hw908 - velocity v(parallel to the wave vector of the EM...

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Classical Electrodynamics Physics 6561 Homework 9. Due: In class on Tuesday, 11/11 1. General polarization of plane waves Prove the statement in class (and Jackson p300) that a generic plane wave of the form ~ E ( ~x,t ) = ( E + ~ ² + + E - ~ ² - ) e i ~ k · ~x - iωt is elliptically polarized with the axes rotated by an angle α/ 2 from the x,y axes, where α is the relative phase between the E + and E - : E - /E + = re . Find the values of the semimajor and semiminor axes. 2. Circular polarization (a) Problem 7.28 from Jackson (b) Problem 7.29 from Jackson 3. Photons in EM waves Problem 7.30 from Jackson 4. Doppler effect (a) A plane wave of frequency ω is reflected from a perfect mirror which is moving with
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Unformatted text preview: velocity v (parallel to the wave vector of the EM wave). What will be the frequency ω of the reflected wave observed by an observer at rest? Assume that “perfect mirror” means that the fields at the surface of the mirror have to vanish. (b) Derive the same relation using Lorentz transformations. Use the fact that ( ω/c, ~ k ) form a 4-vector, and first Lorentz transform the incoming wave to the frame of the mirror, and then Lorentz transform the reflected wave back to the original frame....
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