{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":44070,"title":"Under the sea: Snell's law \u0026 total internal reflection","description":"\u003chttps://en.wikipedia.org/wiki/Snell's_law\u003e\r\n\r\nWhen a light travels from one medium to another medium, depending on the refractive index, the light will bend with a certain angle. For certain combination of materials, it might be that light cannot escape one medium at all from a certain angle (greater than critical angle). It is called total internal reflection. If you point a flashlight from \"under the sea\" the light won't leave the water at all. \r\n\r\nFor given refractive indices, find critical angle where total internal reflection happens. If total internal reflection does not happen for any angle, then return \"-1\".\r\n\r\nExample1: n_in = 1.333, n_out = 1, theta_crit = 48.6 degrees;\r\nExample2: n_out = 1, n_in = 1.333, theta_crit = -1 (total internal reflection does not occur, if you are in the air, and beaming light at the water.)\r\n\r\nInput of function: n_in, n_out (refractive index, positive) \r\nOutput: critical angle (rounded to nearest integer), if total internal reflection occurs. Else return -1.","description_html":"\u003cp\u003e\u003ca href = \"https://en.wikipedia.org/wiki/Snell's_law\"\u003ehttps://en.wikipedia.org/wiki/Snell's_law\u003c/a\u003e\u003c/p\u003e\u003cp\u003eWhen a light travels from one medium to another medium, depending on the refractive index, the light will bend with a certain angle. For certain combination of materials, it might be that light cannot escape one medium at all from a certain angle (greater than critical angle). It is called total internal reflection. If you point a flashlight from \"under the sea\" the light won't leave the water at all.\u003c/p\u003e\u003cp\u003eFor given refractive indices, find critical angle where total internal reflection happens. If total internal reflection does not happen for any angle, then return \"-1\".\u003c/p\u003e\u003cp\u003eExample1: n_in = 1.333, n_out = 1, theta_crit = 48.6 degrees;\r\nExample2: n_out = 1, n_in = 1.333, theta_crit = -1 (total internal reflection does not occur, if you are in the air, and beaming light at the water.)\u003c/p\u003e\u003cp\u003eInput of function: n_in, n_out (refractive index, positive) \r\nOutput: critical angle (rounded to nearest integer), if total internal reflection occurs. Else return -1.\u003c/p\u003e","function_template":"function theta_crit = totalInternalReflection(n_in,n_out)\r\n  theta_crit = -1;\r\nend","test_suite":"%%\r\nn_in = 3; n_out = 3;\r\ntheta_crit_correct = -1;\r\nassert(isequal(totalInternalReflection(n_in,n_out),theta_crit_correct))\r\n\r\n%%\r\nn_in = 1; n_out = 1.333;\r\ntheta_crit_correct = -1;\r\nassert(isequal(totalInternalReflection(n_in,n_out),theta_crit_correct))\r\n\r\n%%\r\nn_in = 1.333; n_out = 1;\r\ntheta_crit_correct = 49;\r\nassert(isequal(totalInternalReflection(n_in,n_out),theta_crit_correct))\r\n\r\n%%\r\nn_in = 4; n_out = 3;\r\ntheta_crit_correct = 49;\r\nassert(isequal(totalInternalReflection(n_in,n_out),theta_crit_correct))\r\n\r\n%%\r\nn_in = 4; n_out = 2;\r\ntheta_crit_correct = 30;\r\nassert(isequal(totalInternalReflection(n_in,n_out),theta_crit_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":6,"created_by":115733,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":58,"test_suite_updated_at":"2017-02-16T21:45:07.000Z","rescore_all_solutions":false,"group_id":37,"created_at":"2017-02-14T00:59:14.000Z","updated_at":"2026-02-08T13:00:17.000Z","published_at":"2017-02-14T00:59:14.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Snell's_law\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://en.wikipedia.org/wiki/Snell's_law\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhen a light travels from one medium to another medium, depending on the refractive index, the light will bend with a certain angle. For certain combination of materials, it might be that light cannot escape one medium at all from a certain angle (greater than critical angle). It is called total internal reflection. If you point a flashlight from \\\"under the sea\\\" the light won't leave the water at all.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor given refractive indices, find critical angle where total internal reflection happens. If total internal reflection does not happen for any angle, then return \\\"-1\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample1: n_in = 1.333, n_out = 1, theta_crit = 48.6 degrees; Example2: n_out = 1, n_in = 1.333, theta_crit = -1 (total internal reflection does not occur, if you are in the air, and beaming light at the water.)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInput of function: n_in, n_out (refractive index, positive) Output: critical angle (rounded to nearest integer), if total internal reflection occurs. Else return -1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":44070,"title":"Under the sea: Snell's law \u0026 total internal reflection","description":"\u003chttps://en.wikipedia.org/wiki/Snell's_law\u003e\r\n\r\nWhen a light travels from one medium to another medium, depending on the refractive index, the light will bend with a certain angle. For certain combination of materials, it might be that light cannot escape one medium at all from a certain angle (greater than critical angle). It is called total internal reflection. If you point a flashlight from \"under the sea\" the light won't leave the water at all. \r\n\r\nFor given refractive indices, find critical angle where total internal reflection happens. If total internal reflection does not happen for any angle, then return \"-1\".\r\n\r\nExample1: n_in = 1.333, n_out = 1, theta_crit = 48.6 degrees;\r\nExample2: n_out = 1, n_in = 1.333, theta_crit = -1 (total internal reflection does not occur, if you are in the air, and beaming light at the water.)\r\n\r\nInput of function: n_in, n_out (refractive index, positive) \r\nOutput: critical angle (rounded to nearest integer), if total internal reflection occurs. Else return -1.","description_html":"\u003cp\u003e\u003ca href = \"https://en.wikipedia.org/wiki/Snell's_law\"\u003ehttps://en.wikipedia.org/wiki/Snell's_law\u003c/a\u003e\u003c/p\u003e\u003cp\u003eWhen a light travels from one medium to another medium, depending on the refractive index, the light will bend with a certain angle. For certain combination of materials, it might be that light cannot escape one medium at all from a certain angle (greater than critical angle). It is called total internal reflection. If you point a flashlight from \"under the sea\" the light won't leave the water at all.\u003c/p\u003e\u003cp\u003eFor given refractive indices, find critical angle where total internal reflection happens. If total internal reflection does not happen for any angle, then return \"-1\".\u003c/p\u003e\u003cp\u003eExample1: n_in = 1.333, n_out = 1, theta_crit = 48.6 degrees;\r\nExample2: n_out = 1, n_in = 1.333, theta_crit = -1 (total internal reflection does not occur, if you are in the air, and beaming light at the water.)\u003c/p\u003e\u003cp\u003eInput of function: n_in, n_out (refractive index, positive) \r\nOutput: critical angle (rounded to nearest integer), if total internal reflection occurs. Else return -1.\u003c/p\u003e","function_template":"function theta_crit = totalInternalReflection(n_in,n_out)\r\n  theta_crit = -1;\r\nend","test_suite":"%%\r\nn_in = 3; n_out = 3;\r\ntheta_crit_correct = -1;\r\nassert(isequal(totalInternalReflection(n_in,n_out),theta_crit_correct))\r\n\r\n%%\r\nn_in = 1; n_out = 1.333;\r\ntheta_crit_correct = -1;\r\nassert(isequal(totalInternalReflection(n_in,n_out),theta_crit_correct))\r\n\r\n%%\r\nn_in = 1.333; n_out = 1;\r\ntheta_crit_correct = 49;\r\nassert(isequal(totalInternalReflection(n_in,n_out),theta_crit_correct))\r\n\r\n%%\r\nn_in = 4; n_out = 3;\r\ntheta_crit_correct = 49;\r\nassert(isequal(totalInternalReflection(n_in,n_out),theta_crit_correct))\r\n\r\n%%\r\nn_in = 4; n_out = 2;\r\ntheta_crit_correct = 30;\r\nassert(isequal(totalInternalReflection(n_in,n_out),theta_crit_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":6,"created_by":115733,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":58,"test_suite_updated_at":"2017-02-16T21:45:07.000Z","rescore_all_solutions":false,"group_id":37,"created_at":"2017-02-14T00:59:14.000Z","updated_at":"2026-02-08T13:00:17.000Z","published_at":"2017-02-14T00:59:14.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Snell's_law\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://en.wikipedia.org/wiki/Snell's_law\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhen a light travels from one medium to another medium, depending on the refractive index, the light will bend with a certain angle. For certain combination of materials, it might be that light cannot escape one medium at all from a certain angle (greater than critical angle). It is called total internal reflection. If you point a flashlight from \\\"under the sea\\\" the light won't leave the water at all.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor given refractive indices, find critical angle where total internal reflection happens. If total internal reflection does not happen for any angle, then return \\\"-1\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample1: n_in = 1.333, n_out = 1, theta_crit = 48.6 degrees; Example2: n_out = 1, n_in = 1.333, theta_crit = -1 (total internal reflection does not occur, if you are in the air, and beaming light at the water.)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInput of function: n_in, n_out (refractive index, positive) Output: critical angle (rounded to nearest integer), if total internal reflection occurs. 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