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

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SUMMARY

The discussion clarifies the meaning of the delta (δ) in the context of Fermat's principle integral, specifically the integral \(\int_{A\to B} n ds\). The δ signifies an infinitesimal variation in the path taken from point A to point B. This variation is crucial as it indicates how the integral changes when the path is slightly altered, emphasizing the relationship between the path and the integral's value.

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manimaran1605
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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.
 

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