Transcript Light & Optics

Light & Optics
Polarization
Updated 2014Nov17
Dr. Bill Pezzaglia
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Outline
A.
Linear Polarization
1.
2.
3.
B.
Polarization Detection
1.
2.
3.
C.
Quarter Wave Plate
Left & Right Circular Polarized Light
Detecting Circular Polarized Light (3D movies!)
Fresnel’s Equations
1.
2.
E.
Detecting polarized Light (Malus’ Law)
Optical Activity
Birefringence
Circular Polarization
1.
2.
3.
D.
Hertz Waves
Linear Polarization Modes
Polarization by Reflection
Fresnel’s Reflection Equations
What we measure in lab
References
A. Linear Polarization
1) Hertz Waves
2) Linear Polarized Light
3) 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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3. Polarization by Reflection
• 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
tan  b  n
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.
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B. Detection of Polarization
1) Detection, Malus’ Law
2) Optical Activity
3) Birefringence
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1. Detecting Polarized Light
• 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:
I  I 0 [cos  ]
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• Hence no light gets through “crossed polarizers” (=±90°)
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2. Optical Activity
•Optically active materials can rotate the polarization
•If such a substance is put between “crossed polarizers” (90º angle) you will
often see interesting colors.
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3. Birefringence
•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.
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C. Circular Polarized Light
1) Quarter Wave Plates
2) Left & Right circular polarized
3) Detecting circular polarized
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1. Quarter Wave Plates
A 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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1. Fresnel’s equations
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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)
 cos  t  n cos  i 
Rp  

 cos  t  n cos  i 
 cos  i  n cos  t 
Rs  

 cos  i  n cos  t 
sin  i  n sin  t
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2. Brewster’s Angle
At Brewster’s angle Rp=0. This
and Snells’ law gives you:
n cosi  cost
sin i  n sin t
Square both, and use the
Pythagorean identity.
Solving, we get Brewster’s angle:
(approx 56 for glass)
tan i  n
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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.