Transcript lecture 33 - more interference

Announcements 11/12/10
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Prayer
Two labs this week (telescope, interferometer)
The missing exams…
Project progress reports: I’m about 75% of the way done
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?
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From last time: what did our two-slit analysis
have 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~


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 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

  
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e
islit1
e
islit 2
 ...  e
ifinal slit
y
two-slit PL  d sin   d
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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How does the phase shift of a light wave switching
between fast and slow media compare to the phase
shift of a wave on a string switching between fast
and slow media?
a. The phase shift is the same
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
What is the phase shift?
 180
Remember these?
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“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
2v2
2n1

v1  v2 n1  n2
T  1 r
2
For arbitrary angle
n1 cos1  n2 cos2
rs polar . 
n1 cos1  n2 cos2
The Truth: if at an angle, you don’t
always get a phase shift, even if
2n1 cos1
going
fast
to slow. (Brewster)
ts polar . 
n1 cos2  n2 cos1
rp polar. 
n1 cos2  n2 cos1
More Truth: sometimes phase
2n1 cos1
shifts
t p polar
. not just 180: complex n,
ncomplex
,netc.
1 cos 2 
2 cos1
n1 cos1  n2 cos2
Back to 1D case
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From low to high index: 180 phase shift
From high to low index: no phase shift
Quick writing: 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
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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/Video
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Video: glass plates in sodium light
Demo: Soap film
Interferometer
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From lab 9:
changing optical
path length,
yields ngas
Interference!
How does this disprove the ether?