Properties of

Light / EM waves

Polarization

Why is that?

In many cases light is radiated/scattered by oscillating electric dipoles.

+

–Intensity lobe

Maximum intensity

Less intensity

No radiation along direction of motion!

Geometric Optics

• So far EM waves in vacuum

• What happens to EM waves (usually light) in different materials?

• Restriction: waves whose wavelength is much shorter than the objects with which it interacts.

• Pretend that light propagates in straight lines, called rays. • Our primary focus will be on the REFLECTION and

REFRACTION of these rays at the interface of two materials.

incident ray

reflected ray

refracted ray

MATERIAL 1

MATERIAL 2

Reflections…

How does light interact with matter?A simple description

• “Charge on spring” description of electrons ‘bound’ to atoms in materials

driven charges re-emit waves that are out of phase with incident wave

o

“natural” or “resonant” frequency of charge on spring

light frequency

• Light interacts with matter by causing internal charges in the material to oscillate

• Due to inertia, “bound” charges in a material respond sluggishly to incident light

Back to capacitors!

• Capacitor with vacuum between plates

• Capacitor with dielectric between plates

– magnitude of E-field is reduced by “relative dielectric constant”

• Why?– dielectric polarization…...

relative dielectric constant can be large

vacuum

+ + + + + + + +

- - - - - - - -0

E

dielectric

+ + + + + + + +

- - - - - - - -0

E

• How are Maxwell’s eqns in matter different? ≡

≈ (for most materials)

• Therefore, the speed of light in matter is related to the speed of light in vacuum by:

Index of Refraction• The wave incident on an interface can not only reflect, but it

can also propagate into the second material.

• The speed of an electromagnetic wave is different in matter than it is in vacuum.

• from Maxwell’s eqns in vacuum:

The index of refraction is frequency dependent: For example, in glass

nblue = 1.53 nred = 1.52

00

1

c

n

cv

where n = “index of refraction” of the material: 1 n

0 0

1 1 cv

Refraction

• How is the angle of refraction related to the angle of incidence?– Unlike reflection, 1 cannot equal 2 !!

» Why?? Remember v = f» n1 n2 v1 v2

but the frequencies (f1, f2) must be the same the wavelengths must be different!

Therefore, 2 must be different from 1 !! 1

2

n1

n2

2

1

1

2

2

1

2

1

n

n

v

v

Snell’s Law• From the last slide:

1 1

1

2

L n1

n2

1

2

2 2 2

The two triangles above each have hypotenuse L

But,

1

2

2

1

2

1

n

n

v

v

1

1

2

2

sinsin

L2

1

2

1

sin

sin

2211 sinsin nn 1

2

2

1

2

1

n

n

v

v

Huygen’s Principle

Dispersion

Inde

x of

re

frac

tion

frequency

ultravioletabsorption

bands

1.50

1.52

1.54

white light

prism

Split into Colors

Dispersion in more detail: Effects of wavelength dependence of n

• Dispersion: n depends on wavelength!

nblue > nred

vblue < Vred

Total Internal Reflection– Consider light moving from glass (n1=1.5) to air (n2=1.0)

I.e., light is bent away from the normal.as 1 gets bigger, 2 gets bigger, but 2 can never get bigger than 90 !!

In general, if sin 1 > (n2 / n1), we have NO refracted ray; we have TOTAL INTERNAL REFLECTION.

For example, light in water which is incident on an air surface with angle 1 > c = sin-1(1.0/1.5) = 41.8°will be totally reflected. This property is the basis for the optical fibers used in communication.

incident ray

reflected ray

refracted ray

2

1 r

GLASS

AIRn2

n11

sin

sin

2

1

1

2 n

n

121

Examples: refraction at water/air interface

• Diver’s illusion

Diver sees all of horizonrefracted into a 97°cone

97º

Why is the sky blue?• Light from Sun scatters off of air particles–“Rayleigh scattering”

– Rayleigh scattering is wavelength-dependent.– Shorter wavelengths (blue end of the visible spectrum) scatter more.

• This is also why sunsets are red!– At sunset, the light has to travel through more of the atmosphere.– If longer wavelengths (red and orange) scatter less…– The more air sunlight travels through, the redder it will appear!– This effect is more pronounced if there are more particles in the atmosphere (e.g., sulfur aerosols from industrial pollution).

http://www.walter-fendt.de/ph14e/emwave.htm

Polarization of Light

Unpolarized Light• We have primarily been considering light that has

a definite polarization (e.g., linear or circular). Most sources – a candle, the sun, any light bulb – produce light that is unpolarized :

– it does not have a definite direction of the electric field

– there is no definite phase between orthogonal components

– the atomic or molecular dipoles that emit the light are randomly oriented in the source

– the intensity of light transmitted through a polarizer is always half the intensity of the unpolarized input, regardless of the orientation of the polarizer

(though of course the output is polarized!)

These are all equivalent ways of describing the same thing.

Polarization

http://www.launc.tased.edu.au/online/sciences/physics/Polari.htm

Absorption

Polarization by absorption

http://www.launc.tased.edu.au/online/sciences/physics/Polari.htm

Polarization by absorption

http://www.colorado.edu/physics/2000/applets/lens.html

Applications

• Sunglasses– The reflection off a

horizontal surface (e.g., water, the hood of a car, etc.) is strongly polarized. Which way?

– A perpendicular polarizer can preferentially reduce this glare.

Double Refraction or Birefrigence

Double Refraction or Birefrigence

Reflection • The angle of incidence equals the angle of reflection i =r ,

where both angles are measured from the normal:• Note also, that all rays lie in the “plane of incidence”.

i r

• Why?

» This law is quite general; we supply a limited justification when surface is a good conductor (reasonable restriction since reflection is dominant in this case)

First consider a wave hitting a conductor at normal incidence:

cos( )xE E kz wt

The electrons on the surface of the metal will experience a force F=eE → acceleration → radiation in .z

e

Brewster’s Law

http://micro.magnet.fsu.edu/

primer/java/polarizedlight/brewster/index.html

n = sin(i)/sin(r)

= sin(i)/sin(90-i)

= tan(i)

Reflection

http://www.launc.tased.edu.au/online/sciences/physics/Polari.htm

L23:Polarization by Scattering• Suppose unpolarized light encounters an atom and scatters

(energy absorbed & reradiated). – What happens to the polarization of the scattered light?

– The scattered light is preferentially polarized perpendicular to the plane of the scattering.

x

y

z

» For example, assume the incident unpolarized light is moving in the z-direction.

» Scattered light observed along the x-direction (scattering plane = x-z) will be polarized along the y-direction.

» Scattered light observed along the y-direction (scattering plane = y-z) will be polarized along the x-direction.

This box contains atoms which “scatter” the light

beam

Scattering

Applications

• Polarized sky– The same argument applies to light scattered off the sky:

Which photo was taken with a polaroid?

http://www.colorado.edu/

physics/2000/applets/polarized.html

http://home3.netcarrier.com/~chan/EM/PROGRAMS/POLARIZATION/

Application: LCD Display

END