12.1: Polarization
I1=.5I0
I2=I1cos2(theta2-theta1)
I3=I2cos2(theta3-theta2)
~~
I2=.5I0cos2(theta2-theta1)
I0/I2=1/.5cos2(theta2-theta1)
~~
I3/I2 = I3/I0 * I0/I2
~~
theta3 = theta2 ± cos-1(sqrt(I3/I2))

12.2: Two Polarizers
a) I1=.5I0
b) E1/E0=1
c) LP along y-axis
d) I2=I1cos2(theta1-theta2) ; I1=.5I0 ; theta1=90°
   I2/I0=.5cos2(90°-theta2)

12.3: Light Passing Through Triangular Medium

First Interface: n1sin(thetaincident) = n2sin(thetarefracted)
Second Interface: thetaincident = thetarefracted)
Third Interface: n1sin(thetaincident) = n2sin(thetarefracted)
~~
nairsin(thetain) = n2sin(theta1) :: solve for theta1
theta2 = 90° - theta1
theta3 = theta2
theta4 = 45° - theta3
n2sin(theta4) = nairsin(theta5) :: solve for theta5
thetaout = 45° + theta5

12.4: Ruler In a Tank of Water
a) x1 = H*tan(theta)
b) nairsin(theta) = nwatersin(thetarefracted) :: solve for thetarefracted
   x0 = (H/2)*tan(theta)
   x1 = (H/2)*tan(thetarefracted)
   x2 = x0 + x1
c) nairsin(theta) = nwatersin(thetarefracted) :: solve for thetarefracted
   x3 = H*tan(thetarefracted)
d) tan(thetarefracted) = x4/H :: solve for thetarefracted
   nairsin(theta) = nliquidsin(thetarefracted) :: solve for nliquid
   v = c / nliquid