Phys_322_HW8

# Phys_322_HW8 - Phys 322 HW8 Solution 1 In phase 1 2 2 2 2 2...

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Unformatted text preview: Phys 322 HW8 Solution 1. In phase: 1 2 , 2 2 2 2 2 E0 E01 E02 2 E01 E02 cos 2 2 E01 E02 2 E01 E02 E01 E02 2 Out of phase: 2 1 , 2 2 2 2 2 E0 E01 E02 2 E01 E02 cos 2 2 E01 E02 2 E01 E02 E01 E02 2 2. sin cos , so E 2 4 sin t 4 cos t . 2 2 2 2 2 E3 E1 E2 , so E03 E01 E02 2 E01 E02 cos 2 2 9 16 25 , so E03 5 . tan E01 sin 1 E02 sin 2 4 , therefore 53 . E3 lags E1. E01 cos 1 E02 cos 2 3 g 2 3. Long wavelength limit, v 4. Assume v a , vg v g dv 1 vk , vg v k k dk 2k gv k2 dv a a 2 2v d 5. f sin . It’s an even function, and the wavelength is π, k 2 . Therefore, f A0 Am cos 2m ; 2 m1 2 Am 2 0 sin cos 2md 2 cos2m 1 2m 1 0 0 sin2m 1d 2 2 cos2m 1 2m 1 0 sin2m 1d 0 2 1 1 4 1 2m 1 2m 1 4m 2 1 1 Then, f 2 4 cos 2m 2 1 m 1 4m 6. xc ct c 3 10 8 m / s 10 8 s 3m . 0 ~ 2 / xc 500 10 9 m 0 2 3m 8.3 10 5 nm . v v 0 0 8.3 10 5 nm 500 nm 1.6 10 7 . 7. v v 1 10 10 m 600 10 9 m 1.67 10 4 . So v c 3 10 8 m 600 10 9 m 5 1014 Hz . v 1.67 10 4 5 1014 Hz 8.35 1014 Hz , so t 1.2 10 11 s . lc ct c 3 10 8 m / s 1.2 10 11 s 3.6 10 3 m 2 ...
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Phys_322_HW8 - Phys 322 HW8 Solution 1 In phase 1 2 2 2 2 2...

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