Does Fermat's Principle Apply in All Special Cases of Light Path Alteration?

[tiny-tim]

… is it bad form to use double quotes?

there's no quota on quotiness

(but it is bad form for a quote to quote itself)

 

[zrek]

As long as we are assuming that the 'ray approximation' works, then at a sharp boundary between two materials, Snell's law is always going to work.

Good, if the Snell's law is working, then we can use it to create a concrete example for the question above. It seems to be not so difficult, almost already solved on the fig 22. I created a new example, see the fig. 24.

If the glass is not cut, the path#1 is the calculated. But if we cut it as the figure shows, the light will still go from A to B, the surface is untouched, still the entrance point will be changed, see the path#2. The point A not necessary to be in the infinity, the cut angle must be the appropriate.
Is this example correct?

... the 'ray approximation' and the Feynman 'sum over paths' are quite analogous, but they are not exactly the same thing. The Feynman 'sum over paths' is an exact quantum calculation, and the 'ray approximation' is an approximate classical calculation.

Thanks for mentioning this, I think I need to look for a reading about this. Maybe this is explained in the book "Feynman lectures on physics", I'll borrow it somehow.

 

[zrek]

tiny-tim, sophiecentaur and BruceW, thanks the help all of you, you gave me the direction where I have to increase my knowledge, now I know that I expected too much from Fermat. I still think that some of my questions are interesting, but this is not matter because the real problem and the solution is lying elsewhere, I need more examination of the topic. Thanks again, have a nice day!

 

[sophiecentaur]

It's been a good conversation. Good luck with taking this further.