Forest UCM CoV

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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

[math]S=vt[/math]

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]


The index of refraction is denoted as

[math]n=\frac{c}{v}[/math]


[math]t = \int_A^B \frac{n}{c} ds =[/math]

Euler-Lagrange Equation

Forest_Ugrad_ClassicalMechanics