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Note 30 Polarization!
!
!
The direction of the electric field in light, electromagnetic radiation, is called the direction of
polarization. most normal light sources are unpolarized. There is no preferential direction for the
electric field. A light source containing only one polarization direction is called plane polarized
light. There are many ways to produce polarized light. Three easy to find sources are reflection
from surfaces or glare, scattering of the blue light from the sun, and LED displays.!
Polarization from Transmission!
Light passing through a plane polarizer becomes plane polarized light. All a plane polarizer does
is absorb all of the light that is polarized in directions other than the direction it wants to let
through. The simplest type of polarizer to talk about is metal wire polarizer. It is just a set of metal
wires held in a certain direction.!
!
When unpolarized light strikes the wires, the electric fields of the light will try to oscillate the
electrons in the wires. A vertical oscillating electric field will attempt to shake the electrons up and
down, and it can do that since the electrons are allowed to travel up and down. However, a
horizontal oscillating electric field will not be able to shake the electrons side way since the
electrons are not allowed to travel in that direction. Therefore, the above oriented polarizer will
produce light that is horizontally polarized. It is a horizontal polarizer.!
polarizer
!
Light that is partially polarized in both directions will be partially absorbed. The amount of electric
field that is transmitted is just the component of the electric field vector that is transmitted.!
y
y
polarizer
θ
electric field
x
polarized
electric field
x
!
This component from the unpolarized electric field Emax is!
E = Emax cos(θ) !
And the intensity, called Malus’ law, is!
2
I = E 2(θ) = Emax
cos2(θ) ≡ I max cos2(θ) !
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If you start out with unpolarized light where the electric field is in equal amounts in all direction, the
plane polarizer will reduce the intensity. Light has an intensity equal to the square of the electric
field. In any direction, the intensity is!
I(θ) = E 2(θ) !
For unpolarized light, the intensity of the light is the same in all directions of polarization.!
2
I(θ) = I max = Emax
!
The total intensity is just the integral of the intensity. It is not the integral of the electric field
because superposition does not apply to these un-correlated waves. !
π
I total =
1
E 2 dθ = I max !
π ∫ max
0
With polarized light, the electric field of the transmitted light is!
E(θ) = Emax cos(θ) !
Its intensity is!
2
I(θ) = Emax
cos2(θ) = I max cos2(θ) !
The total intensity is!
π
I total
π
1
1 2 1
1 2
1
2
= ∫ Emax
cos2(θ)dθ = Emax
(θ + sin(θ)cos(θ)) = Emax
= I max !
0
π
π
2
2
2
0
The conclusion here is that a plane polarizer will reduce the intensity of unpolarized light by a
factor of 2.!
!
!
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Rotating Polarization!
Materials can change the polarization of light passing through them as well. Plastics have a
polarization property that is stress dependent. Polarized light entering plastics will have its
polarization direction rotated. Another polarizer, the exit polarizer, also called the analyzer, is used
to measure the amount of rotation. Since different colors rotate a different amount, the amount of
rotation can be seen a color difference.!
!
!
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Polarization from Reflection!
Light reflecting off of a surface is, in general, partially polarized. The picture looks like this.!
θ1 θ1
θ2
!
The colored arrows denote the primary directions of the polarizations. The amount of resulting
polarization depends on the orientation of the surface relative to the electric field. The red
polarization is perpendicular to the page so it favors re-broadcasting of the light in directions on
the page surface like an antenna. The blue polarization is in the surface so it favors rebroadcasting outside of the surface except along the refracted direction. Much more of the red
polarization can be reflected than the blue polarization.!
The conclusion is that reflected light tends to favored a polarization parallel to the surface and
perpendicular to the direction of propagation. This also means that the reflected light can be
filtered by a plane polarizer.!
!
!
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In fact, there is an angle at which the blue polarization can not be re-broadcasted in the reflected
direction. This is when the angle between the reflection and the refraction is 90°.!
θ1 θ1
θ2
!
The angle of incident at which the condition is met is called Brewster’s angle. This condition is!
θ1 + θ2 = 90° ⇒ θ2 = 90° − θ1 !
Snell’s law says this.!
n1 sin θ1 = n2 sin θ2 = n2 sin(90° − θ1 ) = n2 cos θ1
⇒
tan θ1 =
n2
!
n1
The tangent of Brewster’s angle is the ratio of the indexes of refractions. At Brewster’s angle, all
reflected light is polarized parallel to the surface. This process is also frequency dependent since
refraction is frequency dependent so different colors have slightly different Brewster’s angle.
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