What is the meaning of the delta in Fermat's principle integral?

[manimaran1605]

I am unable understand this Integral, what does it actually saying? What does that "δ" means here? I haven't learned Calculus of variations, explain me with diagrams with possible.

 

[HallsofIvy]

It pretty much says what it means. The integral $\int_{A\to B} n ds$ is the integral of n along some path from point A to point B. The "$\delta$" in front means that we are considering what happens when we vary that path "infinitesimally".

 

[twoslit]

The point that may be giving you trouble is that the integral is taken along the path, while the variation expressed by the delta is varying the path itself. Think of a path from A to B wiggling slightly: the wiggle is the delta.