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Wave Optics
A knowledge of the properties
of light allows us to understand the
blue color of the sky and the design
of optical devices…
Polarization
Interference
Diffraction
Wave Optics
Why is the sky blue?
Why is sunset red?
Dual Nature
 In Newton’s time: light consisted of streams of
particles.
 In 1873, Maxwell predicted the light is a sort of
electromagnetic waves.
 In 1887, Hertz showed light is an electromagnetic wave.
 Thomas young also prove the wave properties of light.
 Particle Model :
The straight line traveling of light,
reflection and refraction, emission
and absorption of light.
 Wave Model :
polarization, interference and
diffraction of light.
Chap 34 Polarization of light
Polarization of light
phenomena
Producing of polarized light
polaroid
reflection
application
birefringence
Chap 34 The nature and propagation of light
Key Terms:
Optics
Physical optics
Wave front
Ray
Reflection
Refraction
Specular/diffuse reflection
Index of refraction
Critical angle
Total internal reflection
Linear polarization
Polarizing filter
Dichroism
Polarizing axis
Malus’s law
Brewster’s law
Birefringence
1. polarization
1.1 What is polarization?
Polarization is characteristic of all transverse waves
Longitudinal wave
transverse wave
1.2 polarization status of light
Unpolarized light: natural light
Linearly polarized light
partial polarized light
Polarized light:
circular polarized light
elliptic polarized light

E
Linearly polarized light
When a wave has only y-displacements (or z), we
say it is linearly polarized in this direction.
y
z

v

E

v
y
x
z

E
x
natural light (unpolarized light)
• The waves emitted by any one molecule may be
linearly polarized, but any actual light source
contains a tremendous number of molecules with
random orientations, so the emitted light is a
random mixture of waves linearly polarized in all
possible transverse directions.
z
z
y

v
y
x
partially polarized light
• Linearly polarized light “+” natural light
circular and elliptical polarized light

E

E
2. How to get polarized light
Polarization by polaroid
polarization by reflection
polarization by birefringence
2.1 Polarization by polaroid
Polarizing
I 0 axis
Nature light
1
I0
2
Linearly
polarized
light
.
I ?
 Malus’s law
If the intensity of incident polarized light is I0, and
the polarizing axis makes an angle  with the
displacement of the incident light, the intensity
of the light transmitted through the polarizer is:
I=I0 cos 2
Eo
Io=
Eo2

Eocos 
I=(Eocos  )2 = Iocos2 
• Polarizing filter can absorb one of the polarized
components, and transmit the components that is
polarized parallel to a certain axis ,called the
polarizing axis. And the transmitted intensity : I=Io
cos 2 .(for natural light: I=Io /2 )
I0
I
2
I  I 0 cos 2 
Example: The natural light has intensity I0. Find the
intensity transmitted by the second polarizer if the
angle between the axes of the two filters is 300.
I0
( A)
2
I0
(B)
4
3 I0
(C )
8
3 I0
(D)
16
30 0
I0
I0 2
Solution:
I0
3 I0
2
0
I  ( ) cos 30 
2
8
Example: The incident light is a mixture of natural
light with intensity I1 and linear polarized light with
intensity I2 , find the transmitted intensity by the
second polarizer.
1
I  ( I1  I 2 cos2  )  cos2 (    )
2
Solution:
I1
I2

1
I 1  I 2 cos 2 
2

2.2 polarization by reflection

For most angles of incidence:
p p
Reflected light: partially polarized (>//)
Refracted light: partially polarized (//>)
At one angle of incidence, called the
polarizing angle:
b
na
nb

Reflected light: completely polarized ()
Refracted light: partially polarized (//>)
: reflected and refracted
//: only refracted
p p
na
b
nb
Brewster’s law
Brewster discovered that when p equals the
polarizing angle, the reflected ray and the refracted
ray are perpendicular to each other.

From the polarizing angle:
sin b= cos p
From the law of refraction:
sinp / sinb=nb / na
Then:
tanp =nb / na
p p
na
b
nb
The natural light is refracted
again and again by a stack of
glasses, with incidence angle
equals the polarizing angle.
Discussion:
1) Reflected light: completely polarized ()
Refracted light: partially polarized (//>)
reflected ray is perpendicular to refracted ray
2) tell the difference of critical angle and brester angle
total internal reflection.
n2
sin 
n1
n1
tg 
n2
critical
angle
brester angle
Polarization by reflection is the reason polarizing
filters are widely used in sunglasses, cameras…
i
n1
i
n2
i0
n1
n2
n1
n2
i0
n1
n2
draw the reflected light and refracted light
i  i0 ,
i
n2
i0  arctg
n1
n1
n2
i0
n1
n2
2.3 polarization by birefringence
• Birefringence: the material has different indexed of
refraction for different directions of polarization.
Here are some examples:
Calcite crystal (方解石晶体):
Extraordinary light
Ordinary light
3. scatter
Why the sky looks blue,and sunsets are red?