Multiple Paths in Fermat's Principle: Which One Will Light Choose?

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Discussion Overview

The discussion revolves around Fermat's principle and the implications of having multiple paths with stationary optical path lengths. Participants explore whether light would choose a specific path when multiple options exist, and they consider classical explanations without delving into quantum mechanics.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions which path light would take if multiple paths yield stationary optical path lengths.
  • Another participant references the "shadow boundary" and the eikonal approximation as relevant to the discussion of ray optics and Fermat's principle.
  • A participant expresses uncertainty about the existence of two paths with stationary optical path lengths and requests a classical explanation.
  • One participant suggests that light from a point source focused by a lens could serve as an example of multiple paths with equal optical path lengths.
  • A question is raised about the behavior of a single photon sent one at a time, specifically whether it takes all paths simultaneously or has equal probabilities for each path.
  • Another participant connects the single photon scenario to the quantum mechanical double slit experiment, noting that detection methods influence the interpretation of the paths taken by photons.
  • A recommendation is made to solidify understanding of classical optics before exploring quantum mechanics.

Areas of Agreement / Disagreement

Participants express differing views on the implications of multiple paths in Fermat's principle, with some exploring classical interpretations while others hint at quantum mechanical considerations. The discussion remains unresolved regarding the specific behavior of light in this context.

Contextual Notes

Participants acknowledge the complexity of the topic, with some limitations in providing concrete examples or definitions. The discussion touches on both classical and quantum perspectives without reaching a consensus.

Joyal Babu
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In fermats principle what if there is more than one path for which the variation in optical path length is stationary.Then which path would light take to reach from one point to another.
 
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Do you have an example where this problem occurs? Of course, there's always a problem at the "shadow boundary" concerning the eikonal approximation, which leads to ray optics as an approximation for wave optics and which (in lowest order) can be formulated in terms of Fermat's principle.
 
Sorry vanhees,I don't have an example to give.This is just something that came to my mind while I was reading the topic.But is it actually possible to have 2 paths for which variation in optical path length is stationary?And if you can could you explain it to me classically if possible without going to quantum mech,its just that I am just a sophomore.
 
Joyal Babu said:
In fermats principle what if there is more than one path for which the variation in optical path length is stationary.Then which path would light take to reach from one point to another.
Would you consider light emitted from a point source and being focused by a lens on another point to be an example? The optical path length is the same along all paths through points equidistant from the central axis from source to center of lens to focal point.
 
Yeah good point,I hadn't considered it that way.One more thing(this might be a stupid question,bare with me) what happens if there is just one photon and we send it one at a time,would we see that the photon is taking all of the paths at once or each path with equal probability of having the photon in it.
 
"if there is just one photon and we send it one at a time "

Say again?
 
:),what I meant was we are sending one photon at a time
 
Joyal Babu said:
Yeah good point,I hadn't considered it that way.One more thing(this might be a stupid question,bare with me) what happens if there is just one photon and we send it one at a time,would we see that the photon is taking all of the paths at once or each path with equal probability of having the photon in it.
Now you're proposing a variant of the quantum mechanical double slit experiment. If we have detectors along the possible paths, then only one detector will trigger for each photon; if we do not have detectors along the possible paths then it is meaningless to ask about which path each photon follows.

I very very strongly recommend that you nail down your understanding of this problem using classical optics before you jump into the world of quantum mechanics.
 
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Thank you for that.
 

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