Is time taken by light always minimum between two points. If yes then what is wrong with Fermat's original statement?
Of what. Time or path
In optics, Fermat's principle or the principle of least time, named after French mathematician Pierre de Fermat, is the principle that the path taken between two points by a ray of light is the path that can be traversed in the least time. This principle is sometimes taken as the definition of a ray of light. However, this version of the principle is not general; a more modern statement of the principle is that rays of light traverse the path of stationary optical length with respect to variations of the path. In other words, a ray of light prefers the path such that there are other paths, arbitrarily nearby on either side, along which the ray would take almost exactly the same time to traverse.
It means there is a path for which time is always minimum and on either side infinitesimally apart there are paths for which travel time is same but different from the actual path (greater than actual path)I believe it is a minimum time path. If it was a minimum distance path, the light would simply travel straight through instead of refracting when entering a lens. If the light is traveling through a constant medium then the minimum time path and the minimum distance path are the same.
This is essentially saying that light takes the minimum time path. The last sentence means that if the light deviated an infinitesimal amount from its shortest-time path in any direction, these new paths all take the same amount of time to traverse. Note that these paths would take longer than the least-time path.
It means there is a path for which time is always minimum and on either side infinitesimally apart there are paths for which travel time is same but different from the actual path (greater than actual path)
Time.Of what. Time or path
Say that I hold a candle in my hand while you stand 10 meters to the north. Consider a range of paths that go at an approximate 30 degree angle east of north to to a line midway between us. The paths then turn left and proceed at an approximate 30 degree angle west of north to your location.Give an example where light takes longer time