Can any body tell me the derivation of fermat's principle without using calculus or any link on that regard?

Answer 1

Fermat's Little Theorem?

If so, then in number theory here's what we learn:

Recall Euler's theorem: if n>0 and gcd(a,n)=1, then:
a^(phi(n)) is congruent to 1(mod n).

So, Fermat's little theorem says that if p is a prime and a is an interger with p does not divide a then:

a^(p-1) is congreunt to 1 (mod p),

since phi(p) = p-1.



Hope this is what you were talking about.

Answer 2

"Fermat's Principle" is one of the laws of physics that works for light. In going from any point A to any point B, that may involve reflections from mirrors and refractions through lenses, Fermat's Principle states that light will follow the path of least time (not shortest distance!). Using Huygen's Principle is a way of deriving Snell's Law of Refraction, a non-calculus way using the wave properties of light. When light enters a medium of a given index of refraction, its wavelength may shorten, because while its frequency remains the same, its speed may be less. Through geometry, the law may be derived. Check link for the derivation and illustration.

Answer 3

Try this links: these may help you explain this principle without the calculus:

Answer 4

There's always forgotten algebra. Many have used calculus thinking it was needed and in fact algebra would have done just fine.

Answer 5

laws of physics that works for light.