Chapter 23 Electromagnetic Waves. Formula Set

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 = E_max sin 2π( t / T – x / λ) = E_max sin (ωt – kx)

B = B_max sin 2π( t / T – x / λ) = B_max sin (ωt – kx)             (23.3)

E_max = cB_max. (23.4)

E = ─E_max sin 2π( t / T + x / λ) = ─E_max sin (ωt + kx)

B = B_max sin 2π( t / T + x / λ) = B_max 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)

S_av = ε₀cE_max²/2 = ( ε₀ / μ₀)^½ E_max²/2 = E_maxB_max / (2μ₀) = cu (sinusoidal wave)          (23.9)

S_av = u_av / ( ε₀ μ₀)^½ = cu_av (sinusoidal wave)                                            (23.10)

I = S_av = ε₀cE_max²/2 = ( ε₀ / μ₀)^½ E_max²/2 = E_maxB_max / (2μ₀) = cu (sinusoidal wave)     (23.11)

I intensity

Radiation Pressure

p / V = ε₀E² / c = EB / (μ₀c²) = S / c²                                                           (23.12)

( Δp / Δt ) / A = ε₀E²/2 = (S_av / c²) c= S_av / 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)

θ_r = θ_a                       (23.15)

sin θ_a / sin θ_b = n_b / n_a n_a sin θ_a = n_b sin θ_b            (23.16)

λ = λ₀ / n                                                                    (23.17)

n_b sin θ_b = n_a sin θ_a → sin θ_b = sin θ_a · n_a / n_b

sin θ_crit = sin 90º · n_a / n_b = 1 · n_a / n_b → sin θ_crit = n_a / n_b                 (23.18)

23.9 Dispersion c = c( f ), n = n( f )

23.10 Polarization

linarly polarized, polarizing filter, dichroizm, polarizing axis, polarizer,

I = I_max cos² ϕ                       (23.19)

Polarization by Reflection

plane of incidence, polarizing angle θ_p, refracted beam, completely polarized

sin θ_p / cos θ_p = tan θ_p = n_b / n_a               Brewster's law                       (23.20)

Photoelasticity

23.11 Huygens's Principle

sin θ_a / sin θ_b = v_a / v_b            (23.21)

23.12 Scattering of light