frustrated total internal reflection. last time: double boundary
TRANSCRIPT
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Frustrated total internal reflection
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Last time: double boundary
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Last time: double boundary
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Analogy to reflection, transmission, tunneling in QM
Frustrated TIR
waves at a single boundary Snell’s law, R, T
http://phet.colorado.edu/en/simulation/quantum-tunneling
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Frustrated total internal reflection for multi-touch displays
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Suppose we have a laser beam entering a piece of glass under special conditions so R = 0.
What is the same for both beams?a) Beam intensityb) Beam powerc) bothd) neither
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R and T from r and t
2t t
i i
nT t
n
coscos
2R r
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Why do we see vivid colors in reflection and not much in transmission?
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Double boundary
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Air-Water (n=1.3)-Air film (soap film) 1 0 1 2
1.3 10.13
1.3 1
r r
Dd/lvac
T
maxtot
21 sin2
TT
F
1 0 1 2
21 0 1 2
4
1
R RF
R R
F = 0.60
F: one kind of “finesse”
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Air-Water (n=1.3)-Air film (soap film)Normal incidence
Dd/lvac
T
Can we make a device with greater contrast in transmission?
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Air-Diamond (n=2.4)-Air film
Dd/lvac
T
1 0 1 2
2.4 1
2.4 1
r r
F = 0.88
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Air- Kryptonite? (n=10) -Air
Dd/lvac
T
1 0 1 2
10 1
10 1
r r
F = 18
Interference ideas for why increasing r makes these peaks so sharp?
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Multiple reflection view of r,t
2 3
0
1 ... n
n
x x x x
1
1 xSimple notation assume n0 = n2 so only have r,r’, t,t’
P. Derive t, the sum of all the terms on the right of the systema) got it right b) tried
2z zik d i k dtt e r r e zik dtt e
t r’
Eo
t’ r
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2 3
0
1 ... n
n
x x x x
1
1 x
2
1
1ikd
total i kdt tte
rre
2z zik d i k dtt e r r e zik dtt e
t r’
Eo
t’ r
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2 3
0
1 ... n
n
x x x x
1
1 x
2
1
1ikd
total i kdt tte
rre
2z zik d i k dtt e r r e zik dtt e
t r’
Eo
t’ r
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Calculation of r
2 3
0
1 ... n
n
x x x x
1
1 xP. Derive r, the sum of all the reflected terms on the left of the
systema) got it right b) tried
2z zik d i k dtt e r r e zik dtt e
t r’
Eo
t’ r