|Principles, philosophy of science: physical principles are not the same as laws of nature. Rather, laws can be gained from principles or traced back to principles. Examples are the principle of the shortest time, the principle of the smallest effect, the uncertainty principle. See also theories, laws of nature, laws, natural constants.|
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Principle/Theory/Feynman: Principles can explain laws. According to what principle should the law of Snellius be clear at all?
Fermat's Principle of the Shortest Time/Refraction/Foucault: from all possible paths the light could take, it takes the path that requires the shortest time.
The path that leads to the object is chosen, if the mirror had not been present. (~).
Refraction: Transition from air to water: e.g. (Feynman): Suppose someone stands on the shore and sees someone falling from a boat into the water.
We can run much faster than we can swim. Therefore, we should choose a path with a longer route on land than the distance in the water. Exactly the same as light does!
Important: there is an area near the optimum point where, in the first approximation, there is no significant change in time. But in the second order.
When the ratio of the speed is n, light should penetrate at such an angle that the ratio of the sinuses of the angles Θi und Θr is the ratio of the velocities of the two media.
sin Θi = n sin Θr.
Principle of the Shortest Time/Fermat/Feynman: Conclusions:
1) Reversibility of direction.
2) E.g. the glass block displaces the beam parallel, since the exit angle is equal to the entrance angle.
E.g. sunset: the light moves slower in the denser air on the ground. The light therefore chooses the shorter path by an acute angle at the entrance. This means that we can still see the sun, even when it has already gone down.
Analogy/Analog/Theory/Principle of the Shortest Time/Fermat/Identity/Physics/Feynman: apparently, the principle of the shortest time and the statement that angles are equal in reflection, and that the sinuses are proportional to the angles at refraction, are the same.
Vom Wesen physikalischer Gesetze München 1993
Vorlesungen über Physik I München 2001