challenge_problem_2.20100307.4b945ebc300a00.33291744

challenge_problem_2.20100307.4b945ebc300a00.33291744 -...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Challenge problem Harry Dankowicz Mechanical Science and Engineering University of Illinois at Urbana-Champaign danko@uiuc.edu Consider Fermat's principle : Among all possible paths through space connecting any two points along a light ray, the actual path followed by the light ray is that which minimizes the elapsed time. 1. Consider two points P and Q along a light ray in an optically homogeneous medium, i.e., a space in which the speed of light c is independent of position and direction of travel. Show that the path followed by the light ray from P to Q is the path of shortest length , i.e., the straight-line segment from P to Q . 2. Consider two points P : ( x P ; y P ) and Q : ( x Q ; y Q ) along a planar light ray, such that P and Q lie in the x; y -plane on either side of the straight line L : y = y ¤ , which separates the plane into two optically homogeneous media with light speeds c P and c Q , respectively. Show that the path followed by the light ray from P to Q consists of a straight-line segment from
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/17/2011 for the course TAM 412 taught by Professor Weaver during the Spring '08 term at University of Illinois, Urbana Champaign.

Page1 / 2

challenge_problem_2.20100307.4b945ebc300a00.33291744 -...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online