# How light is able to choose the path to take? [duplicate]

I'm a student at STEM School (10th grade), and I'm studying optics and light in Physics. I was studying the Fermat principle which say:

The path taken between two points by a ray of light is the path that can be traversed in the least time.

I asked myself, how light is supposed to know which path to take, in so less time (3*10^8 m/s), considering light hasn't mass and how their 'atoms and molecol' set to choose the less time? (Sorry for my english, but english isn't my 1st language)

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You can explain it using the Huygens principle. basically, exery point the lightwave reaches becomes can be treated as origin of a new spherical wave, and all such waves interere with each other to create a macroscopic path for the light ray. In this way, the light checks all neighboring paths, and chooses the one that is locally preferable. The efect is such that, when you look backwards from the point that the light wave has reached, and try to determine from which direction the ray has come from and what path did it take, you see that it came along the path that allowed it to get to the end in a fastest way. Note that it doesn't have to be global minimum, just local, i.e. there are no paths close to the one chosen that are faster.

Alright, first things first, light doesn't choose the path of shortest time. When you say "chose," you mean a conscious entity picking a certain course out of numerous courses. That, however, is not the case.

Fermat's principle can be derived from Huygens Principle, or perhaps is a consequence thereof. Now, to answer your question: light propagates (/traverses) the path of shortest time solely because that is how we can describe it mathematically.

Simply put, since the best way to describe diffraction (and/or light propagation) is by Huygens Principle, its mathematical consequences (one of it being Fermat's Principle) must be accepted as well. That is, we must accept that light "choses" the path of shortest time, by definition, so that we can have a consistent system of optics. That said, if it turns out by the aid of advance instruments, that this description of light is anomalistic, then we will obviously abandon Fermat's Principle.

For the time being, however, it suffices to say light takes that path of shortest distance solely because that is how we have defined it.

1. Huygen Principle is the best explanation.
2. Fermat's Principle is a consequence of (1)
3. therefore, in order to have a consistent system we much accept (2) as long as we do not face physical anomalies because of it.

Light is a wave. The light actually takes all possible paths, but (putting it simply) the wave patterns of most of these paths cancel out. The remaining path after combining all of the possible paths is the shortest one.

Feynman Lectures: Optics: The Principle of Least Time

I don't really have an answer, but here is an analogy.

When you design digital circuits, you can have multiple paths that the electric current can follow. And (to a reasonable approximation) the shortest one is the one that delivers the signal. Cut the shortest one and the next shortest path counts.

By providing multiple paths you can increase the yield of usable chips. If something is wrong with the shortest path, there is a backup with reduced performance.

• Nice answer, but I don't think light works a digital circuits, It could be true, but I (guess) we haven't study that show light works as digital circuits. – Matteo Skd May 29 at 8:12
• The current will flow through all wires in the circuit, not just the shortest one. I also don't think this is a good analogy. – rghome May 29 at 8:36
• It might not be a good analogy. Yes, the current will flow through all wires, and the light will follow all paths. Maybe in both cases, what matters is the one that arrives first. – J Thomas May 29 at 9:41
• No it doesn't. After hundreds of years of studying the nature of light and theories such as Quantum Electrodynamics, we have progressed beyond "Maybe". – rghome May 29 at 10:44
• OK, the light takes all the paths, and all but the fastest cancel each other. So that is the one that matters. – J Thomas May 29 at 11:33