{"id":27689,"date":"2021-09-18T13:00:42","date_gmt":"2021-09-18T13:00:42","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=27689"},"modified":"2024-08-10T23:51:30","modified_gmt":"2024-08-10T23:51:30","slug":"%e5%85%89%e7%9a%84%e6%8a%98%e5%b0%84%e5%92%8c%e6%96%af%e6%b6%85%e5%b0%94%e5%ae%9a%e5%be%8b","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/zh\/%e5%85%89%e7%9a%84%e6%8a%98%e5%b0%84%e5%92%8c%e6%96%af%e6%b6%85%e5%b0%94%e5%ae%9a%e5%be%8b\/","title":{"rendered":"\u5149\u7684\u6298\u5c04\u548c\u65af\u6d85\u5c14\u5b9a\u5f8b"},"content":{"rendered":"<p><center><\/p>\n<h1>\u5149\u7684\u6298\u5c04\u548c\u65af\u6d85\u5c14\u5b9a\u5f8b<\/h1>\n<p><em><strong>\u6458\u8981\uff1a<\/strong><br \/>\n\u5728\u672c\u8bfe\u4e2d\uff0c\u6211\u4eec\u5c06\u901a\u8fc7\u5206\u6790\u65af\u6d85\u5c14\u5b9a\u5f8b\u6765\u63a2\u8ba8\u5149\u7684\u6298\u5c04\u3002\u5c06\u89e3\u91ca\u6298\u5c04\u7387\u7684\u6982\u5ff5\uff0c\u4f7f\u7528\u8d39\u9a6c\u539f\u7406\u63a8\u5bfc\u65af\u6d85\u5c14\u5b9a\u5f8b\uff0c\u5e76\u7814\u7a76\u8be5\u5b9a\u5f8b\u5982\u4f55\u5e2e\u52a9\u6211\u4eec\u8ba1\u7b97\u5149\u7ebf\u5728\u4e0d\u540c\u4ecb\u8d28\u4e2d\u7a7f\u8fc7\u7684\u8def\u5f84\u3002\u6b64\u5916\uff0c\u8fd8\u5c06\u8ba8\u8bba\u53cd\u5c04\u548c\u5168\u53cd\u5c04\u73b0\u8c61\uff0c\u5e76\u5c06\u8fd9\u4e9b\u6982\u5ff5\u5e94\u7528\u4e8e\u4e00\u7cfb\u5217\u5b9e\u9645\u7ec3\u4e60\u4e2d\u3002\u76ee\u6807\u662f\u7406\u89e3\u5e76\u5e94\u7528\u65af\u6d85\u5c14\u5b9a\u5f8b\u89e3\u51b3\u5149\u5b66\u95ee\u9898\u3002<\/em><\/p>\n<p><strong>\u5b66\u4e60\u76ee\u6807<\/strong><\/p>\n<ol style=\"text-align:left\">\n<li><strong>\u7406\u89e3<\/strong>\u6298\u5c04\u7387\u7684\u6982\u5ff5\u53ca\u5176\u4e0e\u5149\u5728\u4e0d\u540c\u4ecb\u8d28\u4e2d\u7684\u901f\u5ea6\u7684\u5173\u7cfb\u3002<\/li>\n<li><strong>\u5e94\u7528<\/strong>\u8d39\u9a6c\u539f\u7406\u7406\u89e3\u5149\u5982\u4f55\u9075\u5faa\u5728\u4e24\u70b9\u4e4b\u95f4\u884c\u8fdb\u65f6\u95f4\u6700\u77ed\u7684\u8def\u5f84\u3002<\/li>\n<li><strong>\u8bc1\u660e<\/strong>\u4ece\u8d39\u9a6c\u539f\u7406\u63a8\u5bfc\u51fa\u65af\u6d85\u5c14\u5b9a\u5f8b\uff0c\u4ee5\u786e\u5b9a\u5149\u7ebf\u5728\u901a\u8fc7\u4e0d\u540c\u4ecb\u8d28\u65f6\u7684\u8def\u5f84\u3002<\/li>\n<li><strong>\u8ba1\u7b97<\/strong>\u5728\u4e0d\u540c\u6298\u5c04\u7387\u7684\u60c5\u51b5\u4e0b\u4f7f\u7528\u65af\u6d85\u5c14\u5b9a\u5f8b\u8ba1\u7b97\u5165\u5c04\u89d2\u548c\u6298\u5c04\u89d2\u3002<\/li>\n<li><strong>\u7406\u89e3<\/strong>\u5168\u5185\u53cd\u5c04\u7684\u6982\u5ff5\u53ca\u5176\u4e0e\u4e34\u754c\u89d2\u548c\u6298\u5c04\u7387\u7684\u5173\u7cfb\u3002<\/li>\n<li><strong>\u786e\u5b9a<\/strong>\u5728\u4e24\u4e2a\u4ecb\u8d28\u4e4b\u95f4\u7684\u754c\u9762\u5904\u7684\u5168\u5185\u53cd\u5c04\u7684\u4e34\u754c\u89d2\u3002<\/li>\n<\/ol>\n<p><strong>\u5185\u5bb9\u7d22\u5f15<\/strong><br \/>\n<a href=\"#1\"><strong>\u6298\u5c04\u7387<\/strong><\/a><br \/>\n<a href=\"#2\">\u8d39\u9a6c\u539f\u7406<\/a><br \/>\n<a href=\"#3\">\u5149\u6298\u5c04\u7684\u65af\u6d85\u5c14\u5b9a\u5f8b<\/a><br \/>\n<a href=\"#4\"><strong>\u5149\u7684\u6298\u5c04\u3001\u53cd\u5c04\u548c\u5168\u53cd\u5c04<\/strong><\/a><br \/>\n<a href=\"#5\"><strong>\u7ec3\u4e60<\/strong><\/a><\/p>\n<p><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/LxhWbErujpo\" title=\"YouTube \u89c6\u9891\u64ad\u653e\u5668\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>\u6298\u5c04\u7387<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=LxhWbErujpo&amp;t=186s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u6298\u5c04\u7387\u5b9a\u4e49\u4e3a<\/span><\/strong><\/a> \u4ecb\u8d28\u4e2d\u5149\u901f\u4e0e\u771f\u7a7a\u4e2d\u5149\u901f\u4e4b\u6bd4\u3002\u5b83\u662f\u4e00\u4e2a\u65e0\u91cf\u7eb2\u91cf\uff0c\u901a\u5e38\u7528\u5b57\u6bcd <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_k:<\/span><\/span> \u8868\u793a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_k=\\displaystyle \\frac{c}{c_k}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u5176\u4e2d <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">c<\/span><\/span> \u4e3a\u771f\u7a7a\u4e2d\u7684\u5149\u901f\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">c_k<\/span><\/span> \u4e3a\u4ecb\u8d28 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k<\/span><\/span> \u4e2d\u7684\u5149\u901f\u3002<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u7531\u4e8e\u5149\u5728\u4efb\u4f55\u4ecb\u8d28\u4e2d\u7684\u4f20\u64ad\u901f\u5ea6\u90fd\u6bd4\u5728\u771f\u7a7a\u4e2d\u6162\uff0c\u56e0\u6b64\u6298\u5c04\u7387\u603b\u662f\u5927\u4e8e\u6216\u7b49\u4e8e1\u3002<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h3>\u8d39\u9a6c\u539f\u7406<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=LxhWbErujpo&amp;t=397s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u5149\u901f\u53d6\u51b3\u4e8e<\/span><\/strong><\/a> \u5b83\u6240\u4f20\u64ad\u7684\u4ecb\u8d28\u3002\u4ecb\u8d28\u7684\u6298\u5c04\u7387\u8d8a\u9ad8\uff0c\u5149\u5728\u5176\u4e2d\u7684\u4f20\u64ad\u901f\u5ea6\u8d8a\u6162\uff1b\u4e0e\u6b64\u76f8\u5173\uff0c\u8d39\u9a6c\u539f\u7406\u5982\u4e0b\u8868\u8ff0\uff1a<\/p>\n<p style=\"text-align: center; color: #000000; background-color: #80ff80;\">\u5149\u4ece\u4e00\u4e2a\u70b9\u4f20\u64ad\u5230\u53e6\u4e00\u4e2a\u70b9\u65f6\uff0c\u9009\u62e9\u4e86\u4f7f\u4f20\u64ad\u65f6\u95f4\u6700\u77ed\u7684\u8def\u5f84\u3002<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u5373\u4f7f\u5149\u7a7f\u8fc7\u4e0d\u540c\u4ecb\u8d28\uff0c\u8fd9\u4e00\u539f\u7406\u4ecd\u7136\u9002\u7528\u3002<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h3>\u5149\u6298\u5c04\u7684\u65af\u6d85\u5c14\u5b9a\u5f8b<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=LxhWbErujpo&amp;t=608s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u57fa\u4e8e\u8d39\u9a6c\u539f\u7406<\/span><\/strong><\/a> \u53ef\u4ee5\u5f62\u6210\u4e00\u4e2a\u4f18\u5316\u95ee\u9898\uff0c\u7528\u4e8e\u786e\u5b9a\u5149\u7ebf\u5728\u4e0d\u540c\u4ecb\u8d28\u4e2d\u4f20\u64ad\u65f6\u7684\u8def\u5f84\u3002\u6700\u7ec8\uff0c\u8fd9\u5f15\u51fa\u4e86\u65af\u6d85\u5c14\u5b9a\u5f8b\uff0c\u6211\u4eec\u5c06\u5728\u4e0b\u6587\u4e2d\u770b\u5230\u5176\u8868\u8ff0\u548c\u8bc1\u660e\u3002<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u5047\u8bbe\u5149\u7ebf\u4ece\u70b9 A \u51fa\u53d1\uff0c\u5230\u8fbe\u70b9 B\uff0c\u7a7f\u8fc7\u4e00\u4e2a\u5c06\u4e24\u4e2a\u6298\u5c04\u7387\u5206\u522b\u4e3a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_1<\/span><\/span> \u548c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_2<\/span><\/span> \u7684\u4ecb\u8d28\u5206\u5f00\u7684\u754c\u9762\u3002\u6211\u4eec\u7684\u76ee\u6807\u662f\u627e\u5230\u4e00\u4e2a\u5173\u7cfb\u5f0f\uff0c\u4f7f\u6211\u4eec\u80fd\u591f\u6839\u636e\u8d39\u9a6c\u6700\u5c0f\u4f20\u64ad\u65f6\u95f4\u539f\u7406\u8ba1\u7b97\u5149\u7ebf\u7684\u8def\u5f84\uff0c\u4e3a\u6b64\uff0c\u6211\u4eec\u6784\u5efa\u4e86\u4ee5\u4e0b\u56fe\u793a\uff1a<\/p>\n<p><center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-1CdoEOp5SHc\/YUDNPnQyOxI\/AAAAAAAAFjE\/RG-kYgV4KKwAE3QwiM9nB3cA-OOXesONQCLcBGAsYHQ\/s0\/n1n2leydeSnell.PNG\" width=\"875\" height=\"518\" alt=\"\u65af\u6d85\u5c14\u5b9a\u5f8b\" class=\"alignnone size-full lazyload\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-1CdoEOp5SHc\/YUDNPnQyOxI\/AAAAAAAAFjE\/RG-kYgV4KKwAE3QwiM9nB3cA-OOXesONQCLcBGAsYHQ\/s0\/n1n2leydeSnell.PNG\" width=\"875\" height=\"518\" alt=\"\u65af\u6d85\u5c14\u5b9a\u5f8b\" class=\"alignnone size-full lazyload\" \/><\/noscript><\/center><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u63a8\u7406\u4ece\u5206\u6790\u5149\u7ebf\u7684\u4f20\u64ad\u65f6\u95f4\u5f62\u5f0f\u5f00\u59cb\u3002\u6211\u4eec\u6709\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}{\u4f20\u64ad\u65f6\u95f4} &amp; =\\displaystyle \\frac{{\u8ddd\u79bb}}{{\u901f\u5ea6}} \\\\ \\\\ &amp; \\displaystyle =\\frac{{\u4ecb\u8d281\u4e2d\u7684\u8ddd\u79bb}}{{\u4ecb\u8d281\u4e2d\u7684\u901f\u5ea6}} + \\frac{{\u4ecb\u8d282\u4e2d\u7684\u8ddd\u79bb}}{{\u4ecb\u8d282\u4e2d\u7684\u901f\u5ea6}}\\\\ \\\\&amp; =\\displaystyle \\frac{\\sqrt{a^2 + x^2}}{c_1} + \\frac{\\sqrt{b^2 + (d-x)^2}}{c_2}\\end{array}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u8fd9\u6837\u505a\u4e4b\u540e\uff0c\u4fdd\u6301\u70b9 A \u548c B \u56fa\u5b9a\uff0c\u4f20\u64ad\u65f6\u95f4\u7531\u5149\u7ebf\u63a5\u89e6\u4ecb\u8d28\u4e4b\u95f4\u754c\u9762\u7684\u70b9 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x<\/span><\/span> \u786e\u5b9a\u3002\u7531\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u5b9a\u4e49\u65f6\u95f4\u51fd\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">t(x)<\/span><\/span> \u4e3a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">t(x) = \\displaystyle \\frac{1}{c_1}\\sqrt{a^2 + x^2} + \\frac{1}{c_2}\\sqrt{b^2 + (d-x)^2}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u73b0\u5728\uff0c\u65e2\u7136\u8d39\u9a6c\u539f\u7406\u89c4\u5b9a\u5149\u7ebf\u9075\u5faa\u4f7f\u4f20\u64ad\u65f6\u95f4\u6700\u77ed\u7684\u8def\u5f84\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u4ece\u4e2d\u627e\u5230\u4f7f\u51fd\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">t(x)<\/span><\/span> \u6700\u5c0f\u5316\u7684 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x.<\/span><\/span> \u8fd9\u5b9e\u9645\u4e0a\u662f\u4e00\u4e2a\u4f18\u5316\u95ee\u9898\u3002<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u5bf9 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">t<\/span><\/span> \u5173\u4e8e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x<\/span><\/span> \u6c42\u5bfc\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\">\\displaystyle \\begin{array}{rl}\\dfrac{dt}{dx} &amp;\\displaystyle = \\frac{1}{c_1}\\frac{d}{dx}\\sqrt{a^2 + x^2} + \\frac{1}{c_2}\\frac{d}{dx}\\sqrt{b^2+(d-x)^2}\\\\ \\\\ &amp;\\displaystyle = \\frac{1}{c_1} \\frac{2x}{2\\sqrt{a^2 + x^2}} + \\frac{1}{c_2}\\frac{2(d-x)(-1)}{2\\sqrt{b^2+(d-x)^2}} \\\\ \\\\ &amp;\\displaystyle = \\frac{1}{c_1} \\frac{x}{\\sqrt{a^2 + x^2}} - \\frac{1}{c_2}\\frac{(d-x)}{\\sqrt{b^2+(d-x)^2}} \\end{array}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u73b0\u5728\u6ce8\u610f\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\\sin(\\theta_1) &amp;\\displaystyle =\\frac{x}{\\sqrt{a^2 + x^2}}\\\\ \\\\ \\sin(\\theta_2) &amp;\\displaystyle = \\frac{(d-x)}{\\sqrt{b^2+(d-x)^2}} \\\\ \\\\ c_1 &amp; \\displaystyle = \\frac{c}{n_1} \\\\ \\\\ c_2 &amp; \\displaystyle = \\frac{c}{n_2} \\end{array} <\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u56e0\u6b64\uff0c\u5c06\u8fd9\u4e9b\u66ff\u6362\u5230\u65f6\u95f4\u5bfc\u6570\u4e2d\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{dt}{dx} = \\frac{n_1}{c} \\sin(\\theta_1) - \\frac{n_2}{c}\\sin(\\theta_2)<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u6700\u540e\uff0c\u5982\u679c\u70b9 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x<\/span><\/span> \u4f7f\u51fd\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">t(x)<\/span><\/span> \u6700\u5c0f\u5316\uff0c\u90a3\u4e48\u5bfc\u6570\u5fc5\u987b\u4e3a\u96f6\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\">\\color{blue}{n_1 \\sin(\\theta_1) = n_2 \\sin(\\theta_2)}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u8fd9\u5c31\u662f\u5149\u7ebf\u5728\u7a7f\u8fc7\u4e24\u79cd\u4ecb\u8d28\u65f6\u7684\u65af\u6d85\u5c14\u6298\u5c04\u5b9a\u5f8b\uff0c\u663e\u793a\u4e86\u5165\u5c04\u89d2 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\theta_1<\/span><\/span> \u4e0e\u6298\u5c04\u89d2 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\theta_2<\/span><\/span> \u4e4b\u95f4\u7684\u5173\u7cfb\u3002<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>\u5149\u7684\u6298\u5c04\u3001\u53cd\u5c04\u548c\u5168\u53cd\u5c04<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=LxhWbErujpo&amp;t=1614s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u6211\u4eec\u5df2\u7ecf\u770b\u5230\uff0c\u5f53\u5149\u7ebf<\/span> <\/strong><\/a>\u4ece\u4e00\u79cd\u4ecb\u8d28\u8fdb\u5165\u53e6\u4e00\u79cd\u4ecb\u8d28\u65f6\uff0c\u4f1a\u53d1\u751f\u6298\u5c04\uff0c\u4f46\u901a\u5e38\u4f1a\u53d1\u751f\u6298\u5c04\u548c\u53cd\u5c04\u7684\u7ec4\u5408\uff1b\u800c\u4e14\u6839\u636e\u6298\u5c04\u7387\u548c\u5149\u7ebf\u7684\u5165\u5c04\u89d2\uff0c\u6298\u5c04\u53ef\u80fd\u6d88\u5931\uff0c\u53ea\u5269\u4e0b\u53cd\u5c04\u3002<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u5047\u8bbe\u4e00\u675f\u5149\u7ebf\u4ece\u6298\u5c04\u7387\u4e3a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_a<\/span><\/span> \u7684\u6750\u6599 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a<\/span><\/span> \u5165\u5c04\u5230\u6298\u5c04\u7387\u4e3a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_b<\/span><\/span> \u7684\u6750\u6599 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b<\/span><\/span> \u4e2d\u3002\u5982\u679c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_a \\gt n_b,<\/span><\/span> \u6839\u636e\u65af\u6d85\u5c14\u5b9a\u5f8b\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 \\sin(\\theta_b) = \\frac{n_a}{n_b}\\sin(\\theta_a)<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u7531\u4e8e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_a\/n_b \\gt 1,<\/span><\/span> \u7ed3\u679c\u662f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\sin(\\theta_b) \\gt \\sin(\\theta_a),<\/span><\/span> \u8fd9\u610f\u5473\u7740\u6298\u5c04\u5149\u7ebf\u8fdc\u79bb\u6cd5\u7ebf\u65b9\u5411\u504f\u8f6c\u3002\u8fd9\u610f\u5473\u7740\u5fc5\u7136\u5b58\u5728\u67d0\u4e2a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\theta_a\\lt 90^o<\/span><\/span>\uff0c\u4f7f\u5f97 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\sin(\\theta_b)=1<\/span><\/span>\uff0c\u56e0\u6b64\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\theta_b=90^o,<\/span><\/span> \u5982\u4e0b\u56fe\u6240\u793a\u3002<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u4f7f\u5149\u7ebf\u6cbf\u754c\u9762\u6298\u5c04\u7684\u5165\u5c04\u89d2\u79f0\u4e3a\u4e34\u754c\u89d2\uff0c\u5e76\u6ee1\u8db3\u4ee5\u4e0b\u5173\u7cfb\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\sin(\\theta_{\u4e34\u754c}) = \\frac{n_b}{n_a}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u8fd9\u76f8\u5f53\u4e8e\u8bf4\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\theta_{\u4e34\u754c} = \\arcsin\\left( \\frac{n_b}{n_a} \\right)<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u5982\u679c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\theta_a \\gt \\theta_{\u4e34\u754c},<\/span><\/span> \u90a3\u4e48\u5c31\u4f1a\u53d1\u751f\u5168\u53cd\u5c04\u3002<\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h2>\u7ec3\u4e60\uff1a<\/h2>\n<ol style=\"text-align: justify; color: #000000;\">\n<li>\u8003\u8651\u4e00\u675f\u5149\u7ebf\u4ece\u6c34\u4e2d\u7a7f\u8fc7\u73bb\u7483\uff0c\u5982\u4e0b\u56fe\u6240\u793a\uff1a<br \/>\n<center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-98FbTK-_FZo\/YT-61nYxRnI\/AAAAAAAAFiM\/JbBsuAnS6IA8aB-4hvroeZ1qDF2ebxQUwCLcBGAsYHQ\/s0\/n1n2snell.PNG\" width=\"442\" height=\"321\" alt=\"\u5149\u7ebf\u4ece\u6c34\u4e2d\u7a7f\u8fc7\u73bb\u7483\" class=\"alignnone size-full lazyload\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-98FbTK-_FZo\/YT-61nYxRnI\/AAAAAAAAFiM\/JbBsuAnS6IA8aB-4hvroeZ1qDF2ebxQUwCLcBGAsYHQ\/s0\/n1n2snell.PNG\" width=\"442\" height=\"321\" alt=\"\u5149\u7ebf\u4ece\u6c34\u4e2d\u7a7f\u8fc7\u73bb\u7483\" class=\"alignnone size-full lazyload\" \/><\/noscript><\/center><br \/>\n\u6c34\u7684\u6298\u5c04\u7387\u4e3a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_1 = 1.33,<\/span><\/span> \u800c\u73bb\u7483\u7684\u6298\u5c04\u7387\u4e3a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_2=1.52.<\/span><\/span> \u5982\u679c\u4e00\u675f\u5149\u7ebf\u4ece\u6c34\u4e2d\u7a7f\u8fc7\u73bb\u7483\uff0c\u4ee5\u76f8\u5bf9\u4e8e\u6cd5\u7ebf <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\theta_1 = 60^o<\/span><\/span> \u7684\u503e\u659c\u89d2\u5ea6\u5165\u5c04\u5230\u5206\u9694\u4e24\u79cd\u4ecb\u8d28\u7684\u754c\u9762\uff0c\u6298\u5c04\u5149\u7ebf\u4ee5 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\theta_2<\/span><\/span> \u4ec0\u4e48\u89d2\u5ea6\u5c04\u51fa\uff1f <span class=\"collapseomatic \" id=\"id69e026a64b679\"  tabindex=\"0\" title=\"\u89e3\u7b54\"    >\u89e3\u7b54<\/span><div id=\"target-id69e026a64b679\" class=\"collapseomatic_content \">\n\u4f7f\u7528\u65af\u6d85\u5c14\u5b9a\u5f8b\uff0c\u6211\u4eec\u6709\uff1a<\/p>\n<table>\n<tbody>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(1)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_1 \\sin(\\theta_1) = n_2 \\sin(\\theta_2)<\/span><\/span><\/td>\n<td>; \u65af\u6d85\u5c14\u5b9a\u5f8b<\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\equiv <\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\sin(\\theta_2) = \\frac{n_1}{n_2}\\sin(\\theta_1)<\/span><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\equiv <\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\theta_2 = \\arcsin\\left(\\frac{n_1}{n_2}\\sin(\\theta_1)\\right)<\/span><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(2)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_1=1.33<\/span><\/span><\/td>\n<td>; \u6c34\u7684\u6298\u5c04\u7387<\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(3)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_2=1.52<\/span><\/span><\/td>\n<td>; \u73bb\u7483\u7684\u6298\u5c04\u7387<\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(4)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\theta_1=60^o<\/span><\/span><\/td>\n<td>; \u5149\u7ebf\u5728\u754c\u9762\u4e0a\u7684\u5165\u5c04\u89d2<\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(5)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\theta_2 = \\arcsin\\left(\\frac{1.33}{1.52}\\sin(60^o)\\right) \\approx 49.268^o<\/span><\/span><\/td>\n<td>; \u4ece (1,2,3,4) \u5f97\u51fa\uff0c\u6298\u5c04\u89d2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div><a href=\"https:\/\/www.youtube.com\/watch?v=LxhWbErujpo&amp;t=1363s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u89c6\u9891]<\/span><\/strong><\/a><\/li>\n<li>\u4e09\u4e2a\u7531\u4e24\u4e2a\u754c\u9762\u5206\u9694\u7684\u6db2\u4f53\u5177\u6709\u4ee5\u4e0b\u6298\u5c04\u7387\uff1a<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_1=1.33,<\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_2=1.41<\/span><\/span> \u548c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_3=1.68,<\/span><\/span> \u5e76\u6309\u5982\u4e0b\u56fe\u6240\u793a\u6392\u5217\uff1a<center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-AAZlxjqC4s4\/YUAdiGNMSQI\/AAAAAAAAFiU\/mOE-xMfybOoxenNH2O8sufjpTuzH6-WIwCLcBGAsYHQ\/s0\/n1n2n3snell.PNG\" width=\"443\" height=\"430\" alt=\"\u65af\u6d85\u5c14\u5b9a\u5f8b\u5e94\u7528\u4e8e\u4e09\u79cd\u4ecb\u8d28\" class=\"alignnone size-full lazyload\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-AAZlxjqC4s4\/YUAdiGNMSQI\/AAAAAAAAFiU\/mOE-xMfybOoxenNH2O8sufjpTuzH6-WIwCLcBGAsYHQ\/s0\/n1n2n3snell.PNG\" width=\"443\" height=\"430\" alt=\"\u65af\u6d85\u5c14\u5b9a\u5f8b\u5e94\u7528\u4e8e\u4e09\u79cd\u4ecb\u8d28\" class=\"alignnone size-full lazyload\" \/><\/noscript><\/center>\u5982\u679c\u5149\u7ebf\u4ece\u6298\u5c04\u7387\u4e3a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_1<\/span><\/span> \u7684\u4ecb\u8d28\u8fdb\u5165\u6298\u5c04\u7387\u4e3a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_2<\/span><\/span> \u7684\u4ecb\u8d28\uff0c\u4ee5 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\theta_1=70^o<\/span><\/span> \u7684\u89d2\u5ea6\u5165\u5c04\u5230\u754c\u9762\uff0c\u6298\u5c04\u89d2\u8fdb\u5165\u6298\u5c04\u7387\u4e3a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_3<\/span><\/span> \u7684\u4ecb\u8d28\u65f6\u4f1a\u662f\u591a\u5c11\uff1f <span class=\"collapseomatic \" id=\"id69e026a64b882\"  tabindex=\"0\" title=\"\u89e3\u7b54\"    >\u89e3\u7b54<\/span><div id=\"target-id69e026a64b882\" class=\"collapseomatic_content \">\n\u7c7b\u4f3c\u4e8e\u524d\u9762\u7684\u7ec3\u4e60\uff0c\u63a8\u7406\u5982\u4e0b\uff1a<\/p>\n<table>\n<tbody>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(1)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_1 \\sin(\\theta_1) = n_2 \\sin(\\theta_2) <\/span><\/span><\/td>\n<td>; \u65af\u6d85\u5c14\u5b9a\u5f8b\u9002\u7528\u4e8e\u4ece n1 \u5230 n2 \u7684\u8fc7\u6e21<\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(2)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_2 \\sin(\\theta_2) = n_3 \\sin(\\theta_3) <\/span><\/span><\/td>\n<td>; \u65af\u6d85\u5c14\u5b9a\u5f8b\u9002\u7528\u4e8e\u4ece n2 \u5230 n3 \u7684\u8fc7\u6e21<\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(3)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n_1 \\sin(\\theta_1) = n_3 \\sin(\\theta_3) <\/span><\/span><\/td>\n<td>; \u4ece (1,2) \u5f97\u51fa<\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\equiv<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\sin(\\theta_3) = \\frac{n_1}{n_3}\\sin(\\theta_1) <\/span><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\equiv<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\theta_3 = \\arcsin\\left(\\frac{n_1}{n_3}\\sin(\\theta_1)\\right) <\/span><\/span><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u6700\u540e\uff0c\u66ff\u6362\u6570\u636e\u5f97\u51fa\uff1a<\/p>\n<p><center><br \/>\n<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\theta_3= \\arcsin\\left(\\frac{1.33}{1.68}\\sin(70^o)\\right) \\approx 48.0667^o <\/span><\/span><\/center><br \/>\n\u8bf7\u6ce8\u610f\uff0c\u8fd9\u79cd\u63a8\u7406\u8868\u660e\u6211\u4eec\u53ef\u4ee5\u53ea\u8003\u8651\u5149\u7ebf\u7684\u5165\u5c04\u548c\u51fa\u5c04\u4ecb\u8d28\u8fdb\u884c\u8ba1\u7b97\uff0c\u800c\u5b8c\u5168\u5ffd\u7565\u4e2d\u95f4\u4ecb\u8d28\u3002<br \/>\n<\/div> <a href=\"https:\/\/www.youtube.com\/watch?v=LxhWbErujpo&amp;t=1417s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u89c6\u9891]<\/span><\/strong><\/a><\/li>\n<li>\u4ece\u6e38\u6cf3\u6c60\u5e95\u90e8\u53d1\u5c04\u4e00\u675f\u5149\u7ebf\u671d\u5411\u7a7a\u6c14\u548c\u6c34\u7684\u754c\u9762\u3002\u786e\u5b9a\u5168\u53cd\u5c04\u53d1\u751f\u7684\u5165\u5c04\u89d2\u3002<center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-GiDk_G3uybI\/YUDhONr0MaI\/AAAAAAAAFjM\/aSGUOspZeCsm7Cz7DG4r-JrCr03QhYyBgCLcBGAsYHQ\/s0\/%25C3%25A1ngulocr%25C3%25ADtico.PNG\" width=\"588\" height=\"358\" alt=\"\u5149\u7ebf\u4ee5\u4e34\u754c\u89d2\u5165\u5c04\" class=\"alignnone size-full lazyload\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-GiDk_G3uybI\/YUDhONr0MaI\/AAAAAAAAFjM\/aSGUOspZeCsm7Cz7DG4r-JrCr03QhYyBgCLcBGAsYHQ\/s0\/%25C3%25A1ngulocr%25C3%25ADtico.PNG\" width=\"588\" height=\"358\" alt=\"\u5149\u7ebf\u4ee5\u4e34\u754c\u89d2\u5165\u5c04\" class=\"alignnone size-full lazyload\" \/><\/noscript><\/center><br \/>\n<span class=\"collapseomatic \" id=\"id69e026a64b96c\"  tabindex=\"0\" title=\"\u89e3\u7b54\"    >\u89e3\u7b54<\/span><div id=\"target-id69e026a64b96c\" class=\"collapseomatic_content \">\n\u4e34\u754c\u89d2\u7531\u4e0b\u5f0f\u7ed9\u51fa\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\theta_{\u4e34\u754c}= \\arcsin\\left(\\frac{1.00}{1.33}\\right) \\approx 48.7535^o<\/span><\/span><\/p>\n<\/div><a href=\"https:\/\/www.youtube.com\/watch?v=LxhWbErujpo&amp;t=1869s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u89c6\u9891]<\/span><\/strong><\/a><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u5149\u7684\u6298\u5c04\u548c\u65af\u6d85\u5c14\u5b9a\u5f8b \u6458\u8981\uff1a 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