Fermat's principle light and time

In summary, the Principle of Stationary Action states that the optical path length must be extremal, which means that it can be either minimal, maximal or a point of inflection (a saddle point). Maxima occur in gravitational lensing. A point of inflection describes the path light takes when it is reflected off of an elliptical mirrored surface.
  • #1
pi-r8
138
30
I don't understand this idea. My terxtbook says that Fermat's principle is that light travels by the path that takes the least amount of time. Does that mean that light will go in crazy, curved paths if those are faster? How does it "know" which path will be the fastest?

For example, let's say I'm shining a flashlight towards a block of some medium with a really high index of refraction, so light traveling in this medium goes really slowly. If light is going in a straight line from the flashlight to a point directly behind the medium, it's going to take a long time to get there. On the other hand, if it follows a curved path up and over the medium, then down behind it, the total time would be much less. Is that what happens?
 
Science news on Phys.org
  • #2
Your understanding of his principle is flawed somewhat, read on Wikipedia or anywhere else to see why!
 
  • #3
This isn't one of my areas, so I'll just give a brief response.
Light does not 'travel' through a refractive medium. When a photon enters the medium, it's absorbed by an atom. A new photon is then emitted, which usually matches the original. That new photon then gets absorbed by another atom, and so on and so on...
 
  • #5
The wikipedia entry on Fermat's principle isn't particularly helpful... just the same old stuff about how you can use it to derive snell's law (which I had to do as a homework problem this year).
 
  • #6
robphy- I know about the principle of least action. What I don't understand is the actual, physical meaning of Fermat's principle. Even if, as Danger said, photons are constantly absorbed and emitted, rather than just traveling straight through, I don't understand why light would take the shortest time path, rather than a straight path.
 
  • #7
Wikipedia! said:
The modern, full version of Fermat's Principle states that the optical path length must be extremal, which means that it can be either minimal, maximal or a point of inflection (a saddle point). Minima occur most often, for instance the angle of refraction a wave takes when passing into a different medium or the path light has when reflected off of a planar mirror. Maxima occur in gravitational lensing. A point of inflection describes the path light takes when it is reflected off of an elliptical mirrored surface.

Hope that helps
 
  • #8
um... not really. How does that explain my example of the flashlight and the block? In real life the light goes straight through the block... but the minimum path would be to go around the block, and the maximum path would be infinitely long. I don't know what the point of inflection path would be though... is that it?
 
  • #9
pi-r8 said:
robphy- I know about the principle of least action. What I don't understand is the actual, physical meaning of Fermat's principle. Even if, as Danger said, photons are constantly absorbed and emitted, rather than just traveling straight through, I don't understand why light would take the shortest time path, rather than a straight path.
The thing you have to remember about the Fermat Principle or the Principle of Stationary Action is that the extrema/stationary-points are local... meaning you have to nudge the path a little bit and compare it to that original path... then nudge it again etc... I believe that if you try to work out your curve-around-the-medium path, it won't be a locally-stationary path.

Although the E.F. Taylor articles are good, the best thing to read is probably the lecture on Least Action in the Feynman Lectures... or Feynman's [little] QED book.

Why does light take the stationary time path?
Of course, one answer is philosophical... That's just what nature does [in this formulation of the physics].
If you want something more constructive, realize that, in the neighborhood of the classical path, there is not as much cancellation of phases [i.e. destructive interference] as compared with that of the other, non-classical paths.
 

FAQ: Fermat's principle light and time

What is Fermat's principle of light and time?

Fermat's principle states that light will always take the path that requires the least time to travel from one point to another. This principle can also be extended to other types of waves, such as sound waves.

How does Fermat's principle relate to the speed of light?

Fermat's principle is based on the assumption that light travels at a constant speed in a given medium. This speed is known as the speed of light, which is approximately 299,792,458 meters per second in a vacuum.

What is the significance of Fermat's principle in optics?

In optics, Fermat's principle is used to explain the behavior of light as it travels through different mediums or encounters obstacles. It allows us to predict the path of light and understand phenomena such as refraction and reflection.

Can Fermat's principle be applied to other areas of science?

Yes, Fermat's principle has applications in various fields of science, including quantum mechanics, relativity, and geophysics. It is a fundamental principle that helps us understand the behavior of waves and particles in different environments.

What is the historical significance of Fermat's principle?

Fermat's principle was first proposed by French mathematician Pierre de Fermat in the 17th century. It played a crucial role in the development of modern optics and has since been applied in many other areas of science, making it one of the most important principles in physics.

Similar threads

Back
Top