What you learned in 123
“Normal incidence”
r
Erefl .
Ei
Etrans.
t
Ei
n1  n2 k1  k2 v2  v1
r


n1  n2 k1 A k2 v2  v1
2
R  r ; T  1 – R
We have complete picture in 471:
• All angles
• Polarization (refers to E direction, not to polarized atoms)
• Complex index (next time)
Plane of incidence
vs
interface plane
Break linear
polarization into
two components
Unknowns we want to
solve for:
Equations we must write:
Any one of these gives us:
• Frequency cons.
• Reflection law
• Snell’s law
Amazing!
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.
n=1
n=2
Points farther down the interface are ahead in phase.
They emit waves with different wavelength.  wave turns
http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=16
Photon picture of Snell’s law
Photon energy
Photon momentum
From our findings for k and w across the interface,
which is not conserved?
a) Photon energy
b) Photon momentum perpendicular to interface
c) Photon momentum parallel to interface
d) All are conserved
e) None are conserved
The B field that must accompany Etp is_______.
a) Parallel to Etp
k  Eo
b) antiparallel to Etp
Bo 
w
c) Into the page
d) Out of the page
e) Along k
The B field that must accompany
has magnitude _____
a) nEtp/c
b) ncEtp
c) cEtp/n
d) Etp/(cn)
e) Etp/c
Etp
Bo 
k  Eo
w
Fresnel Coefficients
sin i  t  ni cosi  nt cost
sint cosi  sini cost
rs 


sint cosi  sini cost
sin i  t  ni cosi  nt cost
2 sint cos i
2 sint cos i
2ni cos i
ts 


sint cos i  sini cos t
sin i  t 
ni cos i  nt cos t
tan i  t  ni cost  nt cosi
cost sint  cosi sini
rp 


cost sint  cosi sini
tan i  t  ni cost  nt cosi
tp 
2 cos i sint
2 cos i sint
2ni cos i


cos t sint  cos i sini sin i  t  cos i  t  ni cos t  nt cos i
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 intensity
b) Beam power
c) both
d) neither
R and T from r and t
R r
2
nt cos t 2
T 
t
ni cos i
nt cos t 2
T 
t
ni cos i
Wave amplitude, energy and
N-photons
A laser puts out power P (watts): How many photons
per second leave it?
The beam is focused to an area A.
What is the average amplitude of the E-field?
What is the photon density
photons/m3 in this case?
References
u field
n o

Eo
2
2
n o c
I 
Eo
2
2
I  uv
Photon picture
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) larger
b) smaller
c) the same