The_Cambridge_Handbook_of_Physics_Formulas

152 Electromagnetism
7.8 Waves in and out of media
Waves in lossless media
Electric field
Magnetic field
∇ 2 E = µɛ ∂2 E
∂t 2 (7.193)
∇ 2 B = µɛ ∂2 B
∂t 2 (7.194)
E electric field
µ permeability (= µ 0 µ r )
ɛ permittivity (= ɛ 0 ɛ r )
B magnetic flux density
t time
Refractive index η = √ ɛ r µ r (7.195)
Wave speed v = 1 √ µɛ
= c η
√
µ0
Impedance of free space Z 0 = ≃ 376.7 Ω (7.197)
ɛ 0
(7.196)
v
η
c
wave phase speed
refractive index
speed of light
Wave impedance Z = E H = Z 0
√
µr
ɛ r
(7.198)
Z 0
Z
H
impedance of free
space
wave impedance
magnetic field strength
Radiation pressure a
Radiation
momentum G = N
density
c 2 (7.199)
Isotropic
radiation
Specular
reflection
G
N
c
momentum density
Poynting vector
speed of light
p n = 1 3 u(1+R) (7.200) u incident radiation
energy density
R (power) reflectance
p n normal pressure
coefficient
p n = u(1+R)cos 2 θ i (7.201)
p t = u(1−R)sinθ i cosθ i (7.202)
p t
θ i
tangential pressure
angle of incidence
u
θi
From an
extended p n = 1+R ∫∫
c
source b
From a point
source, c
luminosity L
p n = L(1+R)
4πr 2 c
I ν (θ,φ)cos 2 θ dΩ dν
(7.203)
(7.204)
I ν
ν
Ω
θ
L
r
specific intensity
frequency
solid angle
angle between dΩ
and normal to plane
source luminosity
(i.e., radiant power)
distance from source
a On an opaque surface.
b In spherical polar coordinates. See page 120 for the meaning of specific intensity.
c Normal to the plane.
z
(normal)
x
φ
θ
dΩ
y