Review for Optics Exam Final
Info

On Apr 22 (Tues) in this classroom o Official time is 11 am – 2 pm; I will allow extra time since the next exam (if you have one) isn’t until 3 pm

Content: o First two-thirds of course: ~35% of exam

There will be at least one problem taken from each of the first two exams! (Not identical, but extremely similar.) o Last third of course: ~65% of exam

Like previous exams: o Closed book, closed notes o I will give you both equation lists from old exams o New equation list for this third of course
 It’s worth 28% of your final course grade
What to study

Sample exam problems from pages 291-295 in P&W

Like before: o HW problems o Class notes o Reading quizzes o Textbook o Etc.

Old exams, old HW, etc.
1

Important equations for last third of Optics course
Will be given if needed
(unless e.g. part of a quiz problem or a derivation problem)
Need to have memorized
(not necessarily comprehensive)
Stuff from last two exams
Integral table integrals
Stefan-Boltzmann constant
Stuff from last two exams : constants and all previous memorized stuff
Need to be able to figure out some derivations
Chapter 9
Eikonal Equation
ABCD matrices:
Translation, distance d


1 d
0 1


Optical path length
Fermat’s principle of least time
Ray vectors
Flat mirror reflection


1
0
0
1


2

Flat surface refraction



1
0
0 n
1 n
2



Curved surface refraction




1
R 


1 n
1 n
2

1



0 n
1 n
2




R = positive for convex, negative for concave
Sph. mirror/thin lens



1
1 f
0
1

 f lens





 n
2 n
1


1



1
R
1

1
R
2






1
R = positive for curving away; negative for curving towards f mirror

R
2
R = positive for concave
Principle Planes
Sylvester’s Theorem
Stability cond. for cavities:

1

A

2
D

1
Aberrations (mainly qualitative)
F-number
3

Chapters 10 and 11
Fresnel-Kirchoff formula
Fresnel formula
Fraunhofer formula (if precise formula needed)
Fraunhofer formula (general idea, I ~ |FT(AF)| 2
Fourier transform variables: k x
= kx / d k y
= ky / d
( k = 2

/

)
Fourier Transforms (no 2

Single slit: a sinc( k x a /2)
Comb function
General radial function
Top hat:
 a
2




2 J k
1

  a




)
Various Bessel function facts
(zeroes, orthogonality, etc) k  = k

/ d
FT of shifted aperture
Array theorem
How to use Fraunhofer and
FT’s to get patterns for single slit, double-slit, etc.
4

Spectrometer:
  xh
   md
 mN
Rayleigh criterion:
 min

1 .
22
 l
Gaussian beams
E
 x , y , z


E
0 w
0 w e
  2 w
2 e ikz
 ik
 2
2 R
 i tan

1

 z z
0

 z
0
 kw
0
2
2
R
 z
 z
0
2 z
Diff. through a lens
I ~ |FT(AF)| 2
, with e.g. kx / f as FT variable terms: “Rayleigh range”
“waist” w
 w
0 z
2
1
 z
0
2 q = z + i z
0 q
2

Aq
1
Cq
1


B
D
Chapter 12
Interferograms/Holograms
(mostly qualitative)
5

 f
 c
3
 e
8
 hf hf k
B
T
3

1

Color
Color matching functions
Chromaticity diagram
Chapter 13
I =

T 4
Hue
Saturation (Purity)
Etc.
6