Thursday, November 27, 2014

23 Electromagnetic Waves

23 Electromagnetic Waves
v = λf
23.2 Speed of a Electromagnetic Wave
E = cB                                                      (traveling wave)                      (23.1)
c = 1 / ( ε0 μ0)½                                                                                                          (23.2)

c = 3.00 × 108 m/s
transverse wave
23.3 Electromagnetic Spectrum
700nm – 400nm
23.4 Sinusoidal Waves
plane wave
E = Emax sin 2π( t / Tx / λ) = Emax sin (ωtkx)
B = Bmax sin 2π( t / Tx / λ) = Bmax sin (ωtkx)                                                          (23.3)
Emax = cBmax. (23.4)
E = Emax sin 2π( t / T + x / λ) = Emax sin (ωt + kx)
B = Bmax sin 2π( t / T + x / λ) = Bmax sin (ωt + kx)                                                          (23.5)
23.5 Energy I Electromagnetic Waves

u = ε0E2 / 2 + B2 / (2μ0)                                                                                                   (23.6)
B = E / c = ( ε0 μ0)½ E
u = ε0E2 / 2 + B2 / (2μ0) = ε0E2 / 2 + ( ( ε0 μ0)½ E)2 / (2μ0) = ε0E2                                    (23.7)
ΔU = u ΔV = (ε0E2) (AcΔt)
S = ( ΔU / Δt ) = ε0cE2
S = ( ΔU / Δt ) = ε0cE2 = ( ε0 / μ0)½ E2 = EB / μ0 = cu                                                        (23.8)
Sav = ε0cEmax2/2 = ( ε0 / μ0)½ Emax2/2 = EmaxBmax / (2μ0) = cu (sinusoidal wave)            (23.9)
Sav = uav / ( ε0 μ0)½ = cuav (sinusoidal wave)                                                                      (23.10)
I = Sav = ε0cEmax2/2 = ( ε0 / μ0)½ Emax2/2 = EmaxBmax / (2μ0)         (sinusoidal wave)       (23.11)
I intensity

Radiation Pressure
p / V = ε0E2 / c = EB / (μ0c2) = S / c2                                                                                (23.12)
( Δp / Δt ) / A = ε0E2/2 = (Sav / c2) c= Sav / c = I / c (sinusoidal wave)                             (23.13)
23.6 Nature of Light
wave front, rays, geometric optic, physical optics
23.7 Reflection and Refraction
n = c / v                                                                                                                             (23.14)
θr = θa                                                                                                                               (23.15)
sin θa / sin θb = nb / na na sin θa = nb sin θb                                                                       (23.16)
λ = λ0 / n                                                                                                                            (23.17)
nb sin θb = na sin θa sin θb = sin θa · na / nb
sin θcrit = sin 90º · na / nb = 1 · na / nb → sin θcrit = na / nb                                                (23.18)
23.9 Dispersion c = c( f ), n = n( f )
23.10 Polarization
linarly polarized, polarizing filter, dichroizm, polarizing axis, polarizer,
I = Imax cos2 ϕ (23.19)
Polarization by Reflection
plane of incidence, polarizing angle θp, refracted beam, completely polarized
sin θp / cos θp = tan θp = nb / na Brewster's law                                                                   (23.20)
Photoelasticity
23.11 Huygens's Principle
sin θa / sin θb = va / vb                                                                                                          (23.21)
23.12 Scattering of light

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