Polarization

Updated 2014Nov17

Dr. Bill Pezzaglia

Light & Optics

OutlineA. Linear Polarization

1. Hertz Waves2. Linear Polarization Modes3. Polarization by Reflection

B. Polarization Detection1. Detecting polarized Light (Malus’ Law)2. Optical Activity3. Birefringence

C. Circular Polarization1. Quarter Wave Plate2. Left & Right Circular Polarized Light3. Detecting Circular Polarized Light (3D movies!)

D. Fresnel’s Equations1. Fresnel’s Reflection Equations2. What we measure in lab

E. References

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A. Linear Polarization

1) Hertz Waves2) Linear Polarized Light3) Polarization by Reflection

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1. EM Hertz Wave Equation(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)

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2. Linear Polarization

[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”)

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• 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

3. Polarization by Reflection6

nb tan

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

1) Detection, Malus’ Law2) Optical Activity3) Birefringence

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• 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°)

1. Detecting Polarized Light8

20 ][cosII

•Optically active materials can rotate the polarization

•If such a substance is put between “crossed polarizers” (90º angle) you will often see interesting colors.

2. Optical Activity9

•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.

3. Birefringence10

C. Circular Polarized Light

1) Quarter Wave Plates2) Left & Right circular polarized3) Detecting circular polarized

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

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2. Circular Polarized Light

Another type of polarized light can be left or right handed circular polarized

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3. Detecting Circular Polarized Light

A quarter wave plate will turn circular back into linear, which can be detected by a linear polarizer

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D. Fresnel Equations

1. Fresnel Reflection Equation

2. Brewster’s angle (lab)

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• 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)

1. Fresnel’s equations16

ti

ti

tis

it

itp

n

n

nR

n

nR

sinsin

coscos

coscos

coscos

coscos

2

2

2. Brewster’s Angle

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)

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ti

ti

n

n

sinsin

coscos

ni tan

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

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Things to Do •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.

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