Problem 44070. Under the sea: Snell's law & total internal reflection

Created by Jihye Sofia Seo

Solve Later

{"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":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Snell's_law\"><w:r><w:t>&lt;https://en.wikipedia.org/wiki/Snell's_law</w:t></w:r></w:hyperlink><w:r><w:t>&gt;</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>When 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.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>For given refractive indices, find critical angle where total internal reflection happens. If total internal reflection does not happen for any angle, then return \"-1\".</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Example1: 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.)</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Input of function: n_in, n_out (refractive index, positive) Output: critical angle (rounded to nearest integer), if total internal reflection occurs. Else return -1.</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

<a href = "https://en.wikipedia.org/wiki/Snell's_law">https://en.wikipedia.org/wiki/Snell's_law</a>When 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.For given refractive indices, find critical angle where total internal reflection happens. If total internal reflection does not happen for any angle, then return "-1".Example1: 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.)Input of function: n_in, n_out (refractive index, positive) 
Output: critical angle (rounded to nearest integer), if total internal reflection occurs. Else return -1.

<https://en.wikipedia.org/wiki/Snell's_law>

When 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.

For given refractive indices, find critical angle where total internal reflection happens. If total internal reflection does not happen for any angle, then return "-1".

Example1: 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.)

Input of function: n_in, n_out (refractive index, positive) 
Output: critical angle (rounded to nearest integer), if total internal reflection occurs. Else return -1.

Solve

Solution Stats

132 Solutions
46 Solvers

Last Solution submitted on Apr 17, 2023

Last 200 Solutions

Problem Comments

4 Comments

4 Comments

Show 1 older comment

Rahul Kalampattel on 15 Feb 2017

The function only has a single (undefined) input in the test suite instead of n_in and n_out.

James on 16 Feb 2017

Anyone else here a fan of The Little Mermaid?

Jihye Sofia Seo on 16 Feb 2017

Thanks Rahul. Made changes to the test suite. Sorry !!

Rafael S.T. Vieira on 29 Jun 2020

James, I've started humming the song after reading the title...

Solution Comments

Show comments

Problem Recent Solvers46

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 44070. Under the sea: Snell's law & total internal reflection

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers46

Suggested Problems

More from this Author9

Problem Tags

Community Treasure Hunt

Problem 44070. Under the sea: Snell's law & total internal reflection

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers46

Suggested Problems

More from this Author9

Problem Tags

Community Treasure Hunt

Players