1. Polarization of Electromagnetic Waves
Polarization is a measure of the degree to which the electric field of an electromagnetic wave oscillates preferentially along a particular direction.
Linear combination of many linearly polarized rays of random orientations
components
partially polarized
linearly polarized
unpolarized
Looking at E head-on
unequal y- and z-amplitudes
equal y- and z-amplitudes

2. Polarizer: polarization by absorption
An electric field component parallel to the transmission axis is passed by a polarizer; a component perpendicular to it is absorbed.
transmission axis
So if linearly polarized beam with E is incident on a polarizer as shown,
Law of Malus
Zero if =/2, I0 if =0
If unpolarized beam is incident instead,
Polarization can rotate in time if linearly polarized beams of different phases are combined.

3. Quiz Question 1
A beam of un-polarized lights with intensity I is sent through two polarizers with transmission axis perpendicular to each other. What’s the outgoing light intensity?
½ I
2 I
1.5 I

4. Example: two polarizers
This set of two linear polarizers produces LP (linearly polarized) light. What is the final intensity?
P1 transmits 1/2 of the unpolarized light:
I1 = 1/2 I0
P2 projects out the E-field component parallel to x’ axis:
= 0 if  = /2
(i.e., crossed)

5. Intensity
When unpolarized light is transmitted through a polarizer, the transmitted intensity is:
I1 = ½ I0
When polarized light is transmitted through a polarizer, the transmitted intensity is:
I2 = I1 cos2θ

6. Quiz Question 2
Unpolarized light of intensity I0 is sent through 3 polarizers, each of the last two rotated 45 from the previous polarizer so that the last polarizer is perpendicular to the first. What is the intensity transmitted by this system?
a) 0.71 I0
b) 0.50 I0
c) 0.25 I0
d) I0
e) 0

7. Polarization by reflection
When initially unpolarized light reflects from a boundary, it is possible for the reflected beam to become polarized
The requirement is that the reflected beam and transmitted (refracted) beam be  one another
Since the incident angle and the reflected angle must be equal, it can be shown that the necessary angle for incidence is:
tan θB = n2/n1
θB = Brewter’s angle

8. Polarization by reflection

9. Example: Sunglasses cut down glare
transmission axis

10. Quiz Question 3
Unpolarized light of intensity I0 is sent through 3 polarizers. The second one is rotated 90 from the first polarizer, but the last one is again aligned in the same direction as the first. What is the intensity transmitted by this system?
a) 0.71 I0
b) 0.50 I0
c) 0.25 I0
d) I0
e) 0

11. Reflection from Fermat’s Principle
The path taken by light traveling from one point to another is such that the time of travel is a minimum.

12. Refraction from Fermat’s Principle
Snell’s law

13. Quiz Question 4
A light ray makes an angle of 42º with the normal to a glass-water surface on the glass side of the surface. The angle q in the water is
42º
36º
63º
49º
27º