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Unformatted text preview: explain why.] 9.3H Electromagnetic waves propagating in a medium with dielectric (x) satisfy the wave equation (x) 2 / t 2 = c 2 2 / x 2 , = (x,t). Suppose (x) = (1 + x 2 /2L 2 ) 2 . The medium is disturbed at x=0 by an antenna with frequency . If L/c >> 1, find the WKB solution for x > 0 for waves propagating to the right, correct to 1 st order. By demanding that |k 1 | << |k |, obtain the condition that the WKB solution is a good approximation. At what x/L do you find the worst violation? Make a sketch of the real part of , to first order, over a scale of length a few Ls. Find x(t), the location of the wavepacket moving with the local group velocity if x(0) = 0. From the constancy of , find k(t)....
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- Fall '11