Fermat Light Ray Model Documents

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Main Document

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.

Last Modified June 6, 2014

This file has previous versions.

Source Code Documents

Fermat Light Ray Source Code 

The source code zip archive contains an XML representation of the Fermat Light Ray Model.   Unzip this archive in your EJS workspace to compile and run this model using EJS.

Last Modified June 25, 2011

This file has previous versions.