Here are some statements about Fermat's Principle taken from Eugene Hecht's Optics book.
The original statement of Fermat's Principle : "The actual path between two points taken by a ray of light is the one that it transverses in the least time."
Reformulated by the book author: "Light, in going from point A to B, traverses the route having the smallest optical path length (OPL)."
Fermat's Principle in its modem form reads: "A light ray in going from point A to point B must traverse an optical path length that is stationary with respect to variations of that path."
The books states that "The original statement of Fermat's Principle of Least Time has some serious failings and is in need of alteration" but does not explain those failings clearly enough.
- The OPL divided by c equals the total time, so, to state that the time must be a minimum is the same of saying that the OPL is a minimum. Doesn't it? If so, statement "1" must be the same of "2".
- What is wrong with Fermat's principle of least time and why do we need to consider the statement "3" and not "2" or "1"?
- When will the OPL will be a maximum instead of a minimum?