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Review for Optics Exam 1

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					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       (not necessarily comprehensive)
problem or a derivation
problem)
Stuff from last exam, such
 as Fresnel equations
Integral table integrals
                                  Stuff from last exam:
                                   constants and eqns such as
                                          1 n
                                     I
                                                       2
                                                E0
                                          2 0c
                                             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:
                           no ne
 n = n o,       no sin 2  2  ne cos2  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:
                       t12 t 23
  t13 
       e ik 2 d cos 2 r21 r23 e ik 2 d cos 2
       n cos  3
  T13  3
                              2
                        t13
       n1 cos  1
   “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
                                             I slow (t ) 
                                                                 2
                                                          E (t )
                                                    2 0c
                                                   d
                                             vg    
                                                  k dk
                                             Defn of Fourier Transform
                                             Defn of Inverse FT
Gaussian wavepacket
FT of Gaussian wavepacket
                                             Parseval’s Theorem
                                             Delta function definitions
                                             Sifting property
                     
                1
               2 
 (t  t 0 )        e i (t t0 ) d
                   
Defn of convolution

                                         4
                                                              Convolution Theorems,
                                                               without factors of sqrt(2)
Dispersion
Linear:
                                          1
         d                  
  vg       Re(k )          
         d                 
                       0 

        d                  
  t      Re(k )        r
       d                  0
                        
         2 kimag (0 )r                2
  I e                       E (t  t , r0 )
Quadratic:
  k  k0 
             1
                  0      0 2
             vg

     n  n 
  1 1
  vg c             0


 
      1
         n  2n
      2c                0

 (Gaussian, thickness z)
   2z
 T   1 2
                                                                        2                       2
                                                       i  z                    1  z     
                 E0ei kz0t 
                                          i                  t    
                                            tan 1                             2 t     

  E t , z  
                                          2            2 T 2  vg
                                                             
                                                                    
                                                                                2T  v g
                                                                                    
                                                                                            
                                                                                            
                                      e                                     e
                 1       2 1/ 4




                                                          5
Chapter 8
Michelson:
Single 
 I det ( )  2 I 0 (1  cos  )
Band of ’s:
             
   0   I ( )d
             
                      
                  1
   ( )             
                  0 
                        I ( )e i d
  

  I   det   ( )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 
       
                    ikyh
                                       ikhy
                     D             
            e
  ( h) 
                0      I ( y)e
                      
                                          R
                                                dy

  I det (h)  2 I oneslit 1  Re  (h)
 Coherence slit separation, hc




                                                      7

				
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