Announcements 3/23/11

Prayer
Two labs this week (telescope, interferometer)

Review:

phaseshift   2 (PL  )
Approx.1: PL  d sin 
 
E  stuff   e   e  
E  stuff  1  ei
i 2
i 2
E  stuff  cos( 2)
I  I0 cos2 ( 2)
Approx.2: sin   y L
Fourier Transforms?

From last time: what did our two-slit analysis
have to do with Fourier transforms?

E  stuff  1  e
e
 E~  e
 E~
i

ieach slit
i
dY
(this is the y-coordinate on the slits,
not the y-coordinate on the screen)
open
areas

E~


compare to:
2
" aperture function " e dY an 
L
i
L2

L 2
 2 nx 
f ( x) cos 
dx

 L 
Adding up phases
…
In short, we need to add up a bunch of vectors that
have the same magnitude (1), but angles (phases)
that go like 0, 20, 40, 60, etc.
For a different position on the screen (measured by y
slits
or , we need to add up a different set of phases…
irel.to ref.
islit1
islit 2
screen
ifinal slit
Etot  perhaps
E0e
 e42, 63,
 ... etc.
e
likee0, 21,


2
y
 PL 
I
E
two-slit PL  d sin   d
  2 
for each slit

L
  

For an equally-spaced pattern of slits, how do the PLs
compare?

Each  is a multiple of 1! (Could have an overall
reference phase…not too important.)
Adding up phases, cont.
…
slits
Etot  E0e
irel.to ref.
 PL 
  2 
for each slit

  


e
islit1
e
islit 2
 ...  e
ifinal slit
two-slit PL  d sin   d
y
L

screen
I
Quick writing: graphically add these three vectors:
10 + 120 + 140
What about 10 + 190 + 1180
E
2
Three Slit Problem: Scanning Theta
Credit: this animation and the next one are from Dr. Durfee
Note: for some reason he picked the overall reference
phase to be about 20
Thought question

How many “sub” peaks are there between
the “main” peaks in a 5-slit interference
pattern?
a. 1
b. 2
c. 3
d. 4
e. 5
Five Slit Problem: Scanning Theta
Note: for some reason he picked the overall reference
phase to be about 20-30
Reading Quiz

When a wave on a string moves from a fast velocity
section to a slow velocity section, the reflected
wave is phase-shifted by 180. When a wave moves
from a slow section to a fast section, however, the
reflected wave has no phase shift.
How does the phase shift of a light wave moving
from one medium to another compare to that?
(close to normal incidence)
a. The phase shift obeys the same rules
b. The phase shift is the same for fast-to-slow, but
reversed for slow-to-fast
c. The phase shift is the same for slow-to-fast, but
reversed for fast-to-slow
d. The phase shift is reversed for both cases
Remember these?

“Fresnel Equations”
Just the same as strings
If near perpendicular (1-D problem)
v2  v1 n1  n2
r

v1  v2 n1  n2
R r
t
2
The Truth (overlooked by textbook):
Fordon’t
arbitrary
angle
you
always get
a phase shift,
even if going
n1 cosfast
1 tonslow.
2 cos 2
rs(Brewster
polar .  marks boundary)
n1 cos1  n2 cos2
n1 cos2  n2 cos1
rp polar. 
n1 cos2  n2 cos1
2v2
2n1

v1  v2 n1  n2
T  1 r
2
2n1 cos1
ts polar . More
 Truth: sometimes phase
n1 cos
1  n180:
2 have
2 coscan
shifts
not just
complex n, complex , etc.
2n1 cos1
t p polar. 
n1 cos2  n2 cos1
Back to 1D case



From low to high index: 180 phase shift
From high to low index: no phase shift
What does the thickness of this slab need to be to
get constructive interference between the two
rays?
air
thin glass
air
What changes if rays
really are at an angle?
Rays drawn at an angle to make
viewing easier. They’re really
perpendicular to surface.
thickness t
Optical path length

OPL = Path Length  n
 since wavelength inside the material is reduced
by a factor of n, the distance “looks” bigger than it
actually is

Constructive interference:
OPL ( any phase shifts) = m

Destructive interference:
OPL ( any phase shifts) = (m+1/2) 
New situation

What does the thickness of the COATING need to
be to get constructive interference between the
two rays?
air
thin coating,
n = 1.3
thick glass,
n = 1.5
Rays drawn at an angle to make
viewing easier. They’re really
perpendicular to surface.
thickness t
Pretty pictures

What’s going on here?
http://superphysics.netfirms.
com/pp_optics.html
http://twilit.wordpress.com/2008/
03/15/bubbles-and-interference/
Demo

Demo: Soap film
Interferometer

From lab 9:
changing optical
path length,
yields ngas
Interference!
How does this disprove the ether?