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fresnel - Physics 8.03 Vibrations and Waves Snells law n1...

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Physics 8.03 Vibrations and Waves November 16, 2004 Snell’s law: n 1 sinθ 1 = n 2 sinθ 2 . This holds in general: sound waves, water waves, E&M waves. Snell’s law is not the result of Maxwell’s equations. The following equations (the Fresnel eqs.) are the result of Maxwell’s eqs.; θ 1 and θ 2 are connected through Snell’s law. r = E 0 r /E 0 i = n 1 cosθ 2 n 2 cosθ 1 n 1 cosθ 2 + n 2 cosθ 1 = tan ( θ 1 θ 2 ) tan ( θ 1 + θ 2 ) (1) r = E 0 r /E 0 i = n 1 cosθ 1 n 2 cosθ 2 n 1 cosθ 1 + n 2 cosθ 2 = sin ( θ 1 θ 2 ) sin ( θ 1 + θ 2 ) (2) t = E 0 t /E 0 i = 2 n 1 cosθ 1 n 1 cosθ 2 + n 2 cosθ 1 = 2 sinθ 2 cosθ 1 sin ( θ 1 + θ 2 ) cos ( θ 1 θ 2 ) (3) t = E 0 t /E 0 i = 2 n 1 cosθ 1 n 1 cosθ 1 + n 2 cosθ 2 = 2 sinθ 2 cosθ 1 sin ( θ 1 + θ 2 ) (4) Special case of normal incidence: θ 1 =0, θ 2 =0 n 1 n 2 2 n 1 (1) & (2) (3) & (4) n 1 + n 2 n 1 + n 2 Notice Bekefi &
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