Transcript ppt

From last time…
Inductors in circuits
I?
+
EM waves
Thurs. Nov. 12, 2009
Physics 208, Lecture 21
1
Mathematical description
x
y
E  E o coskz   t
B  Bo coskz   t
k
2

EB
z
Bo  Eo /c
,   2f


r r
Propagation direction = E  B

Tue. Nov. 9, 2009
Physics 208, Lecture 20
2
Question:
At a particular instant, an EM wave has an
E-field pointing in the y-direction and a Bfield pointing in the x-direction. The
propagation direction is
z
A. z
D. -z
B. y
E. -y
C. X
F. -x
Tue. Nov. 9, 2009
Physics 208, Lecture 20
y
x
3

Radiation Pressure



Saw EM waves carry energy
They also have momentum
When object absorbs energy U from EM wave:




Momentum p is transferred
Power
p  U /c ( Will see this later in QM )
U /t
Result is a force F  p /t 
 P /c
c
Pressure = Force/Area =
P/A
prad 
 I /c
c
Radiation
pressure
Intensity
on perfectly absorbing object
Thurs. Nov. 12, 2009
Physics 208, Lecture 21
4
Radiation pressure & force
EM wave incident on surface exerts a radiation pressure
prad (force/area) proportional to intensity I.
Perfectly absorbing (black) surface: prad  I /c
Perfectly reflecting (mirror) surface: prad  2I /c
Resulting force = (radiation pressure) x (area)


Thurs. Nov. 12, 2009
Physics 208, Lecture 21
5
Question
A perfectly reflecting square solar sail is 107m X 107m. It has
a mass of 100kg. It starts from rest near the Earth’s orbit,
where the sun’s EM radiation has an intensity of 1300 W/m2.
How fast is it moving after 1 hour?
A. 100 m/s
B. 56 m/s
C. 17 m/s
D. 3.6 m/s
E. 0.7 m/s
Thurs. Nov. 12, 2009
prad  2I /c
Frad  prad A  2IA /c 
21300W /m 2 1.145 10 4 m 2 
3 10 m /s
8
 0.1N
a  Frad /m  103 m /s2
v  at  103 m /s2 3600s  3.6m /s
Physics 208, Lecture 21
6
Another way to draw
EM wave
x
z
y


Since E perpendicular B, only
need show E
Wave propagating toward us
r
E  E o coskz   txˆ shown
r
B  Bo coskz   tyˆ not shown
Thurs. Nov. 12, 2009
Physics 208, Lecture 21
x
z
y
7
Polarization of EM waves


Usually indicate the polarization direction by
indicating only the E-field.
Can then be indicated with a line:
Unpolarized
Plane Polarized
x
z
y
E  E o coskz   txˆ
B  Bo coskz   tyˆ
Thurs. Nov. 12, 2009
Superposition of
plane polarized waves
Physics 208, Lecture 21
8
Producing polarized light

Polarization by selective absorption: material that transmits
waves whose E-field vibrates in a plain parallel to a certain
direction and absorbs all others
This polarization
absorbed
This polarization
transmitted
transmission axis
Long-chain hydrocarbon
molecules
Thurs. Nov. 12, 2009
Polaroid sheet
Demo on MW and metal grid
9
Physics 208, Lecture 21
Effect of linear polarizer

After passing through
linear polarizer, light is
polarized along the
transmission axis
Thurs. Nov. 12, 2009
Physics 208, Lecture 21
10
Superposition


Electric fields sum as vectors
Add two different polarized EM waves
+
Thurs. Nov. 12, 2009
=
Physics 208, Lecture 21
11

Transmission at an angle
Plane-polarized
incident wave
y
E inc  E o coskx  t 
Incident wave is equivalent
to 
superposition


x
polarizer
E inc cos xˆ  E inc sin  yˆ
transmitted

absorbed
Transmitted wave =
E trans  E o cos coskx  t xˆ
Thurs. Nov. 12, 2009
Physics 208, Lecture 21
transmission
12
Detecting linearly polarized light

Polarizer



transmits component of E-field parallel to transmission axis
absorbs component of E-field perpendicular to transmission axis
Transmitted intensity: I = I0cos2 I0 = intensity of polarized
beam on analyzer (Malus’ law)
Allowed component
parallel to analyzer axis
Thurs. Nov. 12, 2009
Polaroid
Physicssheets
208, Lecture 21
13
Malus’ law



Transmitted amplitude is Eocos
(component of polarization along polarizer axis)
Transmitted intensity is Iocos2
( square of amplitude)
Perpendicular polarizers give zero intensity.
Thurs. Nov. 12, 2009
Physics 208, Lecture 21
14
Liquid Crystal Display (LCD)
‘oriented’
liquid crystal
Orthogonal linear
polarizers
Oriented
‘scratched’ glass

No electric field


Molecules align with
scratches
Light polarization rotates
with molecules
Thurs. Nov. 12, 2009

Electric field



Molecules align E-field
Light polarization does not
rotate
No light gets through
Physics 208, Lecture 21
15
Laptop LCD displays
Dell Inspiron 4100 Laptop with
Polarized Glasses
Thurs. Nov. 12, 2009
Apple iBook G4 Laptop with Polarized
Glasses, showing perpendicular
polarization from
Physics 208, Lecture 21
16
Polarization by reflection

Unpolarized light reflected
from a surface becomes
partially polarized

Degree of polarization
depends on angle of
incidence
Unpolarized
Incident light
Reflection
polarized
with E-field
parallel to
surface
n
Refracted
light
Thurs. Nov. 12, 2009
Physics 208, Lecture 21
17
Reducing glare


Reflected sunlight partially polarized.
Horizontal reflective surface ->the Efield vector of reflected light has
strong horizontal component.
Transmission axis
Thurs. Nov. 12, 2009
Physics 208, Lecture 21
18
Polarization by scattering
Looking North at sunset
with a horizontal linear polarizer
Different directions relative to sun have different polarizations.
Some insects detect this polarization and use it to navigate.
Thurs. Nov. 12, 2009
Physics 208, Lecture 21
19
Honey Bee vision

Polarization sensitivity


rhodopsin molecules aligned
preferentially parallel to microvilli
tubes axes.
Honeybee ~5,500 ommatidia

Most visual cells of ommatidia
twisted by 180˚,


cancels out polarization sensitivity.
Exception

dorsal (sky-looking) visual cells
responsible for polarized-light vision.
Thurs. Nov. 12, 2009
Physics 208, Lecture 21
20
Bee navigation
Thurs. Nov. 12, 2009
Physics 208, Lecture 21
21
Circular
polarization

The electric field
rotates in time with
constant magnitude

Can be made by superposition:



Superpose two EM waves
Orthogonal linear polarizations
90˚ out of phase.
Thurs. Nov. 12, 2009
Physics 208, Lecture 21
22
y
y
y
x
x
x
t=T/8
t=0
y
t=2T/8
y
y
x
x
0 T/
2T/
8 8 3T/ 4T 5T
8 /8
/8
x

t=4T/8
t=3T/8
t=5T/8

y
y
y

t=6T/6
Thurs. Nov. 12, 2009
x
x
x
t=7T/8
Superposition of two
waves
orthogonal linear
polarizations
90˚ (1/4 wavelength)
out of phase.
t=T
Physics 208, Lecture 21
23
Right and left
circular polarization



Two different types of
circular polarization
These are
inequivalent – like
right- and left-handed
screws.
Defined by direction
of E-field vector
rotation for light
propagating toward
you
Thurs. Nov. 12, 2009
x
z
Right
circularly
polarized
y
Physics 208, Lecture 21
x
z
Left
circularly
polarized
y
24
Recent discovery: some animals
‘see’ circular polarization


Shrimp eye can
detect circular
polarization.
Fin appears
different when
illuminated with
R- or L-circularly
polarized light.
Thurs. Nov. 12, 2009
Physics 208, Lecture 21
25
‘Right’ &‘Left’ not always the same
• Mirror
symmetric
• Achiral
• Chiral
objects
• Right and left
are different
Thurs. Nov. 12, 2009
Circularly
polarized light
Physics 208, Lecture 21
26
Chiral molecules
Many molecules
are chiral.
They are mirror
images of each
other
They are not
equivalent by any
rotation or
translation
Circularly polarized light interacts differently with
these different molecules
Thurs. Nov. 12, 2009
Physics 208, Lecture 21
27
Biological systems have
chosen a particular chirality
Biological amino acids,
proteins, mostly L
Biological sugars mostly D
Thurs. Nov. 12, 2009
Physics 208, Lecture 21
Next week’s lab:
right and lefthanded light
interact differently
with a biological
sugar
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