Fermat's Principle Explained

[peter.ell]

Fermat's principle is also known as the path of least time principle, and it explains why the angle of incidence is equal to the angle of reflection, as well as why light refracts the way it does when it enters certain materials. I understand it pretty well, but then I read that Fermat's principle can be understood through quantum physics in terms of interference effects, with the light actually taking all possible paths from A to C to B, but only interfering constructively along the path of least time. Can someone please explain how this really works for both reflection and refraction?

If the light really does take all possible paths as quantum physics suggests, than there should be multiple angles that a ray of light reflects, not just the angle of incidence. It should interfere constructively along both the path of least time, and the path of most time. Yet we don't seem to see that, why not?

 

[Bill_K]

Peter,

Fermat's principle was asserted in 1657, over 250 years before quantum mechanics came along. And so depending on quantum mechanics to tell us how light ought to behave is quite a bit backward!

Anyway, the principle correctly stated is that the path a light ray takes is a local minimum. Globally, there may be more than one minimum. For example when you stand between two mirrors and see multiple images of yourself, each one represents a different path that light has taken, and each one can be obtained via Fermat's principle.

 

[icflame]

Hi,

I guess what you are talking about are diffraction and interference. The light can actually go beyond the classical path. What Fermat's principle tells us is how 0th order diffracted beam propagates.

Please see the diffraction pattern formed by a rectangular aperture. :D
http://en.wikipedia.org/wiki/Diffraction