If it is not easy to understand, it can be understood that light will travel along the shortest path that takes time to travel.
However, so far, if there is no boundary condition, all the above statements are wrong ... Let's explain the correct thing:
First of all, three axioms of geometric optics:
Light travels along a straight line in a uniform medium without the influence of gravity.
Weak light can pass through another beam without interference under linear conditions, which is called independent propagation of light for short.
The reflection and refraction of light conform to the laws of reflection and refraction.
The existence of these axioms is based on the fact that no one has found them wrong so far, and more facts have been found to prove them right.
Then please introduce the initiator of your so-called "light will travel along the shortest path": Fermat principle.
The concrete expression of Fermat's principle is that light propagates along a time-stable path, or the time required for the path of light propagation may not be the minimum value, but the maximum value, even the inflection point value. -Yes, that's right. This representation has nothing to do with the fact that light travels along the shortest path. ...
If you want to ask Fermat how he came up with this principle-I can tell you that this is actually just his experimental experience of combining experiments with immature calculus ... That is to say, Fermat's principle was first put forward, which can't be strictly proved, but he can only be proved right through experiments. In his time, there were simply not enough mathematical and physical tools to prove his argument. ...
Why do we regard him as the correct principle now-thanks to the great Maxwell and a bunch of scientists and mathematicians in later generations-I must admit that I have forgotten how to prove Fermat's principle with Maxwell's equation, so I directly pulled a link to a webpage/read it for myself. ...
If you have finished reading it, you will find that none of these proofs can match the fact that light will travel along the shortest path, because in fact all the proofs you have seen above are the original explanations to prove Fermat's principle: the time required for the straight-line propagation path may not be the minimum, but the maximum, even the inflection point:
Or translated into mathematical language, the integral sum of the first-order differential ring of the optical path is 0.
Yes, light will travel along the shortest path, which is actually a statement with strict boundary conditions. In some optical paths, light will propagate along the shortest path, and the integral sum of the first-order variational ring of the optical path is zero.
So to sum up, it is wrong to single out "light will travel along the shortest path". If you have to take this sentence out, you must attach conditions other than this law:
Conform to the three laws of geometric optics
Under the condition of 1, light will travel along the shortest path.
I really don't know how to prove that the above statement is the same as the first-order variational ring integral sum of the optical path, so I don't recommend the statement that light will propagate along the shortest path, but "the way of light propagation conforms to Fermat's principle", in which Fermat's principle means that light will propagate along the first-order variational ring integral sum of the optical path to zero.