Announcements 2/21/12



Prayer
Exam results: curved 4 pts, see email
a. If you had Testing Center calculator issues that you feel
affected your grade, please talk to me ASAP.
b. If you did poorly and are concerned about your overall class
grade, you can make an appointment to talk to me. Send me
an email.
c. Students did the worst on the TIR problem (that we did in the
in-class review!), probably due to complex Fresnel
coefficients. There is a very high chance that complex Fresnel
coefficients will show up again in some form on Exam 2.
I’ll be out of town next week, Mon – Thurs.
a. Dr. Peatross will substitute in lecture
b. No office hours from me, obviously
c. TAs will have their usual office hours
About the Fabry-Perot problem…
Reading Quiz

These two graphs were given in the handout, plotted
as a function of w. Which applies to which section of
the handout?
a. Left = Fourier series, Right = Fourier transform
b. Left = Fourier transform, Right = Fourier series
c. Both = Fourier series
d. Both = Fourier transform
Colton’s Fourier Series Summary

with exponentials: f (t ) 

n 
cn e
inw0t
1
cn 
T
T

0
f (t )e  i nw0t dt
Fourier Series Example
cn or c(w)
f(t)
4
 4
f (t )    sin  2 t   
 
 3
 2i
f (t )  ...   
 5

 4
sin
6

t




 5


 i10 t  2i

e

 3

 4
sin
10

t




 7



 sin 14 t   ...

 i 6 t  2i  i 2 t  2i  i 2 t  2i
  e
  e

e

  
 
 3
Why did I list the positive exponents first?
 i 6 t  2i

e

 5
 i10 t
 ...
e

Colton’s Fourier Transform Summary
Fourier Series


f (t ) 
cn e
1
cn 
T
inw0t
n 

f (t ) 

c(w )e
iwt
n 
with cn  c(w)
and nw0  w
T

f (t )e  i nw0t dt
0
1
c(w ) 
T
T

f (t )e  iwt dt
0
Fourier Transforms
f (t ) 
1
2



c(w )e iwt d w
c(w ) 
1
2


f (t )e  iwt dt

A word about units: suppose f(t) is electric field.
What are units of c(w)?
Fourier Transform Example
cn or c(w)
f(t)
4
 4 
 4 
 4 
f (t )    sin  2 t     sin  6 t   
sin 10 t   

 sin 14 t   ...
 
 3 
 5 
 7 
c(w ) 
1  cos w 2  

w
2 i

Remember this?
Reading Quiz

“Group velocity” is given by:
k
a. w
w
c. k
k
b. w
w
d. k
Reading Quiz

Group velocity tracks the speed of the “ripples”
resulting from the superposition of multiple
waves
a. true
b. false
Two interfering plane waves