Fermat's Principle and Snell's Law

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Fermat's principle states that light travels between two points in such a way that the total time traveled is a minimum. Since light travels at different speeds through different media, the path of least time may not be a straight line. In particular, light travels a longer distance in the medium in which it has a higher speed. You can find the path followed by the light ray by dragging the point on the boundary between the two media so as to minimize the total time traveled. At this minimum, , as predicted by Snell's law.

Contributed by: Jim Brandt (August 2011)
Open content licensed under CC BY-NC-SA


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Details

The upper and lower media are each one meter thick, and we are looking for the path of least time between the two corners. This is a minimization problem. As you drag the boundary point to find the minimum total time, it may be helpful to hold down the Alt key (Windows) or the Option key (Mac OS). This will slow the motion of the boundary point and allow you to more accurately locate the minimum. As the index of refraction increases, the speed of light in the media decreases.



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