Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I Apply Fermat's principle to a Concave mirror

  1. Mar 30, 2017 #1
    I am now taking optics class at my school. Fermat principle can be applied on mirror of course.
    Fermat.png
    Then what about Concave mirror? According to the calculus of variation. the optimized path(actual path of the light) should be the shortest path. but in the concave mirror case, it goes through the longest path.
    Fermat2.png
    Like above.

    How can I apply Fermat's principle on concave mirror?
     
  2. jcsd
  3. Mar 30, 2017 #2

    stevendaryl

    User Avatar
    Staff Emeritus
    Science Advisor

    With variational principles, the path is not the absolute minimum (or maximum) it is only a local extremum. What this means is the following: If you shift the path slightly to the dotted path shown in the figure below, by shifting the location where the light ray hits the mirror by [itex]\Delta x[/itex], then the change in the path length will be of order [itex](\Delta x)^2[/itex]. That's a statement about the limit as [itex]\Delta x \rightarrow 0[/itex]. Fermat's principle doesn't say anything about paths that are very different from the given path, it only applies to infinitesimally different paths.

    fermat.jpg
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Apply Fermat's principle to a Concave mirror
  1. Concave mirror (Replies: 1)

Loading...