Exam Review Chapters 1-5
Equations that will be given on the exam (fundamental constants will also be given)
Fresnel Eqns   cos  2 ,   n2
cos 1
n1
(p-polarization) r     , t  2
 
 
(s-polarization) r  1   , t  2
1  
1  
Two interfaces
General E&M:
D = 0E + P = 0rE
  D   free
H =B/0 – M,  B/0
D
  H  J free 
t

 J  
t
J
2 E
2 P 1
 0 free  0 2  (  P)
2
t
t
t
0
Lorentz model
Nq 2
p 
m 0
 2 E   0 0
 p2
Dielectrics  
0 2   2  i
p
  2  i
2
Metals:  
Poynting
u field
u
S 
  medium
t
t
 B
S  E  
 0 
0
u field  2 E 2  2 10 B 2
umedium
 EJ
t
I  S  12 n 0cE 2
t02 
e
 ik1d cos1
t01t12
 r10 r12eik1d cos1
2
T02   02  02 t02 
2
Tmax 
F
1 
R10 R12
4 r10 r12
1  r
10
r12


2
FWMH 
FSR 
j
1
2n0 cos  0
 cos  N 1
cos  0  N
  M j 
 cos  0  j 1
 n N 1
 n0

 n0
A
1
2n 0 cos  0
 n 0 cos  0

 n 0 cos  0

1  N
1
  M j 
 1 j 1
 n N 1 cos  N 1
2
2
2
uy
ux
uz
1



n 2 n 2  nx 2 n 2  n y 2 n 2  nz 2
Uniaxial
2
n  no ,
no ne
no sin  2  ne cos 2  2
2
2
2
p-polar, optic axis  to surface:
n
sin 1
tan  2  e
no n 2  sin 2 
4
F
2
e
 n1d cos 1 F
tan  S 
2
no
ne
1
sin 1
ne 2  sin 2 1
2n1d cos 1
Multilayers
t02 = 1/a11
Equations that you won’t need to know by heart (i.e. if you need them for a problem, I’ll give them to you)
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“Hard” integrals
o I’ll give you an integral table if you need to do any hard integrals. “Hard” integrals do not include things
like polynomials, sines/cosines, or eu (not an exhaustive list of the non-hard integrals).
Coordinate transformations, to/from rectangular
o Cylindrical
o Spherical
Vector Calculus Theorems
o Gradient theorem
o Divergence theorem
o Stokes’ theorem
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Misc vector theorems, such as   (  A)  (  A)   2 A ,     A  0 , etc.
Coulomb’s Law in vector form (calculating E from an arbitrary charge density)
Biot-Savart Law (calculating B from an arbitrary current density)
Solution to driven/damped harmonic oscillator
Long equation for evanescent field
Formula to get the “magic direction” where the indices of refraction for the two polarizations are equal
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Exam 1 Review – pg 1
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0

0 
 i sin  j 

n j cos j 
cos  j 


cos  j
Mj 
  in cos sin 
j
j
j

Crystals
2
  10  12  2k1d cos 1
 FW MH 
 i sin  j cos  j 


nj


cos  j



 cos  j


 in j sin  j

 cos 
j

s-polar:
Tmax
1  F sin 2 ( 2)
T01T12
M
A
2
t01 t12
n cos  2
T02  2
n0 cos 1 1  r r ei 2 k1d cos1
10 12
r = a21/a11
j = kjljcosj
p-polar:
0

0 
Equations that you may need to know by heart (i.e. I won’t give them to you, but may test on them; almost certainly not
an exhaustive list)
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How to perform basic high-symmetry integrals in cylindrical and spherical coordinates
o how to integrate the charge density (dV) to get the charge enclosed by a Gaussian surface
o how to integrate the current density (dA) to get the current passing through an Amperian loop
Vector calculus derivatives (how to calculate in rectangular coordinates)
o Gradient
o Divergence
o Curl
o Laplacian
Maxwell’s equations, “microscopic version”, integral and differential form, and what their physical meaning is
o Gauss’s Law
o Gauss’s Law for B
o Faraday’s Law
o Ampere’s Law with Maxwell’s correction
How to use Gauss’s Law and Ampere’s law to calculate E and B for high symmetry situations
Polarization current and polarization charge density
c = 1/sqrt(00)
Definition of dipole moment, polarization
Definition of 
Relationships between n, , and r
Complex number basics
Basic wave stuff: relationships between , f, v, T, k, , etc.
Definition of k (wave vector)
General equation for a traveling plane wave
Relationships between , k, c, and n
Relationship between magnitudes of E and B
Relationship between directions of E, B, and k
Skin depth, and how kimag (the imaginary part of the wave vector) relates to  (the imaginary part of index of
refraction)
o Both types of skin depths (fall off of fields vs. fall off of intensities)
What “oscillator strength” strength is; how to extend Lorentz model to multiple resonances
Snell’s Law
R = |r|2; T =  |t|2 = 1 – R (sometimes T = 1 – R – A)
Brewster angle
Critical angle
Fabry Perot equation: what Tmin is
Definition of resolving power
Definition of finesse, f
Index of refraction matrix for crystals, including special form for uniaxial
Index of refraction for waves entering uniaxial crystal at normal incidence, optic axis // to surface
Exam 1 Review – pg 2