Derivation Of The Fermat's Law Formula?

[deleted-64204]

Hie,
I did the project titled 'Measuring Sugar Content of a Liquid with a Laser Pointer' (https://www.sciencebuddies.org/science ... &from=TSW) and made it to the regionals with fantastic setup, results and presentation. Now I require the exact derivation of the formula which uses the apex angle of the prism, refractive index of air, and the angle of minimum deviation to calculate the refractive index of the solution tested.
I am aware it came from the Fermat's Refraction Law/Principle.
The Regional fair is being held on April 1st, 2011.
Thanks alot,
Jivy

[deleted-71417]

Ho,

Here is an algebraic argument proving Fermat’s Principle:

http://www.maths.bris.ac.uk/~mahah/Noncalculus.pdf

The more customary proof is based on the Calculus of Variations, a discussion of which is here:

http://www.eftaylor.com/pub/HancEulerEJP.pdf

http://www.physics.miami.edu/~nearing/m ... tional.pdf

You might be interested in these:

http://en.wikipedia.org/wiki/Calculus_o ... _principle

http://www.math.wayne.edu/~isaksen/Expository/dogs.pdf

http://en.wikipedia.org/wiki/Fermat's_p ... Derivation

If you can understand the Calculus of Variations approach you will find it helpful, as variation principles permeate the study of physics (look into Hamiltonisn and Lagrange formulations), but this is pretty advanced stuff for high school.

Good luck and best regards,

Barrett L Tomlinson