Transcript 7- Polarization

2nd & 3th N.U.T.S. Workshops
Gulu University
Naples FEDERICO II University
7 – Polarization
2nd & 3th NUTS Workshop ( Jan 2010)
Transverse Waves Exhibit Polarization Effect
Oscillation of a rope in a plane
along the slit, it passes
through the slit
Oscillation of a rope in a plane
perpendicular to the slit, it
does not pass through the slit
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E.M. Wave Polarization
… is a property that specifies the electric field (E) direction.
Why do we pick the electric field out of the two (E, B)? Aren’t they on an equal footing?
z
x
z
x
Both E.M. waves are propagating in the +z direction but have different
polarization. The polarization direction is that of the Electric field: in (a) it is
vertically polarized (i.e. E is along y axis); in (b) it is horizontally polarized (i.e.
E is along x axis). Unpolarized light would be a mix of such waves, with their E
oriented at random in many different directions.
They are on an equal footing, but it is mostly the electric field, which interacts with matter
– atoms, electrons, nuclei.
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Polarization -2
EM waves from a TV tower are perfectly polarized – the Electric field has a very
well defined direction, which stays always the same.
In contrast, the light coming from the Sun or from a light bulb is unpolarized.
What does it mean unpolarized? Doesn’t the electric field have some direction?
It certainly does at every instant. BUT this direction does not stay constant and
changes very rapidly and randomly.
So, averaging over any reasonable time interval you do not find any particular
polarization!
polarized
unpolarized
The frequency of light (at the center of its spectrum) is about 5×1014 Hz, which
means 5×1014 wave crests per second. If the polarization changes once every 500
crests it will still change 1012 times per second. Too fast to be detectable!
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Polarizing the Light -1
Any way to make a polarized wave (light) out of unpolarized wave?
Yes, but it is going to cost us some intensity loss… (No free meals…)
We can use a polarizer - a piece of material, whose molecular or crystal
structure has a preferred direction called the transmission axis.
A polarizer “decomposes” the e.m. wave into a component with the
electric field, E║, parallel to the transmission axis, which passes through,
and a component with the E┴ field perpendicular to the transmission axis,
which gets totally absorbed.
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Polarizing the Light - diff. view
Natural light incident on a linear polarizer: the transmitted
light is only the light component polarized in the plane
defined by transmission axis and light propagation
direction
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Polarizing the Light -2
 

E0
E
z
The magnitude of the component of
the electric field along the
transmission axis :
E  E0 cos 
Intensity of the wave is proportional to
the square of the amplitude
I~E
2
I  I 0 E / E  I 0 cos 
2
2
0
2
Law of Malus
transmission axis
In an unpolarized wave the angle  changes randomly
After passing through a polarizer the average intensity is
I  I 0 cos   I 0 / 2
2
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The light gets polarized, but it
looses 1/2 of its intensity...
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Crossing the polarizers
If the axis of a polarizer is set at  = 90° to the axis of polarization:
cos  0
no light is passing through!
A system of two crossed polarizers never lets any light through.
Whatever passes through the first one is blocked by the second.
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Stack of polarizers
What happens to
the intensity, I,
and axis of
polarization of Io
unpolarized light
upon passing
through three
polarizers (fig.) ?
E
I1  I 0 / 2
I
I1
I2
I 2  I1 cos 2 25
I 3  I 2 cos 2 (70  25)
I = I3
 I 2 cos 2 45
I 3  I 0 1 / 2  cos 2 25  cos 2 45  0.205  I 0
Without the second polarizer:
I 3  I 0 1 / 2  cos 2 70  0.058  I 0
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Types of Polarization
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Polarization by Reflection from Dielectric Media
It’s the most common source of polarized light
Linear Polarization States
θi
Wave
pointing
to you
n1
n2
β
Wave
moving
this
direction
The reflected beam is partially polarized, in a
plane perpendicular to the incidence plane.
For the incidence angle θi = θB (Brewster's angle) such that the angle
between the reflected and refracted beam, β, is 900, the reflected ray is
totally polarized !
n
tan  B 
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n1
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Brewster's Angle Exercises
N1: Derive the Brewster's angle formula, tan(θB )=n2/n1,
from the reflection and refraction laws.
N2: Which is the Brewster's angle for the air - water
(n=1.33) surface ?
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Polarized Skylight
Skylight is polarized if the Sun is to your side.
Right-angle scattering
is polarized
This polarizer transmits
horizontal polarization
(of which there is very little).
Polarizer transmitting vertical polarization
Multiple scattering yields some light of the other polarization. In clouds, much
multiple scattering occurs, and light there is unpolarized.
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