1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Calculus of variation

  1. Nov 10, 2007 #1
    Im supposed to show that a ligth beam travelling in a vertical plane satisfies
    d^2z/dx^2=1/n(z) dn/dz[1+(dz/dx)^2]. Using calculus of variations to minimize the total time. The vertical plane got a refracting index n=n(z) there z is the vertical position and z=z(x) there x is the horisontal direction.

    I have started with to minimize the time and have used Euler-Lagrange equation. I have also simplified and got d^2z/dx^2=1/n(z) {dn/dz+n(z)dz/dx/[1+(dz/dx)^2]}. I don't think this is the same equation as above. is the right way to go or shall i do something else?

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

Can you help with the solution or looking for help too?