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