How does Fermat's Principle follow from Huygen's principle?

[nhmllr]

How does Fermat's principle of least time (that if light goes from one point to another, any small deviation in the path will result in a path that takes the same time on the first order) follow from Huygen's wave principle?

Everyone always says that Fermat's principle can be derived from Huygen's principle for when the distances you're looking at are much bigger than the wavelength, but no one actually every proves it.

I'm giving a little talk to my class about Fermat's principle, and I'd like to connect it to Huygen's principle. Can anyone direct me to a treatment, because I can't find one.

Thank you

 

[UltrafastPED]

This is done for you in Chapter 10 - Connections to Optics of my Notes on Analytical Mechanics. Fermat's Principle, the eikonal equation, and Huyghens' wavelets are shown to be equivalent.