Polarization Updated 2014Nov17 Dr. Bill Pezzaglia Light & Optics

Outline 2 Linear Polarization Polarization Detection Hertz Waves Linear Polarization Modes Polarization by Reflection Polarization Detection Detecting polarized Light (Malus’ Law) Optical Activity Birefringence Circular Polarization Quarter Wave Plate Left & Right Circular Polarized Light Detecting Circular Polarized Light (3D movies!) Fresnel’s Equations Fresnel’s Reflection Equations What we measure in lab References

Linear Polarized Light Polarization by Reflection A. Linear Polarization 3 Hertz Waves Linear Polarized Light Polarization by Reflection

1. EM Hertz Wave Equation 4 (a) 1865 Maxwell shows his equations predict that electromagnetic waves can exist in vacuum (note E & B are perpendicular to each other and direction of wave)

2. Linear Polarization 5 [1812 Fresnel develops wave theory of transverse polarized light, well before the electromagnetic nature was known] light has two perpendicular linear polarizations (electric field) can be horizontal or vertical 1888 Hertz shows electromagnetic waves have transverse polarization (equivalent to “light”)

3. Polarization by Reflection 6 1808 Malus’s Law: Reflected light is often polarization 1812 Fresnel develops wave theory of transverse polarized light 1815 Brewster’s angle: at this angle of incidence the reflected light is entirely “s” polarized such that electric field is parallel to the interface surface Note: “Plane of incidence” is the plane defined by the three beams above. The normal also lies in this plane. The plane is perpendicular to the surface.

B. Detection of Polarization 7 Detection, Malus’ Law Optical Activity Birefringence

1. Detecting Polarized Light 8 Linear polarizer can be used to detect polarized light, only lets one polarization through! 1808 Malus’s Law: Linear polarized light passing through a second polarizer tilted at angle  to first will be attenuated: Hence no light gets through “crossed polarizers” (=±90°)

2. Optical Activity 9 Optically active materials can rotate the polarization If such a substance is put between “crossed polarizers” (90º angle) you will often see interesting colors.

3. Birefringence 10 1669 Erasmus Bartolinus (Denmark) discovers the birefringence (double refraction) of calcite crystals. When polarization was understood better, it was realized the two different polarizations took different paths (they are “refracted” differently, or the index of refraction is dependent upon polarization) Index of refraction: n=c/v, so the different polarizations travel at slightly different speeds.

C. Circular Polarized Light 11 Quarter Wave Plates Left & Right circular polarized Detecting circular polarized

1. Quarter Wave Plates 12 A quarter wave plate retards horizontal polarization by 90º to vertical. It can be used to make circular polarized light from linear polarized light.

2. Circular Polarized Light 13 Another type of polarized light can be left or right handed circular polarized

3. Detecting Circular Polarized Light 14 A quarter wave plate will turn circular back into linear, which can be detected by a linear polarizer

D. Fresnel Equations Fresnel Reflection Equation 15 Fresnel Reflection Equation Brewster’s angle (lab)

1. Fresnel’s equations 16 Fresnel’s equations generally show that the amount of light reflected is a function of the angle of incidence. Further, the different polarizations of light have different reflective equations. In particular, he shows that at Brewster’s angle, the “p” wave (electric field parallel to plane of incidence) has no reflectance, hence the reflected rays are entirely “s” polarized (electric field perpendicular to plane of incidence, which is parallel to surface)

2. Brewster’s Angle 17 At Brewster’s angle Rp=0. This and Snells’ law gives you: Square both, and use the Pythagorean identity. Solving, we get Brewster’s angle: (approx 56 for glass)

18 References http://www.thestargarden.co.uk/RefractionReflectionDiffraction.html http://www.olympusmicro.com/primer/lightandcolor/reflectionintro.html http://maxwell.byu.edu/~spencerr/phys442/node4.html http://en.wikipedia.org/wiki/Timeline_of_Fundamental_Physics_Discoveries http://www.sparkmuseum.com/GLASS.HTM http://keelynet.com/spider/b-103e.htm

Things to Do 19 Find tesla museum stuff Who first predicted circular polarized light? Can we make a 3D image for students using polarized light? Need two projectors? Ideally we’d use circular polarized light, but one test so far shows either the transparency projector or the screen does not preserve the circular polarization.