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

In summary, the conversation discusses the concept of an integral and its notation, specifically the use of the symbol "δ" to represent infinitesimal variation in the path of the integral. The speaker also mentions the concept of Calculus of Variations and suggests using diagrams to aid in understanding. The main point is that the integral is taken along a path, while the delta represents small changes in that path.
  • #1
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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  • #2
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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  • #3
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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What is Fermat's principle Integral?

Fermat's principle Integral is a principle in optics that states that light will travel between two points in such a way that it takes the path that requires the least time.

Who came up with Fermat's principle Integral?

Fermat's principle Integral was first proposed by French mathematician Pierre de Fermat in the 17th century.

How is Fermat's principle Integral used in optics?

In optics, Fermat's principle Integral is used to calculate the path of light through different mediums, such as air, water, or glass. It helps in determining the direction in which light will travel from one point to another.

What is the mathematical representation of Fermat's principle Integral?

The mathematical representation of Fermat's principle Integral is known as the Fermat's principle equation, which states that the optical path length between two points is minimized when light takes the path that requires the least time.

What are the real-life applications of Fermat's principle Integral?

Fermat's principle Integral is used in various real-life applications, such as designing lenses, mirrors, and other optical instruments. It is also used in the study of atmospheric refraction, fiber optics, and the design of optical communication systems.

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