Difference between revisions of "Forest UCM CoV"
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light takes the time <math>t</math> to travel between two points can be expressed as | light takes the time <math>t</math> to travel between two points can be expressed as | ||
| − | :<math>t = \int_A^B dt =\int_A^B \frac{1}{v} ds | + | :<math>t = \int_A^B dt =\int_A^B \frac{1}{v} ds </math> |
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:<math>n=\frac{c}{v}</math> | :<math>n=\frac{c}{v}</math> | ||
| + | |||
| + | |||
| + | :<math>t = \int_A^B \frac{n}{c} ds =</math> | ||
== Euler-Lagrange Equation== | == Euler-Lagrange Equation== | ||
Revision as of 01:15, 13 October 2014
Calculus of Variations
Fermat's Principle
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 to travel between two points can be expressed as
The index of refraction is denoted as