WHAT's the fermat principle?

Question

I mean, I know what it is ( that light goes through the path wich takes less time or so..) I just would like to have a detailed explanation of it
...pls drop the references or sites unless they are necessary ; I just need a clear and simple explanation of it (simple not simplistic ) ,thanks a lot.

Answer 1

As you know, Fermat's principle states that light always travels the path between points that requires the least amount of time. Before Fermat, people believed that light always travels the shortest distance between points (Hero's principle I believe). Hero's principle explains the law of reflection...that the angle of incidence=the angle of reflection, but it doesn't explain refraction. As you're probably aware, refraction is the bending of light that occurs when light travels into different substances. If Hero's princple were true, you wouldn't expect the light's path to bend. Fermat realized that since light traveled different speeds in different substances, the path of least time would necessarily be a bent path. Thus he came up with the idea that light always travels the path of shortest time between two points. If you like, Fermat's principle can also be thought of as a consequence of Hamilton's principle and the therory of relativity. I personally like to think of Hamilton's principle as a Fermatlike principle governing the motion of physical objects. When veiwed quantum mechanically, Fermat's principle is kind of interesting...hence the other people's reference to Feynmann.

Answer 2

Fermat’s Last Theorem

Fermat’s Last Theorem, in mathematics, famous theorem which has led to important discoveries in algebra and analysis. It was proposed by the French mathematician Pierre de Fermat. While studying the work of the ancient Greek mathematician Diophantus, Fermat became interested in the chapter on Pythagorean numbers—that is, the sets of three numbers, a, b, and c, such as 3, 4, and 5, for which the equation a^2 + b^2 = c^2 is true. He wrote in pencil in the margin, “I have discovered a truly remarkable proof which this margin is too small to contain.” Fermat added that when the Pythagorean theorem is altered to read an + b n = cn, the new equation cannot be solved in integers for any value of n greater than 2. That is, no set of positive integers a, b, and c can be found to satisfy, for example, the equation a^3 + b^3 = c^3 or a^4 + b^4 = c^4.



Fermat’s simple theorem turned out to be surprisingly difficult to prove. For more than 350 years, many mathematicians tried to prove Fermat’s statement or to disprove it by finding an exception. In June 1993, Andrew Wiles, an English mathematician at Princeton University, claimed to have proved the theorem; however, in December of that year reviewers found a gap in his proof. On October 6, 1994, Wiles sent a revised proof to three colleagues. On October 25, 1994, after his colleagues judged it complete, Wiles published his proof.



Despite the special and somewhat impractical nature of Fermat’s theorem, it was important because attempts at solving the problem led to many important discoveries in both algebra and analysis.





Contributed By:

James Singer



Reviewed By:

J. Lennart Berggren

Answer 3

You seem to have about the most detailed description that is possible. It is the principle that light follows the path of minimal (or actually stable) time. This is enough to deduce things like the equal angle law of reflection and Snell's law of refraction as well as how light will travel in media with varying indices of refraction.



Such minimization principles are very important in modern physics, where even particle paths are described through minimization of something called a Lagrangian. In the case of light, the Lagrangian just describes the time of travel.

Answer 4

U can chk Feynnman's Lectures on Physics-thats a very good source of fermat principle

Answer 5

..seeand i thought it had to do w/ prime numbers... i just cant keep up w/ you math and science guys... now where is that puzzels and games catigory??

Answer 6

Thanks for the question. I learned a lot.