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The Open Source Physics Project is supported by NSF DUE-0442581.

Computer Program Detail Page

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Fermat Light Ray Model
written by Wolfgang Christian
The Fermat Light Ray model shows a light ray traveling left to right through N homogeneous regions with different refractive indicies. Because light travels in a straight line through a homogenous medium, the path is determined by the vertical coordinates at each boundary. A data table allows users to set the region width w[i] and the refractive index n[i].
Fermat's principal states that the path taken by the light ray between the source and the detector is the path that requires the least time. The speed of light in each region is proportional to the refractive index in that region so the traversal time for region [i] is ?t=n[i]D where D is the ray-segment's length and we have chosen units such that the speed of light in vacuum c=1. The model begins with a straight path (light ray) connecting a source and a detector and computes the travel time for this ray. The travel time is recomputed when the boundary points, the source, or the detector are dragged. The simulation uses a simple Monte Carlo method to find for the minimum-time path when the run button is pressed.

The Fermat Light Ray model was developed using the Easy Java Simulations (EJS) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_csm_ch07_FermatLightRay.jar file will run the program if Java is installed.

Please note that this resource requires at least version 1.5 of Java.
1 source code document is available
Subjects Levels Resource Types
- Geometrical Optics
= Refractive Index
= Straight Line Propagation
Thermo & Stat Mech
- Probability
= Random Walks
- Upper Undergraduate
- Lower Undergraduate
- Instructional Material
= Interactive Simulation
Intended Users Formats Ratings
- Learners
- Educators
- application/java
  • Currently 0.0/5

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Access Rights:
Free access
Program released under GNU-GPL. Narrative is copyrighted.
This material is released under a GNU General Public License Version 3 license.
Rights Holder:
Wolfgang Christian
Monte Carlo
Record Cloner:
Metadata instance created May 4, 2011 by Wolfgang Christian
Record Updated:
June 6, 2014 by Andreu Glasmann
Last Update
when Cataloged:
May 3, 2011

AAAS Benchmark Alignments (2008 Version)

4. The Physical Setting

4E. Energy Transformations
  • 6-8: 4E/M4. Energy appears in different forms and can be transformed within a system. Motion energy is associated with the speed of an object. Thermal energy is associated with the temperature of an object. Gravitational energy is associated with the height of an object above a reference point. Elastic energy is associated with the stretching or compressing of an elastic object. Chemical energy is associated with the composition of a substance. Electrical energy is associated with an electric current in a circuit. Light energy is associated with the frequency of electromagnetic waves.

AAAS Benchmark Alignments (1993 Version)


E. Energy Transformations
  • 4E (9-12) #2.  Heat energy in a material consists of the disordered motions of its atoms or molecules. In any interactions of atoms or molecules, the statistical odds are that they will end up with less order than they began?that is, with the heat energy spread out more evenly. With huge numbers of atoms and molecules, the greater disorder is almost certain.
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Record Link
AIP Format
W. Christian, Computer Program FERMAT LIGHT RAY MODEL, Version 1.0 (2011), WWW Document, (https://www.compadre.org/Repository/document/ServeFile.cfm?ID=11182&DocID=2232).
W. Christian, Computer Program FERMAT LIGHT RAY MODEL, Version 1.0 (2011), <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=11182&DocID=2232>.
APA Format
Christian, W. (2011). Fermat Light Ray Model (Version 1.0) [Computer software]. Retrieved June 22, 2024, from https://www.compadre.org/Repository/document/ServeFile.cfm?ID=11182&DocID=2232
Chicago Format
Christian, Wolfgang. "Fermat Light Ray Model." Version 1.0. https://www.compadre.org/Repository/document/ServeFile.cfm?ID=11182&DocID=2232 (accessed 22 June 2024).
MLA Format
Christian, Wolfgang. Fermat Light Ray Model. Vers. 1.0. Computer software. 2011. Java 1.5. 22 June 2024 <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=11182&DocID=2232>.
BibTeX Export Format
@misc{ Author = "Wolfgang Christian", Title = {Fermat Light Ray Model}, Month = {May}, Year = {2011} }
Refer Export Format

%A Wolfgang Christian %T Fermat Light Ray Model %D May 3, 2011 %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=11182&DocID=2232 %O 1.0 %O application/java

EndNote Export Format

%0 Computer Program %A Christian, Wolfgang %D May 3, 2011 %T Fermat Light Ray Model %7 1.0 %8 May 3, 2011 %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=11182&DocID=2232

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The AIP Style presented is based on information from the AIP Style Manual.

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Fermat Light Ray Model:

Is Based On Easy Java Simulations Modeling and Authoring Tool

The Easy Java Simulations Modeling and Authoring Tool is needed to explore the computational model used in the Fermat Light Ray Model.

relation by Wolfgang Christian
Is a Teaching Guide For Physics Classroom: Snell's Law

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