1. Wave Optics
• Geometric Optics – Light rays move in
6.1 Polarization straight lines.
– Okay for interaction with objects much larger
than the wavelength
Polarized Light
Polarization by absorption
• Wave Optics – Light propagates as
Polarization by reflection spherical waves.
Polarization by scattering – Describes interactions with objects with the
same size as the wavelength.
Wave Properties of Light Polarization
Wave optics or Physical optics is the study • Polarized light has it E field in one direction.
of the wave properties of light. • Light is normally unpolarized
• Light can be polarized by several different
Some wave properties are: processes
Interference, diffraction, and polarization. – Absorption – Polaroid filter
– Reflection – Brewster’s angle
These properties have useful applications in
– Scattering – Light from the sky
optical devices such as compact discs, • Polarized light has many applications
diffraction gratings, polarizers. – Polaroid sunglasses, Polarization microscopy, liquid
crystal display.
Light is a transverse wave Polarized and un-polarized light
A plane wave with Electric field in the y direction
Unpolarized Light Polarized Light
has E field at any instant has E field in a
can have E in any direction. certain direction
1

2. Polarized light passing through a
Polarization by absorption
polarizer at angle θ
θ parallel component
Oriented molecules Eo
Ey Eo cosθ transmitted
absorb light with E
along y direction Eo cosθ
Ez Esinθ
un-polarized
Ez
polarized But I ∝ E2
Polaroid film
Therefore transmitted intensity
for an ideal polarizer the intensity 1 I = Iocos2θ
I polarized = Iunpolarized
is reduced by 1/2 2
Polarized light passing though
a polarizer Two polarizers
The angle of I=Io cos2θ
polarization changes
Io
Io cos2θ
Decrease in intensity when polarized light passes θ=45o θ=90o
through a polarizer
θ=0
Law of Malus “Crossed-polarizers”
I= Io cos2θ
Example Polarization by reflection
Un-polarized light can be polarized by
Un-polarized light is incident upon two polarizers reflection at a specific polarization angle θp
that have their polarization axes at an angle of (Brewster’s angle)
45o. If the incident light intensity is Iowhat is the
final intensity? 45o
θp θp Fully polarized
Un-polarized
n1
Io Io Io
cos2 θ
2 2 n2
n θ2
Io I ⎛ 1⎞ I tanθ p = 2
I= cos2 45 = o ⎜ ⎟ = o n1
2 2 ⎝2⎠ 4
2

3. Polarization by reflection Example
Suppose you wanted to have fully polarized light
E is by reflection at the air water interface. What
⊥to plane conditions would you use? What would be the
of incidence direction of the polarized E field?
Angle of incidence equal
This E θp n1 =1.00 to the polarizing angle
component
is absent • n2
• tan θp = = 1.333
n1
n2 =1.333 θp = 53o
Reflected beam is Reflected beam is E would be ⊥ to the plane of
Partially polarized Fully polarized incidence.
Polarization by reflection Polarization by scattering
A transverse wave has no E field in the
direction of propagation
Scattering particle has oscillations partially polarized
in the plane ⊥ to the direction of propagation
scattered light is partially
polarized with E field ⊥ to
no filter polarizing filter observer the direction of propagation
The reflected light is polarized - of the incident light
Polarization of light by air Polarization of scattered light
Light from the sky is partially polarized
no filter polarizing filter
3

4. Applications- Crossed Polarizers
Crossed polarizers used to detect materials that rotate
the plane of polarized light (optically active materials) including
many biological materials and materials under mechanical stress
Applications – Liquid crystal display
(LCD)
Oriented molecules
rotate the plane of
the polarized light
When an electric field
is applied the molecules
reorient so that the
light is not rotated.
4