Transcript lecture 33 - more interference

Announcements 11/14/11
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Prayer
HW 29 problem
Labs 8 & 9 due Saturday
Progress Reports…
Review:
phaseshift   2 (PL  )
Approx.1: PL  d sin 


E  stuff   e   e  
E  stuff  1  ei
i 2
i 2
E  stuff  cos( 2)
I  I0 cos2 ( 2)
Approx.2: sin   y L
Rubes
Fourier Transforms?
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How can our two-slit analysis possibly have
anything to do with Fourier transforms?
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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
  
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For an equally-spaced pattern of slits, how do the PLs
compare?
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Each  is a multiple of 2! (Could have an overall
reference phase for 1…not too important.)
Adding up phases, cont.
…
slits
Etot  E0e
irel.to ref.
 PL 
  2 
for each slit

  
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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
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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
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When a light wave travels from a low index to
a high index material at normal incidence
(perpendicular to surface), what is the phase
shift of the reflected wave?
a. 0
b. 45
c. 90
d. 180
e. depends on whether it is s- or p-polarization
Remember these?
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“Fresnel Equations”
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
Same as
strings
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
Air to glass (n=1 to n=1.5)
p-polarization
field amplitudes vs 
1.0
t
0.8
0.6
0.4
r
0.2
20
40
60
80
0.2
Brewster
180 phase shift
(close to perpendicular)
0 phase shift
(close to glancing)
Back to “near normal incidence”
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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?
If rays at an angle…
air
thin glass
air
determine if above/
Rays drawn at an angle to make
below
Brewster
angle
viewing easier.
They’re really
perpendicular
to surface.
(if p-polarization).
thickness t
Optical path length
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OPL = Path Length  n
 since wavelength inside the material is reduced
by a factor of n, the distance “looks” bigger than it
actually is
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Constructive interference:
OPL ( any phase shifts) = m
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Destructive interference:
OPL ( any phase shifts) = (m+1/2) 
New situation
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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
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What’s going on here?
http://superphysics.netfirms.
com/pp_optics.html
http://twilit.wordpress.com/2008/
03/15/bubbles-and-interference/
Demo
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Demo: Soap film
Interferometer
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From lab 9:
changing optical
path length,
yields ngas
Interference!
How does this disprove the ether?