Fermat's principle states that light travels the path of stationary time, I've read up on this from several sources and I've come to realize that this means that it will travel paths of extrema, (maxima, minima & saddle points).(adsbygoogle = window.adsbygoogle || []).push({});

For minima, refraction is often given as an example (minizing the action or time of path)

For saddle/inflection points, Elliptical mirrors are given as examples (multiple paths given the same time from one focus to the other)

I understand these two examples... (atleast the first one very well).

My question is about the Maximal timec/ action path which is often applied gravitional lensing. How can there ever be a maximal time path, shouldn't the maximal time be infinite?

Here is a blurb from the following source

http://relativity.livingreviews.org/open?pubNo=lrr-2007-4&key=vuiss07 [Broken]

"4.1.1 Basics of lensing

Light is bent by the action of a gravitational field. In the case where a galaxy lies close to the line of sight to a background quasar, the quasar’s light may travel along several different paths to the observer, resulting in more than one image.

The easiest way to visualise this is to begin with a zero-mass galaxy (which bends no light rays) acting as the lens, and considering all possible light paths from the quasar to the observer which have a bend in the lens plane. From the observer’s point of view, we can connect all paths which take the same time to reach the observer with a contour, which in this case is circular in shape. The image will form at the centre of the diagram, surrounded by circles representing increasing light travel times. This is of course an application of Fermat’s principle; images form at stationary points in the Fermat surface, in this case at the Fermat minimum. Put less technically, the light has taken a straight-line path between the source and observer.

If we now allow the galaxy to have a steadily increasing mass, we introduce an extra time delay (known as the Shapiro delay) along light paths which pass through the lens plane close to the galaxy centre. This makes a distortion in the Fermat surface. At first, its only effect is to displace the Fermat minimum away from the distortion. Eventually, however, the distortion becomes big enough to produce a maximum at the position of the galaxy, together with a saddle point on the other side of the galaxy from the minimum. By Fermat’s principle, two further images will appear at these two stationary points in the Fermat surface. This is the basic three-image lens configuration, although in practice the central image at the Fermat maximum is highly demagnified and not usually seen.

If the lens is significantly elliptical and the lines of sight are well aligned, we can produce five images, consisting of four images around a ring alternating between maxima and saddle points, and a central, highly demagnified Fermat maximum. Both four-image and two-image systems (“quads” and “doubles”) are in fact seen in practice. The major use of lens systems is for determining mass distributions in the lens galaxy, since the positions and brightnesses of the images carry information about the gravitational potential of the lens. Gravitational lensing has the advantage that its effects are independent of whether the matter is light or dark, so in principle the effects of both baryonic and non-baryonic matter can be probed.

"

So gravitational lensing demonstrates this maximal path. I understand how a maxima is an extrema, but I can't reconcile how you could have such a path.

help!!

Thanks

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Fermats P & Gravitational Lensing

Loading...

Similar Threads - Fermats Gravitational Lensing | Date |
---|---|

B Newton's Law of Gravitation | Thursday at 7:31 AM |

B Electron-positron annihilation and gravitation | Feb 4, 2018 |

B Inertial and gravitational mass | Feb 2, 2018 |

Fermat principle and light | Nov 24, 2008 |

Can Fermat's principle be applied to gravitational lensing? | Jun 27, 2007 |

**Physics Forums - The Fusion of Science and Community**