{"id":27730,"date":"2021-10-06T13:00:18","date_gmt":"2021-10-06T13:00:18","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=27730"},"modified":"2024-08-11T16:57:30","modified_gmt":"2024-08-11T16:57:30","slug":"%e7%90%83%e9%9d%a2%e7%95%8c%e9%9d%a2%e7%9a%84%e6%8a%98%e5%b0%84","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/zh\/%e7%90%83%e9%9d%a2%e7%95%8c%e9%9d%a2%e7%9a%84%e6%8a%98%e5%b0%84\/","title":{"rendered":"\u7403\u9762\u754c\u9762\u7684\u6298\u5c04"},"content":{"rendered":"<p><center><\/p>\n<h1>\u7403\u9762\u754c\u9762\u7684\u6298\u5c04<\/h1>\n<p><em><strong>\u6458\u8981\uff1a<\/strong><br \/>\n\u5728\u672c\u8bfe\u7a0b\u4e2d\uff0c\u6211\u4eec\u5c06\u5206\u6790\u7403\u9762\u754c\u9762\u7684\u6298\u5c04\uff0c\u91cd\u70b9\u4ecb\u7ecd\u5149\u5728\u901a\u8fc7\u7403\u9762\u65f6\u7684\u884c\u4e3a\u4ee5\u53ca\u56fe\u50cf\u7684\u5f62\u6210\u3002\u4ecb\u7ecd\u4e86\u8ba1\u7b97\u56fe\u50cf\u4f4d\u7f6e\u548c\u5927\u5c0f\u7684\u5173\u952e\u65b9\u7a0b\u3002\u8fd8\u63a2\u8ba8\u4e86\u900f\u955c\u548c\u8868\u89c2\u6df1\u5ea6\u4f30\u7b97\u7b49\u5b9e\u9645\u6848\u4f8b\u3002<\/em><\/p>\n<p><strong>\u5b66\u4e60\u76ee\u6807\uff1a<\/strong><br \/>\n\u5728\u672c\u8bfe\u7a0b\u7ed3\u675f\u65f6\uff0c\u5b66\u751f\u5c06\u80fd\u591f\uff1a<\/p>\n<ol style=\"text-align:left;\">\n<li><strong>\u7406\u89e3<\/strong>\u5149\u901a\u8fc7\u7403\u9762\u754c\u9762\u65f6\u7684\u6298\u5c04\u73b0\u8c61\u3002<\/li>\n<li><strong>\u63a8\u5bfc<\/strong>\u5e76\u5e94\u7528\u7403\u9762\u754c\u9762\u7684\u7269\u4f53-\u56fe\u50cf\u5173\u7cfb\u3002<\/li>\n<li><strong>\u5e94\u7528<\/strong>\u65af\u6d85\u5c14\u5b9a\u5f8b\u5728\u7403\u9762\u754c\u9762\u4e2d\u7684\u5e94\u7528\u3002<\/li>\n<li><strong>\u786e\u5b9a<\/strong>\u7403\u9762\u754c\u9762\u5f62\u6210\u7684\u56fe\u50cf\u4f4d\u7f6e\u3002<\/li>\n<li><strong>\u8ba1\u7b97<\/strong>\u901a\u8fc7\u7403\u9762\u8868\u9762\u6298\u5c04\u7684\u56fe\u50cf\u653e\u5927\u7387\u3002<\/li>\n<li><strong>\u7406\u89e3<\/strong>\u7269\u4f53\u548c\u56fe\u50cf\u4f4d\u7f6e\u53ca\u5927\u5c0f\u7684\u7b26\u53f7\u7ea6\u5b9a\u3002<\/li>\n<li><strong>\u5c06<\/strong>\u7403\u9762\u754c\u9762\u4e0e\u5e73\u9762\u754c\u9762\u4f5c\u4e3a\u6781\u9650\u60c5\u51b5\u8fdb\u884c\u6bd4\u8f83\u3002<\/li>\n<li><strong>\u5206\u6790<\/strong>\u901a\u8fc7\u7403\u9762\u754c\u9762\u5f62\u6210\u7684\u6269\u5c55\u56fe\u50cf\u3002<\/li>\n<\/ol>\n<p><strong>\u5185\u5bb9\u7d22\u5f15<\/strong><br \/>\n<a href=\"#1\"><strong>\u7b80\u4ecb<\/strong><\/a><br \/>\n<a href=\"#2\"><strong>\u7403\u9762\u754c\u9762\u7684\u7269\u4f53-\u56fe\u50cf\u5173\u7cfb<\/strong><\/a><br \/>\n<a href=\"#3\">\u89d2\u5ea6\u5173\u7cfb\u7684\u63d0\u53d6<\/a><br \/>\n<a href=\"#4\">\u5f15\u5165\u65af\u6d85\u5c14\u5b9a\u5f8b<\/a><br \/>\n<a href=\"#5\"><strong>\u901a\u8fc7\u7403\u9762\u754c\u9762\u6298\u5c04\u5728\u53e6\u4e00\u4fa7\u5f62\u6210\u7684\u6269\u5c55\u56fe\u50cf<\/strong><\/a><br \/>\n<a href=\"#6\">\u603b\u7ed3<\/a><br \/>\n<a href=\"#7\"><strong>\u7403\u9762\u754c\u9762\u7684\u6781\u9650\u60c5\u51b5\uff1a\u5e73\u9762\u754c\u9762<\/strong><\/a><br \/>\n<a href=\"#8\"><strong>\u7ec3\u4e60<\/strong><\/a><\/p>\n<p><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/13kntUA9n-I\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><br \/>\n<\/center><\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>\u7b80\u4ecb<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=13kntUA9n-I&amp;t=146s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u6211\u4eec\u5df2\u7ecf\u7814\u7a76\u4e86\u6298\u5c04\u7684\u5de5\u4f5c\u539f\u7406;<\/span><\/strong><\/a> \u4e5f\u5c31\u662f\u8bf4\uff0c\u5f53\u5149\u4ece\u4e00\u79cd\u4ecb\u8d28\u8fdb\u5165\u53e6\u4e00\u79cd\u4ecb\u8d28\u65f6\u4f1a\u53d1\u751f\u4ec0\u4e48\u3002\u4f46\u6211\u4eec\u6240\u6709\u7684\u7814\u7a76\u90fd\u5047\u8bbe\u5206\u9694\u4ecb\u8d28\u7684\u754c\u9762\u662f\u5e73\u9762\u3002\u7136\u800c\uff0c\u65e0\u8bba\u662f\u5728\u81ea\u7136\u754c\u8fd8\u662f\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u7403\u9762\u754c\u9762\u4e0a\u7684\u6298\u5c04\u73b0\u8c61\u5e76\u4e0d\u7f55\u89c1\u3002\u4f8b\u5b50\u5305\u62ec\u4eba\u773c\uff08\u4ee5\u53ca\u51e0\u4e4e\u6240\u6709\u52a8\u7269\u7684\u773c\u775b\uff09\u548c\u5927\u591a\u6570\u5728\u65e5\u5e38\u751f\u6d3b\u548c\u5de5\u4e1a\u5e94\u7528\u4e2d\u4f7f\u7528\u7684\u5149\u5b66\u8bbe\u5907\u3002<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u5728\u4e0b\u56fe\u4e2d\uff0c\u6211\u4eec\u770b\u5230\u900f\u955c\u662f\u5982\u4f55\u901a\u8fc7\u4e24\u4e2a\u7403\u9762\u8868\u9762\u6784\u6210\u7684\u3002<\/p>\n<p><center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-xuCmdVLtNcc\/YVuCvXoOfZI\/AAAAAAAAFmc\/mCuYiHaNfxM4I6RcxEJcLln6uLC5MMIKQCLcBGAsYHQ\/s0\/lente%2Bde%2Bvidrio.PNG\" width=\"661\" height=\"378\" alt=\"\u901a\u8fc7\u4e24\u4e2a\u7403\u9762\u8868\u9762\u5f62\u6210\u7684\u73bb\u7483\u900f\u955c\" class=\"alignnone size-full lazyload\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-xuCmdVLtNcc\/YVuCvXoOfZI\/AAAAAAAAFmc\/mCuYiHaNfxM4I6RcxEJcLln6uLC5MMIKQCLcBGAsYHQ\/s0\/lente%2Bde%2Bvidrio.PNG\" width=\"661\" height=\"378\" alt=\"\u901a\u8fc7\u4e24\u4e2a\u7403\u9762\u8868\u9762\u5f62\u6210\u7684\u73bb\u7483\u900f\u955c\" class=\"alignnone size-full lazyload\" \/><\/noscript><\/center><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u4e3a\u4e86\u8be6\u7ec6\u7814\u7a76\u8fd9\u7c7b\u8bbe\u5907\uff0c\u6709\u5fc5\u8981\u56de\u987e\u5149\u5728\u901a\u8fc7\u7403\u9762\u754c\u9762\u4ece\u4e00\u79cd\u4ecb\u8d28\u8fdb\u5165\u53e6\u4e00\u79cd\u4ecb\u8d28\u65f6\u7684\u884c\u4e3a\u3002<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u7403\u9762\u754c\u9762\u7684\u7269\u4f53-\u56fe\u50cf\u5173\u7cfb<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=13kntUA9n-I&amp;t=235s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u6211\u4eec\u5c06\u5f00\u59cb\u7814\u7a76<\/span><\/strong><\/a>\u5149\u901a\u8fc7\u7403\u9762\u754c\u9762\u4ece\u4e00\u79cd\u4ecb\u8d28\u8fdb\u5165\u53e6\u4e00\u79cd\u4ecb\u8d28\u65f6\u7684\u884c\u4e3a\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u5c06\u8003\u8651\u4e00\u4e2a\u534a\u5f84\u4e3a<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">R<\/span><\/span>\u7684\u7403\u4f53\uff0c\u8be5\u7403\u4f53\u7531\u6298\u5c04\u7387\u4e3a<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_b<\/span><\/span>\u7684\u6750\u6599\u5236\u6210\uff0c\u6d78\u5165\u6298\u5c04\u7387\u4e3a<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_a.<\/span><\/span>\u7684\u4ecb\u8d28\u4e2d\u3002<\/p>\n<p><center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-x0g44iZ6LDo\/YVuDO2nkD3I\/AAAAAAAAFmk\/8gQHFBnQxvEG-5B6XUAgTTZHtxntx6YogCLcBGAsYHQ\/s0\/inteface%2Besf%25C3%25A9rica.PNG\" width=\"987\" height=\"371\" alt=\"\u5206\u9694\u4e24\u79cd\u4ecb\u8d28\u7684\u7403\u9762\u754c\u9762\" class=\"alignnone size-full lazyload\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-x0g44iZ6LDo\/YVuDO2nkD3I\/AAAAAAAAFmk\/8gQHFBnQxvEG-5B6XUAgTTZHtxntx6YogCLcBGAsYHQ\/s0\/inteface%2Besf%25C3%25A9rica.PNG\" width=\"987\" height=\"371\" alt=\"\u5206\u9694\u4e24\u79cd\u4ecb\u8d28\u7684\u7403\u9762\u754c\u9762\" class=\"alignnone size-full lazyload\" \/><\/noscript><\/center><\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h3>\u89d2\u5ea6\u5173\u7cfb\u7684\u63d0\u53d6<\/h3>\n<p style=\"text-align: justify; color: #000000;\">\u5982\u679c\u6211\u4eec\u5206\u6790\u6b64\u56fe\u4e2d\u7684\u89d2\u5ea6\uff0c\u4f1a\u6ce8\u610f\u5230\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rll}\n\n{(1)}&amp; \\theta_a &amp; =\\alpha + \\phi \\\\ \\\\\n\n{(2)}&amp; \\phi &amp; =\\beta + \\theta_b\n\n\\end{array}<\/span><\/span><\/p>\n<h4>\u8bc1\u660e<\/h4>\n<p style=\"text-align: justify; color: #000000;\">\u7b2c\u4e00\u4e2a\u65b9\u7a0b\u662f\u4ece\u4e09\u89d2\u5f62\u7684\u5185\u89d2\u4e4b\u548c\u7b49\u4e8e\u4e24\u4e2a\u76f4\u89d2\u7684\u4e8b\u5b9e\u5f97\u51fa\u7684\uff1a<\/p>\n<p><center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-0ILYFKDJRo0\/YVvJaKwoZxI\/AAAAAAAAFms\/arUYkIwSz18wvNntSE_WHuknjoYolOXSQCLcBGAsYHQ\/s0\/triangulorectangulo-optica.PNG\" width=\"346\" height=\"148\" class=\"alignnone size-full lazyload\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-0ILYFKDJRo0\/YVvJaKwoZxI\/AAAAAAAAFms\/arUYkIwSz18wvNntSE_WHuknjoYolOXSQCLcBGAsYHQ\/s0\/triangulorectangulo-optica.PNG\" width=\"346\" height=\"148\" class=\"alignnone size-full lazyload\" \/><\/noscript><\/center><\/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; \\alpha + \\phi + (\\pi - \\theta_a) = \\pi\\\\ \\\\\n\n\\equiv &amp; \\alpha + \\phi - \\theta_a = 0 \\\\ \\\\\n\n\\equiv &amp; \\color{blue}{\\theta_a = \\alpha + \\phi}\n\n\\end{array}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u7b2c\u4e8c\u4e2a\u65b9\u7a0b\u7c7b\u4f3c\u5730\u5f97\u51fa\uff1a<\/p>\n<p><center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-R5siuLq4gJs\/YVvJ22k7m6I\/AAAAAAAAFm0\/D6gmIAHjXFY4cNmUwrnq4yvxQ_2PcBSjgCLcBGAsYHQ\/s0\/triangulorectangulo-optica2.PNG\" width=\"329\" height=\"216\" class=\"alignnone size-full lazyload\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-R5siuLq4gJs\/YVvJ22k7m6I\/AAAAAAAAFm0\/D6gmIAHjXFY4cNmUwrnq4yvxQ_2PcBSjgCLcBGAsYHQ\/s0\/triangulorectangulo-optica2.PNG\" width=\"329\" height=\"216\" class=\"alignnone size-full lazyload\" \/><\/noscript><\/center><\/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; \\beta + \\theta_b + (\\pi - \\phi) = \\pi\\\\ \\\\\n\n\\equiv &amp;  \\beta + \\theta_b - \\phi = 0\\\\ \\\\\n\n\\equiv &amp; \\color{blue}{\\phi = \\beta + \\theta_b }\n\n\\end{array}<\/span><\/span><\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h3>\u5f15\u5165\u65af\u6d85\u5c14\u5b9a\u5f8b<\/h3>\n<p style=\"text-align: justify; color: #000000;\">\u4ece\u56fe\u4e2d\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u5f97\u5230\u4ee5\u4e0b\u8868\u8fbe\u5f0f\uff1a<\/p>\n<p><center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-x0g44iZ6LDo\/YVuDO2nkD3I\/AAAAAAAAFmk\/8gQHFBnQxvEG-5B6XUAgTTZHtxntx6YogCLcBGAsYHQ\/s0\/inteface%2Besf%25C3%25A9rica.PNG\" width=\"987\" height=\"371\" alt=\"\u5206\u9694\u4e24\u79cd\u4ecb\u8d28\u7684\u7403\u9762\u754c\u9762\" class=\"alignnone size-full lazyload\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-x0g44iZ6LDo\/YVuDO2nkD3I\/AAAAAAAAFmk\/8gQHFBnQxvEG-5B6XUAgTTZHtxntx6YogCLcBGAsYHQ\/s0\/inteface%2Besf%25C3%25A9rica.PNG\" width=\"987\" height=\"371\" alt=\"\u5206\u9694\u4e24\u79cd\u4ecb\u8d28\u7684\u7403\u9762\u754c\u9762\" class=\"alignnone size-full lazyload\" \/><\/noscript><\/center><\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rll}\n\n{(3)}&amp;\\tan(\\alpha) &amp;=\\displaystyle \\frac{h}{s+\\delta}\\\\ \\\\\n\n{(4)}&amp;\\tan(\\beta) &amp;=\\displaystyle \\frac{h}{s^\\prime - \\delta}\\\\ \\\\\n\n{(5)}&amp;\\tan(\\phi) &amp;=\\displaystyle \\frac{h}{R - \\delta}\n\n\\end{array}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u6839\u636e\u65af\u6d85\u5c14\u5b9a\u5f8b\uff0c\u6211\u4eec\u6709<\/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{(6)} &amp;  n_a\\sin(\\theta_a) = n_b \\sin(\\theta_b)\\end{array}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u73b0\u5728\uff0c\u5982\u679c\u6211\u4eec\u91c7\u7528<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\theta_a<\/span><\/span>\u548c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\theta_b<\/span><\/span>\u90fd\u5f88\u5c0f\u7684\u8fd1\u4f3c\u503c\uff0c\u90a3\u4e48<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha, \\beta<\/span><\/span>\u548c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\phi<\/span><\/span>\u4e5f\u4f1a\u5f88\u5c0f\uff0c\u5e76\u4e14\uff1a<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u4ece\u56fe\u4e2d\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u5f97\u5230\u4ee5\u4e0b\u8868\u8fbe\u5f0f\uff1a<\/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\\sin(\\theta_a) &amp;\\approx \\theta_a \\\\ \\\\\n\n\\sin(\\theta_b) &amp;\\approx \\theta_b \\\\ \\\\\n\n\\delta &amp;\\approx 0 \\\\ \\\\\n\n\\tan(\\alpha) &amp;\\approx \\alpha \\\\ \\\\\n\n\\tan(\\beta) &amp;\\approx \\beta \\\\ \\\\\n\n\\tan(\\phi) &amp;\\approx \\phi\n\n\\end{array}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u7136\u540e\uff0c\u6839\u636e\u8fd9\u4e00\u70b9\u548c\u65af\u6d85\u5c14\u5b9a\u5f8b\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u51fa\uff1a<\/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{(7)} &amp; n_a \\theta_a \\approx n_b \\theta_b \\\\ \\\\\n\n\\equiv &amp;  \\theta_b \\approx \\displaystyle \\frac{n_a}{n_b} \\theta_a\n\n\\end{array}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u73b0\u5728\uff0c\u6839\u636e(7)\u3001(1)\u548c(2)\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230<\/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{(8)} &amp; \\phi - \\beta \\approx \\displaystyle \\frac{n_a}{n_b}(\\alpha + \\phi) \\\\ \\\\\n\n\\equiv &amp; \\phi \\approx \\beta + \\displaystyle  \\frac{n_a}{n_b}(\\alpha + \\phi) \\\\ \\\\\n\n{}\\equiv &amp;  n_b\\phi \\approx n_b\\beta + n_a \\alpha + n_a\\phi \\\\ \\\\\n\n\\equiv &amp; \\color{blue}{n_a \\alpha + n_b\\beta \\approx (n_b - n_a) \\phi }\n\n\\end{array}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u6700\u540e\uff0c\u6839\u636e(8)\u3001\u8fd1\u4f3c\u503c\u548c(3)\u3001(4)\u3001(5)\u5f0f\uff0c\u6211\u4eec\u5f97\u5230\uff1a<\/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{(9)} &amp; \\displaystyle n_a \\left( \\frac{\\color{red}{h}}{S + \\underbrace{\\delta}_{\\to 0}} \\right) + n_b \\left(\\frac{\\color{red}{h}}{S^\\prime - \\underbrace{\\delta}_{\\to 0} } \\right) \\approx (n_b - n_a) \\left(\\frac{\\color{red}{h}}{R-\\underbrace{\\delta}_{\\to 0}}\\right) \\\\ \\\\\n\n\\equiv &amp; \\displaystyle \\color{blue}{\\frac{n_a}{S } + \\frac{ n_b}{S^\\prime } \\approx \\frac{n_b - n_a}{R} }\n\n\\end{array}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u6700\u540e\u8fd9\u4e2a\u65b9\u7a0b\u6211\u4eec\u79f0\u4e4b\u4e3a<strong>\u7403\u9762\u754c\u9762\u7684\u7269\u4f53-\u56fe\u50cf\u5173\u7cfb\u3002<\/strong><\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h2>\u901a\u8fc7\u7403\u9762\u754c\u9762\u6298\u5c04\u5728\u53e6\u4e00\u4fa7\u5f62\u6210\u7684\u6269\u5c55\u56fe\u50cf<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=13kntUA9n-I&amp;t=1211s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u73b0\u5728\u8ba9\u6211\u4eec\u770b\u770b\u5f53\u6211\u4eec\u5c06<\/span><\/strong><\/a>\u70b9\u5149\u6e90\u66ff\u6362\u4e3a\u6269\u5c55\u7269\u4f53\u65f6\u4f1a\u53d1\u751f\u4ec0\u4e48\u3002\u8fd9\u5728\u4e0b\u56fe\u4e2d\u6709\u6240\u8bf4\u660e\uff1a<\/p>\n<p><center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-Nnk1qsJET0k\/YVvLLFbEWPI\/AAAAAAAAFm8\/zWNnZMpqHSMT_38PJgKqIhqzLO53CCMSwCLcBGAsYHQ\/s0\/objeto-extendido-frente-interfaz-esferica.PNG\" width=\"1005\" height=\"409\" alt=\"\u7403\u9762\u754c\u9762\u524d\u7684\u6269\u5c55\u7269\u4f53\" class=\"alignnone size-full lazyload\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-Nnk1qsJET0k\/YVvLLFbEWPI\/AAAAAAAAFm8\/zWNnZMpqHSMT_38PJgKqIhqzLO53CCMSwCLcBGAsYHQ\/s0\/objeto-extendido-frente-interfaz-esferica.PNG\" width=\"1005\" height=\"409\" alt=\"\u7403\u9762\u754c\u9762\u524d\u7684\u6269\u5c55\u7269\u4f53\" class=\"alignnone size-full lazyload\" \/><\/noscript><\/center><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u524d\u9762\u7684\u5206\u6790\u5df2\u7ecf\u8868\u660e\u4e86<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">S<\/span><\/span>\u548c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">S^\\prime,<\/span><\/span>\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u73b0\u5728\u6211\u4eec\u53ea\u9700\u8981\u627e\u5230\u7269\u4f53\u548c\u56fe\u50cf\u5927\u5c0f\u4e4b\u95f4\u7684\u5173\u7cfb\u3002<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u4ece\u56fe\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u770b\u5230\uff1a<\/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\\tan(\\theta_a) &amp; =\\displaystyle \\frac{y}{S} \\\\ \\\\\n\n\\tan(\\theta_b) &amp; =\\displaystyle - \\frac{y^\\prime}{S^\\prime}\n\n\\end{array}\n\n<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u6211\u4eec\u5c06\u628a\u8fd9\u4e00\u70b9\u4e0e\u65af\u6d85\u5c14\u5b9a\u5f8b\u7ed3\u5408\u8d77\u6765<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_a\\sin(\\theta_a) = n_b\\sin(\\theta_b). <\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u4e3a\u6b64\uff0c\u6211\u4eec\u5c06\u57fa\u4e8e\u4ee5\u4e0b\u4e8b\u5b9e\uff0c\u5373\u5bf9\u4e8e\u5c0f\u89d2\u5ea6\uff0c\u8fd1\u4f3c\u9002\u7528<\/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\\sin(\\theta_a) &amp; \\approx \\tan(\\theta_a) \\\\ \\\\\n\n\\sin(\\theta_b) &amp; \\approx \\tan(\\theta_b)\n\n\\end{array}\n\n<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u5199\u6210<\/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 n_a \\frac{y}{S} \\approx- n_b \\dfrac{y^\\prime}{S^\\prime} \\\\ \\\\\n\n\\equiv &amp; \\displaystyle \\dfrac{y^\\prime}{y} \\approx - \\dfrac{n_a S^\\prime}{n_b S} \\\\ \\\\\n\n\\end{array}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u73b0\u5728\uff0c\u56de\u60f3\u6211\u4eec\u5728\u7403\u9762\u955c\u4e2d\u770b\u5230\u7684\u5185\u5bb9\uff0c\u6211\u4eec\u6709\u7c7b\u4f3c\u7684\u4e1c\u897f\u3002\u5728\u8fd9\u4e00\u70b9\u4e0a\uff0c\u6211\u4eec\u53ef\u4ee5\uff08\u91cd\u65b0\uff09\u5b9a\u4e49\u653e\u5927\u56e0\u5b50<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">m<\/span><\/span>\u4e3a\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\nm=\\displaystyle \\frac{y^\\prime}{y}\n\n<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u56e0\u6b64\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\displaystyle \\color{blue}{m\\approx -\\frac{n_a S^\\prime}{n_b S}}\n\n<\/span><\/span><\/p>\n<p><a name=\"6\"><\/a><\/p>\n<h3>\u603b\u7ed3<\/h3>\n<p style=\"text-align: justify; color: #000000;\">\u603b\u800c\u8a00\u4e4b\uff0c\u5230\u76ee\u524d\u4e3a\u6b62\uff0c\u6211\u4eec\u5df2\u7ecf\u5f97\u51fa\u4e86\u4e24\u4e2a\u7ed3\u679c\uff0c\u8fd9\u4e9b\u7ed3\u679c\u4f7f\u6211\u4eec\u80fd\u591f\u63a8\u65ad\u51fa\u5f53\u5149\u4ece\u7269\u4f53\u53d1\u51fa\u5e76\u901a\u8fc7\u7403\u9762\u754c\u9762\u65f6\uff0c\u56fe\u50cf\u662f\u5982\u4f55\u5f62\u6210\u7684\u3002\u8fd9\u4e9b\u65b9\u7a0b\u5982\u4e0b\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\n\\displaystyle \\dfrac{n_a}{S} + \\dfrac{n_b}{S^\\prime} &amp; \\approx \\dfrac{n_b - n_a}{R} \\\\ \\\\\n\nm &amp; \\displaystyle \\approx - \\dfrac{n_a S^\\prime}{n_b S}\n\n\\end{array}\n\n<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u901a\u8fc7\u8fd9\u4e24\u4e2a\u65b9\u7a0b\uff0c\u4f60\u53ef\u4ee5\u8ba1\u7b97\u56fe\u50cf\u7684\u4f4d\u7f6e\uff0c\u4ee5\u53ca\u56fe\u50cf\u7684\u65b9\u5411\u548c\u5927\u5c0f\uff0c\u8fd9\u65e0\u8bba\u754c\u9762\u662f\u51f9\u9762\u8fd8\u662f\u51f8\u9762\u90fd\u9002\u7528\u3002\u7136\u800c\uff0c\u5728\u8fd9\u4e00\u70b9\u4e0a\uff0c\u6709\u5fc5\u8981\u8bf4\u660e\u7b26\u53f7\u7ea6\u5b9a\u3002<\/p>\n<h4>\u7b26\u53f7\u7ea6\u5b9a<\/h4>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=13kntUA9n-I&amp;t=1682s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u901a\u8fc7\u8fd9\u4e24\u4e2a\u65b9\u7a0b\uff0c\u4f60\u53ef\u4ee5\u8ba1\u7b97<\/span><\/strong><\/a>\u56fe\u50cf\u7684\u4f4d\u7f6e\uff0c\u4ee5\u53ca\u56fe\u50cf\u7684\u65b9\u5411\u548c\u5927\u5c0f\uff0c\u8fd9\u65e0\u8bba\u754c\u9762\u662f\u51f9\u9762\u8fd8\u662f\u51f8\u9762\u90fd\u9002\u7528\u3002\u7136\u800c\uff0c\u5728\u8fd9\u4e00\u70b9\u4e0a\uff0c\u6709\u5fc5\u8981\u8bf4\u660e\u7b26\u53f7\u7ea6\u5b9a\u3002<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u754c\u9762\u5c06\u7a7a\u95f4\u5206\u4e3a\u4e24\u90e8\u5206\uff0c\u4e00\u90e8\u5206\u662f\u7269\u4f53\u6240\u5728\u7684\u4f4d\u7f6e\uff0c\u53e6\u4e00\u90e8\u5206\u662f\u56fe\u50cf\u6240\u5728\u7684\u4f4d\u7f6e\u3002\u57fa\u4e8e\u6b64\uff0c\u6211\u4eec\u6709\uff1a<\/p>\n<ul style=\"text-align: justify; color: #000000;\">\n<li><strong>\u7269\u4f53\u4f4d\u7f6e<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">S<\/span><\/span>:<\/strong>\u5982\u679c\u5728\u7269\u4f53\u4fa7\u4e3a\u6b63\uff0c\u5728\u56fe\u50cf\u4fa7\u4e3a\u8d1f\u3002<\/li>\n<li><strong>\u56fe\u50cf\u4f4d\u7f6e<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">S^\\prime<\/span><\/span>\u548c\u66f2\u7387\u534a\u5f84<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">R<\/span><\/span>:<\/strong>\u5982\u679c\u5728\u56fe\u50cf\u4fa7\u4e3a\u6b63\uff0c\u5728\u7269\u4f53\u4fa7\u4e3a\u8d1f\u3002<\/li>\n<li><strong>\u7269\u4f53\u548c\u56fe\u50cf\u7684\u5927\u5c0f\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y<\/span><\/span>\u548c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y^\\prime<\/span><\/span>:<\/strong>\u5982\u679c\u5728\u5149\u8f74\u4e0a\u65b9\u4e3a\u6b63\uff0c\u5728\u5149\u8f74\u4e0b\u65b9\u4e3a\u8d1f\u3002<\/li>\n<\/ul>\n<p><a name=\"7\"><\/a><\/p>\n<h2>\u7403\u9762\u754c\u9762\u7684\u6781\u9650\u60c5\u51b5\uff1a\u5e73\u9762\u754c\u9762<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=13kntUA9n-I&amp;t=1897s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u6211\u4eec\u4e3a\u7403\u9762\u754c\u9762\u5f00\u53d1\u7684\u6240\u6709\u5185\u5bb9<\/span><\/strong><\/a>\u4e5f\u6709\u52a9\u4e8e\u66f4\u597d\u5730\u7406\u89e3\u5e73\u9762\u754c\u9762\u3002\u5b9e\u9645\u4e0a\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u5e73\u9762\u754c\u9762\u7406\u89e3\u4e3a\u5177\u6709\u975e\u5e38\u5927\u66f2\u7387\u534a\u5f84\u7684\u7403\u9762\u754c\u9762\u7684\u4e00\u90e8\u5206\uff1b\u4e8b\u5b9e\u4e0a\uff0c\u5982\u679c\u6211\u4eec\u5728\u7403\u9762\u754c\u9762\u7684\u7269\u4f53-\u56fe\u50cf\u5173\u7cfb\u4e0a\u53d6\u6781\u9650\uff0c\u5f53\u66f2\u7387\u534a\u5f84\u8d8b\u4e8e\u65e0\u9650\u5927\u65f6\uff0c\u6211\u4eec\u6709\uff1a<\/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 } + \\frac{ n_b}{S^\\prime} = \\lim_{R\\to \\infty} \\frac{n_a}{S } + \\frac{ n_b}{S^\\prime } \\approx \\lim_{R\\to \\infty} \\frac{n_b - n_a}{R} = 0\n\n<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u5982\u679c\u6211\u4eec\u6839\u636e\u8fd9\u4e00\u70b9\u8ba1\u7b97\u653e\u5927\u56e0\u5b50\uff0c\u6211\u4eec\u5f97\u5230\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">m=1\n\n<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u4e5f\u5c31\u662f\u8bf4\uff0c\u56fe\u50cf\u4fdd\u6301\u5176\u5927\u5c0f\u548c\u65b9\u5411\uff0c\u53d8\u5316\u7684\u662f\u5176\u89c2\u5bdf\u5230\u7684\u4f4d\u7f6e\u3002<\/p>\n<p><a name=\"8\"><\/a><\/p>\n<h2>\u7ec3\u4e60<\/h2>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/bwGJYhN3Gv8\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/center><\/p>\n<ol style=\"text-align: justify; color: #000000;\">\n<li>\u5728\u4e00\u6839\u5706\u67f1\u5f62\u73bb\u7483\u68d2\u524d\u9762\u653e\u7f6e\u4e00\u4e2a\u7c92\u5b50\uff0c\u5982\u4e0b\u56fe\u6240\u793a<center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-ayoBx1gP-cM\/YVvMd0Dv6rI\/AAAAAAAAFnE\/TBz3MtCOMvw5SxoNk0XlR70M11UCopfbACLcBGAsYHQ\/s0\/varilla-de-vidrio1.PNG\" width=\"945\" height=\"327\" class=\"alignnone size-full lazyload\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-ayoBx1gP-cM\/YVvMd0Dv6rI\/AAAAAAAAFnE\/TBz3MtCOMvw5SxoNk0XlR70M11UCopfbACLcBGAsYHQ\/s0\/varilla-de-vidrio1.PNG\" width=\"945\" height=\"327\" class=\"alignnone size-full lazyload\" \/><\/noscript><\/center>\u5982\u679c\u7c92\u5b50\u8ddd\u79bb\u73bb\u7483\u68d230[\u5398\u7c73]\uff0c\u4e14\u68d2\u7684\u9876\u7aef\u4e3a\u5927\u7ea6\u534a\u5f84\u4e3a<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">R=1,5[\u5398\u7c73],<\/span><\/span>\u7684\u7403\u9762\uff0c\u8ba1\u7b97\u73bb\u7483\u68d2\u5185\u5f62\u6210\u7684\u56fe\u50cf\u4f4d\u7f6e\u3002<\/li>\n<li>\u8003\u8651\u4e0a\u4e00\u4e2a\u7ec3\u4e60\u4e2d\u7684\u540c\u4e00\u6839\u73bb\u7483\u68d2\uff0c\u4f46\u8fd9\u6b21\u5b83\u5728\u6c34\u4e0b\u3002\u5982\u679c\u5728\u8ddd\u517630[\u5398\u7c73]\u7684\u76f8\u540c\u8ddd\u79bb\u5904\u653e\u7f6e\u4e00\u6839\u9ad8\u5ea6\u4e3a<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1[\u5398\u7c73]<\/span><\/span>\u7684\u9488\uff0c\u8ba1\u7b97\u56fe\u50cf\u7684\u4f4d\u7f6e\u548c\u9ad8\u5ea6\u3002<center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-2Zr1OfLvpAU\/YVvM1MQr1UI\/AAAAAAAAFnM\/9HCljhcB8Ss97L3tLzyXM2E3JzqioJNHgCLcBGAsYHQ\/s0\/varilla-de-vidrio2.PNG\" width=\"948\" height=\"446\" class=\"alignnone size-full lazyload\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-2Zr1OfLvpAU\/YVvM1MQr1UI\/AAAAAAAAFnM\/9HCljhcB8Ss97L3tLzyXM2E3JzqioJNHgCLcBGAsYHQ\/s0\/varilla-de-vidrio2.PNG\" width=\"948\" height=\"446\" class=\"alignnone size-full lazyload\" \/><\/noscript><\/center><\/li>\n<li>\u4e00\u4e2a\u4eba\u770b\u7740\u6cf3\u6c60\u7684\u5e95\u90e8\uff0c\u8bd5\u56fe\u4f30\u7b97\u5176\u6df1\u5ea6\u3002\u4f5c\u4e3a\u53c2\u8003\uff0c\u4ed6\u4f7f\u7528\u4e86\u4e00\u6839\u753b\u5728\u6c60\u5e95\u7684\u7bad\u5934\u3002\u771f\u5b9e\u6df1\u5ea6\u548c\u8868\u89c2\u6df1\u5ea6\u4e4b\u95f4\u6709\u4ec0\u4e48\u5173\u7cfb\uff1f<center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-G8Lr7rWgyCw\/YVvNQqC6rLI\/AAAAAAAAFnU\/mF2xOr5TPPgG62N8FZqQYijhYQg8_co0ACLcBGAsYHQ\/s0\/profundidad-real-y-aparente.PNG\" width=\"957\" height=\"658\" class=\"alignnone size-full lazyload\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-G8Lr7rWgyCw\/YVvNQqC6rLI\/AAAAAAAAFnU\/mF2xOr5TPPgG62N8FZqQYijhYQg8_co0ACLcBGAsYHQ\/s0\/profundidad-real-y-aparente.PNG\" width=\"957\" height=\"658\" class=\"alignnone size-full lazyload\" \/><\/noscript><\/center><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u7403\u9762\u754c\u9762\u7684\u6298\u5c04 \u6458\u8981\uff1a 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