HW3 - PHYS 3202 Classical Mechanics II Homework#3 Due at...

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Unformatted text preview: PHYS 3202 Classical Mechanics II - Homework #3 Due at 12:05pm, Friday Feb 11, 2011 in the class In homework, quizzes, and final exam, please show intermediate steps of your calculations. Whenever appropriate, you may draw diagram(s). If a problem is difficult, you may do easier ones first and then return to the hard one. Problem 1 (20 points): A man-made glass pipe (whose axis coincides with the z-axis) has inner radius r 1 and outer radius r 2 ( > r 1 ). Its index of refraction n ( r ) depends on the distance r from the z-axis, but is independent of the z and φ coor- dinates in the cylindrical coordinate system (see Thornton and Marion, 5th edition, Appendix F.2 ). • (10 points) Design the function n ( r ) such that a light beam in the glass can form a circle (surrounding the z-axis) whose radius is between r 1 and r 2 but otherwise arbitrary. Calculate the beam’s travel time in each revolution as a function of the circle’s radius....
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HW3 - PHYS 3202 Classical Mechanics II Homework#3 Due at...

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