Transcript Hour Exam 3
Polarization Properties of Light / EM waves
Why is that?
In many cases light is radiated/scattered by oscillating electric dipoles.
Maximum intensity + Intensity lobe – 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 Our primary focus will be on the REFLECTION REFRACTION and rays .
of these rays at the interface of two materials.
incident ray refracted ray reflected 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
•
Light interacts with matter by causing internal charges in the material to oscillate
light frequency “ natural” or “resonant” frequency o of charge on spring •
Due to inertia, “bound” charges in a material respond sluggishly to incident light
driven charges re-emit waves that are out of phase with incident wave
Back to capacitors!
•
Capacitor with vacuum between plates
•
Capacitor with dielectric between plates
–
magnitude of E-field reduced by “relative dielectric constant” is
E
0
E
0 + + + + + + + + vacuum + + + + + + + + dielectric •
Why?
–
dielectric polarization…...
relative dielectric constant can be large
• • • •
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: where
n
=
c
m 1
How are Maxwell’s eqns in matter different?
m 0 0 ≡ 0 m ≈ m 0
(for most materials)
v
0 0 1 m 1 m 0 0 •
c
Therefore, the speed of light in matter is related to the speed of light in vacuum by:
v
c n
“index of refraction” of the material:
n
1
The index of refraction is frequency dependent: For example, in glass
n
blue = 1.53 n red = 1.52
•
Refraction
How is the angle of refraction related to the angle of incidence?
–
Unlike reflection,
»
Why??
q
1 cannot equal
q
2 Remember
v = f
l
!!
»
n
1
n
2
v
1
v
2 but the frequencies (
f
1 ,
f
2 ) must be the same the wavelengths must be different!
Therefore,
q
2 must be different from
q
1 !!
q 1 q 2
n
1
n
2 l l 1 2
v v
2 1
n
2
n
1
Snell’s Law
•
From the last slide:
l l 1 2
v v
2 1
n
2
n
1 q 2 q 1
L
q 2 q 1 q 2 q 1 q 2
n
1
n
2 \ But,
L
Huygen’s
sin l 2 q l l 1 2 2
v
1
v
2
n
1
n
1 2 l l
n
1 1 2 sin sin sin q 1 q q
L
1 2
n
2 sin q 2
Dispersion
1.54
1.52
1.50
frequency ultraviolet absorption bands
white light prism
Split into Colors
Dispersion in more detail: Effects of wavelength dependence of n
•
Dispersion: n depends on wavelength!
n blue > n red v blue < V red
Total Internal Reflection
n
1
incident ray
n
2
–
Consider light moving from glass (
n
1 =1.5
) to air (
n
2 =1.0
)
q 1 q r q 2 refracted ray reflected ray GLASS AIR sin sin q q 1 2
n n
1 2 1 q 2 1 q 1 I.e., light is bent away from the normal.
as q 1 gets bigger
,
q
2
gets bigger, but can never get bigger than 90 ° !!
q 2 In general, if sin q 1 > (
n
2
/
n
1
) , we have NO refracted ray; we have TOTAL INTERNAL REFLECTION.
For example, light in water which is incident on an air surface with angle q 1 > q 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.
Examples: refraction at water/air interface
•
Diver’s illusion
Diver sees all of horizon refracted into a 97 ° cone 97 º
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).
Polarization of Light
http://www.walter-fendt.de/ph14e/emwave.htm
•
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
Polarization by absorption
http://www.launc.tased.edu.au/online/sciences/physics/Polari.htm
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
q
i where both angles are measured from the normal: Note also, that all rays lie in the “plane of incidence” .
=
q
r ,
• q i q 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) normal incidence:
E
m
E x
cos(
kz
wt
)
The electrons on the surface of the metal will experience a force
F=eE
z
ˆ
→ acceleration →
e
Reflection Brewster’s Law
n = sin(i)/sin(r) = sin(i)/sin(90-i) = tan(i)
http://micro.magnet.fsu.edu/ primer/java/polarizedlight/br ewster/index.html
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.
» »
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.
y This box contains atoms which “scatter” the light beam x z
Scattering
Applications
•
Polarized sky
–
The same argument applies to light scattered off the sky:
Which photo was taken with a polaroid?
http://www.colorado.e
du/physics/2000/apple ts/polarized.html
http://home3.netcarrier.com/~chan/EM/PROGRAMS/POLARIZATION/
Application: LCD Display
END