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.

polaroid polaroid reflectionreflection birefringencebirefringence

Producing of polarized lightProducing of polarized lightphenomenaphenomena

Polarization of lightPolarization of light

applicationapplication

Chap 34 Polarization of light

Chap 34 The nature and propagation of light

Key Terms:Optics Physical opticsWave front RayReflection RefractionSpecular/diffuse reflectionIndex of refraction Critical angleTotal internal reflection Linear polarizationPolarizing filter DichroismPolarizing axis Malus’s lawBrewster’s lawBirefringence

transverse waveLongitudinal wave

1. polarization

1.1 What is polarization?

Polarization is characteristic of all transverse waves

1.2 polarization status of light

Unpolarized light: natural light

Polarized light:

Linearly polarized light

partial polarized light

circular polarized light

elliptic polarized light

E

When a wave has only y-displacements (or z), we say it is linearly polarized in this direction.

y

z x

v

y

z x

v

E

E

Linearly polarized 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.

yz

v

x

natural light (unpolarized light)

y

z

partially polarized light

• Linearly polarized light “+” natural light

circular and elliptical polarized light

E

E

2. How to get polarized light2. How to get polarized light

Polarization by polaroid

polarization by reflection

polarization by birefringence

2.1 Polarization by polaroid

.

Nature light

Polarizing axis

0I2

10I

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=I

0 cos 2

I=(Eocos )2 = Iocos2

Eo

Io= Eo2

Eocos

• 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 )

2

II 0 2

0 cosII

2

I)A( 0

4

I)B( 0

8

I3)C( 0

16

I3)D( 0

8

I330cos)

2

I(I 0020

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.

030

Solution:

0I 2I0

1I

2I

221 cosII

2

1

)(cos)cos2

1( 22

21 III

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.

Solution:

2.2 polarization by reflection

pp

b

an

bn

bn

anpp

b

For most angles of incidence:

Reflected light: partially polarized (>//)

Refracted light: partially polarized (//>)

At one angle of incidence, called the polarizing angle:

Reflected light: completely polarized ()

Refracted light: partially polarized (//>)

: reflected and refracted

//: only refracted

Brewster’s law

bn

anpp

b

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: sinp / sinb=nb / na

Then: tanp =nb / na

The natural light is refracted again and again by a stack of glasses, with incidence angle equals the polarizing angle.

Discussion:

2) tell the difference of critical angle and brester angle

total internal reflection.

1) Reflected light: completely polarized ()

Refracted light: partially polarized (//>)

reflected ray is perpendicular to refracted ray

1

2sinn

n

2

1

n

ntg brester angle

critical angle

Polarization by reflection is the reason polarizing filters are widely used in sunglasses, cameras…

draw the reflected light and refracted light

n1

n2

i i

n1

n2

n1

n2

n1

n2

i

i0 i0 i0

,ii 01

20 n

narctgi

n1

n2

n1

n2

2.3 polarization by birefringence

• Birefringence: the material has different indexed of refraction for different directions of polarization. Here are some examples:

Extraordinary light

Ordinary light

Calcite crystal (方解石晶体 ):

3. scatter3. scatterWhy the sky looks blue,and sunsets are red?