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a11f01 - INTERMEDIATE MECHANICS II — PHY 4936 HOME AND...

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Unformatted text preview: INTERMEDIATE MECHANICS II — PHY 4936 HOME AND CLASS WORK – SET 1 (August 27, 2011) (1) Consider light passing from medium 1 into medium 2. Use Fermat’s principle to derive Snell’s law between the velocities of light, v 1 and v 2 , in two media and the angles of refraction, θ 1 and θ 2 (a figure will be given in class). Due in class (8 points). (2) Method of 2D projections for spherical coordinates. Each of the following tasks counts one point. Follow the instructions given in class (no other methods). 1. Write x, y in cylindrical coordinates ρ, φ . 2. Write dx 2 + dy 2 in cylindrical coordinates. 3. Write cylindrical coordinates ρ, z in spherical coordinates r, θ . 4. Write dρ 2 + dz 2 in spherical coordinates. 5. Write dx 2 + dy 2 + dz 2 in spherical coordinates. 6. Write v 2 , the velocity squared, in cartesian coordinates. 7. Write v 2 , in ccylindrical coordinates. 8. Write v 2 , in spherical coordinates....
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