a what you learned in 123 “normal incidence” we have complete picture in 471: all angles...
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Equations we must write: Unknowns we want to solve for: Any one of these gives us: Frequency cons. Reflection law Snell’s law Amazing!TRANSCRIPT
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A
What you learned in 123
1 2 1 2 2 1
1 2 1 2 2 12
1
refl trans
i i
E Er t
E En n k k v v
rn n k k v v
R r T R
. .
; –
“Normal incidence”
We have complete picture in 471:• All angles• Polarization (refers to E direction, not to polarized atoms)• Complex index (next time)
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Break linear polarization into two components
Plane of incidencevs interface plane
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Equations we must write:
Unknowns we want to solve for:
Any one of these gives us:• Frequency cons.• Reflection law• Snell’s law
Amazing!
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n=2n=1
Huygen’s principle and Snell’s law: Each point of space or matter can be imagined as a point source of forward semicircular waves. The sum of the circular wavefronts gives a wavefront of the real wave.
http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=16
Points farther down the interface are ahead in phase.They emit waves with different wavelength. wave turns
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Photon picture of Snell’s lawPhoton energy
Photon momentum
From our findings for k and w across the interface, which is not conserved?a) Photon energyb) Photon momentum perpendicular to
interfacec) Photon momentum parallel to interfaced) All are conservede) None are conserved
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The B field that must accompany Etp is_______.
a) Parallel to Etp
b) antiparallel to Etp
c) Into the paged) Out of the pagee) Along k
ook EB
w
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The B field that must accompany Etp
has magnitude _____a) nEt
p/cb) ncEt
p
c) cEtp/n
d) Etp/(cn)
e) Etp/c
ook EB
w
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i tt i i t i i t t
st i i t i t i i t t
n nr
n n
sinsin cos sin cos cos cossin cos sin cos sin cos cos
2 2 2t i t i i i
st i i t i t i i t t
nt
n n
sin cos sin cos cos
sin cos sin cos sin cos cos
i tt t i i i t t i
pt t i i i t i t t i
n nr
n n
tancos sin cos sin cos coscos sin cos sin tan cos cos
2 2 2i t i t i i
pt t i i i t i t i t t i
nt
n n
cos sin cos sin cos
cos sin cos sin sin cos cos cos
Fresnel Coefficients
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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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2t t
i i
nT t
n
coscos
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References
Wave amplitude, energy and N-photons
The beam is focused to an area A. What is the average amplitude of the E-field?
2
2o
o
n cI E
2
2o
field on
u E
I uv
A laser puts out power P (watts): How many photons per second leave it?
What is the photon density photons/m3 in this case?
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Suppose we have a laser beam entering a piece of glass at normal incidence. Assume it’s anti-reflection coated so we can ignore reflection.
In the glass the photons move slower.
The energy density u is ____ than in air.a) largerb) smallerc) the same
Photon picture