Exam Review Chapters 1-5
Equations that will be given on the exam (fundamental constants will also be given)
Exam 1 Review – pg 1
General E&M:
D = e0E + P = e0erE
H =B/m0 – M, » B/m0
Lorentz model
Dielectrics
Metals:
Poynting
Fresnel Eqns
(p-polarization)
(s-polarization)
Two interfaces
Multilayers
t02 = 1/a11
r = a21/a11
bj = kjljcosqj
p-polar:
s-polar:
Crystals
Uniaxial
p-polar, optic axis ^ to surface:
Exam 1 Review – pg 1
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)
· “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
· Misc vector theorems, such as , , 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
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)
· 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(e0m0)
· Definition of dipole moment, polarization
· Definition of c
· Relationships between n, c, and er
· Complex number basics
· Basic wave stuff: relationships between l, f, v, T, k, w, etc.
· Definition of k (wave vector)
· General equation for a traveling plane wave
· Relationships between w, 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 k (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 = ab|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 1