Register to reply

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

by hadoque
Tags: conic, fermat, perfect, principle, reflector
Share this thread:
Mar19-09, 01:42 PM
P: 41
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?
Phys.Org News Partner Science news on
Experts defend operational earthquake forecasting, counter critiques
EU urged to convert TV frequencies to mobile broadband
Sierra Nevada freshwater runoff could drop 26 percent by 2100

Register to reply

Related Discussions
Perfect practice makes perfect! General Math 0
Show that n+2 is not a perfect square Calculus & Beyond Homework 7
More conic section exercises General Math 1
Volume of a conic section Precalculus Mathematics Homework 3