the lens maker&#039;s equation. 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