Review for Optics Exam 2
Info
 Take in the Testing Center, 3/13 (Thurs) through 3/18
(Tues)
 Like last time:
o 3 hour time limit, 1% penalty per minute if over
o Late fee if you start it last day after 6 pm
o Closed book, closed notes
o I will give you the most difficult equations; the
simpler equations you need to memorize
o It’s worth 16% of your final course grade
 I will be out of town from 3/10 afternoon until 3/14
evening. I should be emailable, though.
What to study
 Sample exam problems from pages 203-207 in P&W
 Like last time:
o HW problems
o Class notes
o Reading quizzes
o Textbook
o Old exams from students who took this class from
other profs in the past
o Problems from the book that were not assigned
o Problems from other Optics books, such as Hecht
1
Important equations
Will be given if needed
Need to have memorized
(unless e.g. part of a quiz
problem or a derivation
problem)
(not necessarily comprehensive)
Stuff from last exam, such
as Fresnel equations
Integral table integrals
Stuff from last exam:
constants and eqns such as
I

1 n
E0
2 0c
2
c
  vp
k n
Chapter 5
Definition of  for crystals
 as a diagonal tensor
 for uniaxial crystals
nx, ny, and nz for uniaxial
crystals
Fresnel crystal equation
Uniaxial Crystals
For optic axis // to surface:
n = no, ne
2
For optic axis  to surface:
n = no,
no ne
no sin 2  2  ne cos 2  2
2
2
(but you need to know
which n = which polar)
s-polar Snell’s Law
p-polar Snell’s Law
p-polar Poynting vector 
Optical path length
Phase factor from path length
difference
Chapter 6
Two interfaces:
t13 
t12t 23
 r21r23e ik2d cos2
e ik2d cos2
n cos  3
T13  3
t13
n1 cos 1
2
“Fabry-Perot Equation”
Definition of Tmax
Definition of F
Definition of 
FWHM
FWHM
FSR
3
Resolving power
Definition of f
R+T+A=1
Multilayer method:
j = kjljcosj
p-polar eqns for Mj and A
s-polar eqns for Mj and A
t13 = 1/a11
r = a21/a11
Chapter 7
1 n
2
E (t )
2 0c
 d
vg 

k dk
I slow (t ) 
Defn of Fourier Transform
Defn of Inverse FT
Gaussian wavepacket
FT of Gaussian wavepacket
Parseval’s Theorem
Delta function definitions
Sifting property

1
 i ( t  t 0 )
 (t  t 0 ) 
e
d

2 
Defn of convolution
4
Convolution Theorems,
without factors of sqrt(2)
Dispersion
Linear:
 d
vg  
Re( k )
 d
 0





1


d
t 
Re( k )
 r
d
 0
I e


2 kimag (0 )r
 2
E (t  t , r0 )
Quadratic:
k  k0 
1
  0      0 2
vg
1 1
 n  n 
vg c
  0

1
n  2n
2c
  0
(Gaussian, thickness z)
  2z
T   1 2
E t , z  
E0 ei kz 0t 
1   
2 1/ 4
e
i
i  
z
tan 1  
t
2

2
2 T  vg
5




2
e
1  z
 2 t
2T  v g




2
Chapter 8
Michelson:
Single 
I det ( )  2 I 0 (1  cos  )
Band of ’s:

 0   I ( )d

 ( ) 

I
det
1
0

i
I
(

)
e
d


( )dt  2 0 1  Re  ( ) 

I det ( )  2 I onebeam 1  Re  ( )
Coherence time, tc
FT NormSig 
 2 0    I    I   
2
Defn of visibility
V = ||
Coherence length, lc
Young:
Point source:

 kyh

I det (h)  2 I 0 1  cos
   
 D


6
Extended source:

 0   I ( y )dy 

 ( h) 
e

ikyh
D 
0
 I ( y)e

ikhy
R
dy 

I det (h)  2 I oneslit 1  Re  (h)
Coherence slit separation, hc
7