All Questions
31
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Relating Brachistochrone problem to Fermat's principle of least time [closed]
When I came across the Brachistochrone problem, my teacher said we could relate it to Fermat's principle of least time.
So, we could make many glass slabs of high $\mathrm dx$, and every slab has a ...
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2
votes
2
answers
135
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What does the optical Hamiltonian mean?
So I was trying to demonstrate Snell's law with Hamilton's equations, and when I got the Hamiltonian:
$$H = -\sqrt{n^2-p_{1}^2-p_{2}^2}.$$
I had a question about what this Hamiltonian indicates. I ...
- 21
0
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0
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50
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Can anyone explain convergence of parallel rays on the focus of a parabolic reflector using Fermat's Principle?
Can anyone explain convergence of parallel rays on the focus of a parabolic reflector using Fermat's Principle? using optimization techniques from calculus?
1
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0
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87
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How to derive that Optical path length should be stationary from Fermat's principle?
I read above eq. (5.3) in "Optics" by Eugene Hecht
Fermat's Principle maintains that the optical path length OPL will be stationary; that is, its derivative with respect to the position ...
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0
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1
answer
58
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Fermat least time and snell's law for multiple layers of medium
I am reading a differential equation book that discusses the Brachistochrone problem. The book discusses Bernoulli's solution that uses Snell's law. The book says that a ray would follow the fastest ...
1
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1
answer
34
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Why is the time taken for light propagation between two points in anisotropic media independent of $y$?
Background
Light propagating in an anisotropic medium does not (in general) take a straight-line path between two points. The propagation time between those points, then, is dependent on the total ...
8
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2
answers
1k
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Fermat's principle and a non-physical conclusion
Fermat's Principle is the statement that a ray will follow a minimum-time path between a point, A, to a point, B.
So, if I have a block of material of high refractive index, so that it slows the light ...
- 737
1
vote
2
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289
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How to determine $n(x)$ when the functional depends exclusively on $n(x)$ and $x$? (Fermat's principle)
Recently I was taught an introduction to calculus of variations in reference to a course on analytical mechanics, where one problem involved Fermat's principle, stating that the path taken by a light ...
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0
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0
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124
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How does one derive Fermat's principle of Least Time? [duplicate]
Fermat's principle states that the path taken by a ray between two given points is the path that can be traveled in the least time.
I understand that Fermat's principle of Least time is crucial in ...
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1
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0
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39
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Mathematical expression for refraction within a spherical lens
Qs: How do I show that for a point object, for a ray at a large angle from the optical axis, spherical aberration (SA) produces a distorted focal length $f_{SA}$ that is shorter than the normal focal ...
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2
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81
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How does principle of least time suggest a relation between three indices of refraction?
In the 26th Feynman Lecture, Fermat's principle of least time is discussed and this point about refractive index is brought up:
It is easy to show that there are a number of new things predicted by ...
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0
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0
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49
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Can light travel in closed loops indefinitely?
For simplicity, consider the two dimensional space. My question is that can there be a refractive index $(x, y)\mapsto n(x, y)$ such that the there is at least one closed permissible path (which can ...
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1
vote
1
answer
196
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Is it possible to think an example of refraction in which Fermat principle involve a maximum without using reflection?
In a question What is incorrect about the original statement of Fermat's principle? is showed an example of reflection in which Fermat principle involve a maximum, and in comments is said that it ...
- 1,139
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1
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838
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Path of light ray through varying refractive index
Suppose light ray passing through a medium with refractive index $n=n(y)$. In the case of an inhomogeneous medium in which $n$ varies continuously in the $y$-direction, We have curved rays that ...
- 11.9k
2
votes
2
answers
404
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What is the proper way to understand Fermat's principle?
I am studying Fermat's principle for the first time and the basic knowledge that I could gather said that it states that "that the path taken by a ray between two given points is the path that ...
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