1. Office Hours Office hours are posted on the website. –Molly: Tuesdays 2-4pm –Dr. Keister: Wednesdays 10am-12 –Prof. Goldman: Wednesdays 2-3:30pm All office hours are in the help room downstairs If none of these work and you need extra help before the exam, please email one of us as far in advance as you can

2. Scattering and Polarization Adding vectors Polarization by reflection Polarization by scattering 3D movies Polarizers and analyzers

3. Adding Vectors We can decompose any polarization direction into an x- component and a y-component x-component y-component X Y P Q But we don’t have to use x and y. We can use any axes that are perpendicular to one another

4. Adding Vectors Now a polarization that was just x in the first set of axes has two components, p and q x-component y-component X Y P Q q-component p-component

5. Concept Question Which polarization has the largest x-component? x y x y x y ABC

6. Electromagnetic Waves The polarization is defined as the direction of oscillation of the electric field Polarized “along the z-axis”

7. Polarizing Filters

8. Polarization by Reflection Incident ray Reflected ray Transmitted (refracted) ray AIR GLASS Review reflection and refraction:

9. Brewster’s Angle Consider the special case where the transmitted and reflected rays are at right angles to one another Incident ray Reflected ray Transmitted (refracted) ray AIR GLASS

10. Brewster’s Angle We can decompose the incident light into two parts: polarized in the plane of the figure, and perpendicular to the figure. We will consider the part in the plane of the figure Incident ray Reflected ray Transmitted (refracted) ray AIR GLASS Electric field oscillation

11. Brewster’s Angle The oscillating charges in the glass are what produce the reflected ray. However, they cannot radiate along their direction of travel. Thus there CANNOT be a reflected ray in this special situation. Incident ray Reflected ray Transmitted (refracted) ray AIR GLASS Electric field oscillation

12. Brewster’s Angle This special angle of incidence is called “Brewster’s Angle” For light incident at this angle, there is not reflected ray polarized in the plane of the figure. Thus the reflected light is polarized perpendicular to the plane of the figure

13. Brewster Windows This effect is also used when you have polarized light and you don’t want any of it to be reflected Laser light is typically polarized, so this can be used inside a laser to make sure we aren’t losing energy to surface reflections Brewster window

14. Polarizing Sunglasses and Glare Sunglasses lenses with a polarizer in them can eliminate specular surface reflections

15. Polarizing Sunglasses and Glare The light coming from everywhere else in the scene will be unpolarized Half of it will be transmitted by the glasses

16. Concept Question Which polarization should sunglasses reject to eliminate glare from water puddles and other shiny surfaces? Assume the surface is horizontal, as shown in the diagram. A.Sideways B.Up and down The reflections from the horizontal puddle will be polarized horizontally. So to eliminate glare from this surface, we want to reject the horizontal polarization, thus rejecting the surface reflections

17. Polarizing Lenses: Example Without Polarizing lenses With Polarizing lenses

18. Polarizing Camera Filters

19. Polarization by Scattering Consider the following analogy: If we wiggle the rope up and down, a wave is generated in the cross rope If we wiggle the rope sideways, there is no wave generated in the cross rope

20. Polarization by Scattering If we wiggle the rope at an angle, the resulting wave in the cross rope will only be up and down The resulting wave will be linearly polarized, even though the “incident wave” was not Sideways component Does nothing Up and down component Creates new wave in rope X Y Incident wave

21. Polarization by Scattering Light from the sun is unpolarized. It hits particles in the atmosphere, causing them to oscillate The oscillating particles then radiate light X Y Z

22. Polarization by Scattering There will be no oscillation in the z direction The wave traveling in the y-direction will thus be polarized in the x-direction X Y Z

23. Concept Question Along which axis will the wave traveling in the x- direction by polarized? (views E3 and E4, circled) A.X B.Y C.Z X Y Z

24. Polarization by Scattering Recall the we see the blue in the sky because of light scattered by the atmosphere The light coming from points in the sky 90°from the sun will be linearly polarized When the sun is overhead, the sky near the horizon will be most polarized

25. Polarization by Scattering When the sun is at the horizon, the point of maximum polarization will be straight up in the sky. The part of the sky directly opposite the sun will be unpolarized, as will areas of the sky very near the sun Other areas of the sky will be partially polarized

26. Camera Filters and the Sky

27. 3D Movie Projection and Viewing 3D movies are actually stereograms, which create the illusion of depth by showing your eyes slightly different images This was originally done using glasses with red and cyan lenses and pictures that looked like this:

28. 3D Movie Projection and Viewing Modern 3D movies are projected using different polarizations instead of different colors. Without glasses, the images look like this:

29. 3D Movie Projection and Viewing The two overlapping images are actually projected through a polarizing filter, alternating in rapid succession The glasses separate the polarized light and each eye sees something different, creating the illusion of depth The system actually uses circularly polarized light, so the glasses won’t work like your polarized sunglasses

30. Polarizers and Analyzers Polarizing filters can also be used to detect the presence of polarized light When used in this way, it is called an analyzer How is this useful?

31. Polarizers and Analyzers By changing the relative orientation of the two polarizing filters, the intensity of the light that makes it all the way through can be adjusted

32. Polarizers and Analyzers

33. This is useful for adjusting the intensity of light without changing the parameters of the beam An aperture reduces the size of the beam Dimming a light bulb often changes the color temperature Filters are impossible to adjust continuously This is very common way to control laser beam intensity

34. Next Time We will do a review, I still haven’t figured out the exact format I will put together a study guide for the material covered since the last exam I will send out emails with this information, so don’t delete them!