# Reformatting of Fermat's Principle

#### Dr.Brain

The Real Statement

The actual path between two points taken by a beam of light is the one which is traversed in the least time.

Modern Restructured Statement

To travel from one point to another ,Light would choose the path such that all other paths nearby take almost exactly the same time.

Although from my readings I have found that this law explains majority of the light phenomena's like reflection, refraction and interference.Reflection and refraction studied by the geometrical optics and interference studied through wave character of light, and each of these phenomena are studied using different light-spectrum components , interference can be best studied through radiowaves , and reflection/refraction through lights with smaller wavelengths.And all of these light phenomena have closely followed the F.P which has further predicted new things.

The modern statement says that the light ray will choose a path with minimum obstructions (as in refraction), and will take a path such that all other paths nearby take similar exact time.So is it that light sorts of smells and checks other paths against each other? and then finally selects the correct path. The modern statement also asserts that "If light wants to choose the path which will take the least time to reach the destination, the path may not be the shortest'.

Lets say we take a radiowave-source , a detector and a slit-setup as in the diagram, when the detector is at S , the light simply takes the smallest path and travels straight to S when slight is wide , now when slit is narrowed , S is further illuminated (correct me if I am wrong) . Now lets widen the slit again and move S to S' , Now light wont reach S' properly (because all other paths nearby take different times), now when we narrow the slight again , more light reaches S' because as I said before they sort of sense that now only one path is available and that is throught perfectly narrowed slit and they would take it! . So what does this experiment tell us? It tells us that light still reached S' , so light need not travel always in straight lines.

Q.1. Now what does Fermat's Principle has to say about 'narrowing off slit' helped more light reaching S' , but when the slit was wide , light had more options , and if it had correctly sensed the paths , they all take similar times' dont they?

Q.2 Nature always acts by the shortest and simplest path, is only a moral principle, not a physical one—it is not and can not be the cause of any effect in nature
Principle

BJ

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#### Dr.Brain

Till someone replies this thread , I would like to quote Clerselier, an expert in optics and leading spokesman for the Cartesians on this matter. he objects Fermat's Principle:

This same principle must make nature irresolute, not knowing which way to go when it makes a ray of light pass from a less dense to a more dense medium. For I ask you: if it is true that nature must always act by the shortest and simplest path, and given that the straight line is undoubtedly shorter and simpler than any other, would it not make nature hesitate, (if you wish that it act by this principle), when a ray of light, passing from a point in a rare medium to a point in a dense one, must simultaneously follow both the straight line and the bent one, since if the one proves shorter in time, the other is shorter and simpler in length? Who will decide, and who judge?"

#### ZapperZ

Staff Emeritus
2018 Award
OK, I'll bite.

This is verging on silliness. I will tell you why. NOWHERE in your posting did you even address the Principle of Least Action. I find this a horribly glorified omission.

If you have to ask what does the Principle of Least Action have anything to do with Fermat's principle of least time, then I'd say you have formulated your posting without first understanding ALL the physics involved. A quick browse through the calculus of variation will immediately tell you that Lagrangian/Hamiltonian mechanics, and Fermat's principle, all came from the same principle. Why you can knock down one and not the other is beyond my comprehension. If you have a problem with Fermat's principle, then you have a problem with mechanics (both classical and QM - path integral) in general. So go after that!

Zz.

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