Revision as of 22:52, 12 October 2014

Calculus of Variations

Fermats principle is thatlight takes a path between two points that requires the least amount of time.

If we let S represent the path of light between two points then

light takes the time [math]t[/math] to travel between two points can be expressed as

t = \int_A^B dt =\int_A^B dt =

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-Fermats principle is used to derive the index of refraction formula for light passing between two media.
+Fermats principle is thatlight takes a path between two points that requires the least amount of time.
+If we let S represent the path of light between two points then
+:<math>S=vt_{min}</math>
+light takes the time <math>t</math> to travel between two points can be expressed as
+:t = \int_A^B dt =\int_A^B dt =
 == Euler-Lagrange Equation==