hw6solns

# 1 1 3 2 2 2 2 2 2 2 2 2 2 2 v v v1 v v2 v

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Unformatted text preview: 1 1 1 1 1 1 n2 v i i Det [M] = - 2+ 2 - 2+ 2 - 2+ 2 + n2 (8) i 2 - v2 v v1 v v2 v v3 i=1,2,3 v i i=1,2,3 From (8) we can see that for Det [M] = 0 in general, n2 i 2 =0 v 2 - vi i=1,2,3 Alternate derivation: (6) can be written as ni 1 1 (n E0 ) + - 2 + 2 Ei = v2 v vi Ei Now, looking at 3 i=1 (9) 0 2 ni v i 2 (n E0 ) -v 2 + vi = (10) n i Ei = = n E0 = n E0 n E0 2 n2 v i i 2 -v 2 + vi i=1 3 2 2 v 2 - v i n2 + n2 v i i i =0 2 - v2 v i i=1 3 i=1 3 3 i=1 2 n2 v i i (n E0 ) 2 + v2 -v i v2 n2 i 2 = 0, in general - vi (11) The Fresnel equation is quadratic in v there are, in general, two distinct modes of propagation with different phase velocities. 2 (c) A B is an invariant under rotations. Corollary : if A B=0 in a "convenient" frame, A B = 0 in all frames. For...
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## This note was uploaded on 04/26/2013 for the course PHYS 6561 taught by Professor Csaki, c during the Fall '09 term at Cornell.

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