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

[Joyal Babu]

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.

 

[vanhees71]

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.

 

[Joyal Babu]

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.

 

[Nugatory]

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.

 

[Joyal Babu]

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.

 

[houlahound]

"if there is just one photon and we send it one at a time "

Say again?

 

[Joyal Babu]

:),what I meant was we are sending one photon at a time

 

[Nugatory]

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.

 

[Joyal Babu]

Thank you for that.