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challenge_problem_2.20100307.4b945ebc300a00.33291744

challenge_problem_2.20100307.4b945ebc300a00.33291744 -...

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Challenge problem Harry Dankowicz Mechanical Science and Engineering University of Illinois at Urbana-Champaign [email protected] 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 P
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