1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Show that perfect a perfect reflector is a conic section with Fermat's principle

  1. Mar 19, 2009 #1
    1. The problem statement, all variables and given/known data
    Show, using Fermat's principle, that perfect reflecting surfaces are conic sections.

    2. Relevant equations
    Equations for the ellipse, parabola and hyperbola

    3. The attempt at a solution
    Ok, the ellipse seems easy. All rays coming from one focus reflecting to the other focus travels an equal distance if the mirror is an ellipse, since that's the definition of the ellipse.
    I'm having problems with the hyperbola. If I understand the question correctly, I'm supposed to show that the rays traveling from one focus to the other (virtual image) are equal in length, but they clearly arent.
    Where is the error in my thinking?
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted