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

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The integral \int_{A\to B} n ds represents the integral of the refractive index n along a path from point A to point B. The "δ" indicates an infinitesimal variation of that path, suggesting that the path can wiggle slightly. This variation is crucial for understanding how changes in the path affect the integral's value. The integral is computed along the original path, while the delta signifies the slight adjustments made to it. Understanding this concept is essential for grasping Fermat's principle in optics.
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 \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".
 
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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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