R, T for complex index
When k is complex: metals and absorbing dielectrics.
ni cosi  nt cost
rs 
ni cosi  nt cost
2ni cosi
ts 
A
ni cosi  nt cost
k still determines decay of wave
Meaning of complex r and t?
Brewster’s angle
Occurs only for ___ polarization
A
Brewster’s angle
Occurs when reflected and transmitted rays are _____,
but only for ___ polarization
rp  
rs  
tan i  t 
p-polarization:
s-polarization:
tan i  t 
sin i  t 
sin i  t 
Dipole radiation
interpretation of
why R0
A
Sunlight is essentially unpolarized.
Why are the best sunglasses polarized?
P1. What direction do you want to
orient the transmitting axis of the
polarizer in your sunglasses to let
through only the polarization that
reflects the least from the water?
a) Horizontal
b) Vertical
Apparent vs true depth
Waves at an Interface, (Quicktime format 02:46)
P- and S-Polarized Reflection and Transmission
(Quicktime format 01:21)
Glass to air interface (internal reflection)
Fresnel’s coefficients:
ni  nt
Total internal reflection
A
Notice internal Brewster’s angle
is the ______________ of the
external one.
Phase of reflected E-fields come from sign of r
P2. Check Phy123 rule: “180 degree reflection phase change occurs______”
a) going from high to low index at all angles
b) going from low to high index at all angles
c) rule changes at Brewster’s angle for one polarization
d) rule changes at Brewster’s angle for both polarizations
R
Rs s r
p
rs
RRpp
100% reflectors without metal
And they reflect back to the light source!
Can you do anything from the
outside to destroy the TIR?
Total internal reflection
nt
sinc 
ni
Derivation from Snell’s law:
Above this angle,
sint  ___
A
cost becomes________
r becomes________
2
R  r  r * r  ________
Simple way to think about complex functions
(probably doesn’t help much in using them)
sin   
cos   1 

3
3
2
2



5
5
4
4
 ...
 ...
A
In TIR the wave decays not from ik, but from i cos 
Photon picture of TIR
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