Revision as of 11:52, 13 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

The index of refraction is denoted as

for light traversing an interface with an nindex of refraction $n_1$ on one side and $n_2$ on the other side we would hav e

@@ Line 22: / Line 22: @@
-:<math>t = \int_A^B \frac{n}{c} ds =</math>
+:<math>t = \int_A^B \frac{n}{c} ds </math>
+for light traversing an interface with an nindex of refraction $n_1$ on one side and $n_2$ on the other side we would hav e
+:<math>t = \int_A^I \frac{n_1}{c} ds+ \int_I^B \frac{n_2}{c} ds </math>