Download More on EM waves, Polarization Next Honor Lecture, Fri. 27 Midterm

More on EM waves, Polarization
Next Honor Lecture, Fri. 27
This lecture: start review on
X-ray spectroscopy of proteins by Prof. P. Gilbert
EM waves (Ch 34)
Polarization (38.6)
Normal

Light without red
Light without green
Midterm Exam 2: Nov 1, 5:30 pm
Duration 1:30 hrs, Location TBA
CH 29: Magnetic fields, Motion of charged particles in B, magnetic force on a
current, magnetic dipole moment and potential energy, forces between
currents
CH 30: Sources of magnetic fields, Biot-Savart law, field from a circular loop,
solenoid, Ampere’s law and magnetic field calculations, Ampere-Maxwell’s law
CH 31: Faraday’s law, Lentz’s law, Motional emf, Eddy currents, AC
generators
CH 34: Maxwell’s equations and their solutions, electromagnetic waves and
their properties, velocity, frequency and wavelength, direction of propagation,
Pointyng vector, radiation pressure
38.6: Polarization of light waves
CH 35: 35.3, 35.4, 35.5: reflection and refraction of light


Have clear in mind!

FB = q v x B
RH rule:
RH rotation rule
solenoid
Facts on EM waves

Quick Quiz pn EM waves
Which orientation will have the largest induced emf?
EM waves are solutions of Maxwell’s equations.
E
y

In empty space: sinusoidal wave propagating along x with
velocity
 E = E max cos (kx – ωt)
 B = B max cos (kx – ωt)
• E and B are perpendicular oscillating vectors
λ
E·B=0
•The direction of propagation is
perpendicular to E and B
ExB=0
z
x
B
loop in xz
plane
loop in xy
plane
Transverse
waves
1
2
3
yz
in
op
lo a n e
pl
Faraday’s law: Loops use B not E!
Only the loop in the xy plane will have a magnetic flux through
it as the wave passes. The flux will oscillate with time and
induce an emf.
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Quick Quiz on EM waves
Quick Quiz on EM waves
What is the phase difference between the sinusoidal oscillations
of the electric and magnetic fields in this figure?
(a) impossible to determine
(b) 180°
T=0
An electromagnetic wave propagates in the –y direction. The
electric field at a point in space is momentarily oriented in
the +x direction. The magnetic field at that point is
momentarily oriented in the
T/4
(a) –x direction
(c) 90°
(b) +y direction
(d) 0
T/2
z
(c) +z direction
3T/4
(d) –z direction
B
c
y
x
E
Quick Quiz on EM waves
Relation between E and B

E = Emax cos (kx – ω t)
B = B max cos (kx – ωt)
Sources of EM waves: oscillating charges,
accelerated/decellerated charges, electron transitions between
energy levels in atoms, nuclei and molecules
z
c
E
y
x
Intensity and Radiation pressure
Energy carried by EM waves: Poynting Vector

Power per unit area: rate at which energy flows through a unit
area perpendicular to direction of wave propagation
B

Wave intensity I = time average of S over one or more cycle
<cos2 (kx - ω t)> = 1/2
I ∝ E2


In a given volume, the energy
is shared equally between E and B fields
u E = u B since B = E/c and
Total instantaneous energy density
Radiation pressure:
 Perfectly absorbing surface P = S/c
 Perfectly reflecting surface P = 2S/c
u =u E + uB = 1/2 ε o E2 + B 2 /(2µo )
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Quick Quiz on Poynting vector
Quick Quiz on radiation pressure
Which of the following is constant for a plane
electromagnetic wave?
To maximize the radiation pressure on the sails of a spacecraft
using solar sailing, the sheets must be
(a) magnitude of the Poynting vector
(a) very black to absorb as much sunlight as possible
(b) energy density uE
(b) very shiny, to reflect as much sunlight as possible
(c) energy density uB
(d) wave intensity
Which is the value of the radiation pressure in the above
case?
Answer: (d). The first three choices are instantaneous values
and vary in time. The wave intensity is an average over a
full cycle.
(a) P = 2S/c
Quick Quiz on EM spectrum
The EM Spectrum



(b) P = S/c
In many kitchens, a microwave oven is used to cook food.
The frequency of the microwaves is of the order of 1010 Hz.
The wavelengths of these microwaves are on the order of
Note the overlap
between types of
waves
Visible light is a
small portion of
the spectrum
Types are
distinguished by
frequency or
wavelength
(a) kilometers
(b) meters
(c) centimeters
(d) micrometers
" =c/ f =
3 #10 8 m /s
= 3cm
1010 /s
!
Polarization of Light Waves (38.6)

plane of polarization: contains E and S
Sun light is unpolarized
Direction of E changes
randomly
Linearly polarized
light: E-field has
one spatial
orientation
Circularly polarized light: direction of E rotates with time and the tip of the
vector describes a circle. Superposition of 2 waves of equal amplitude with
orthogonal linear polarizations, and 90˚ out of phase.

http://webphysics.davidson.edu/physlet_resources/dav_optics/Examples/polarization.html
Polarization by selective absorption
If linearly polarized light of intensity I0 passes through a polarizing
filter with transmission axis at an angle θ along y
y
Polaroid sheet
θ
Einc = E0sinθ i + E0 cosθ j
x transmission axis
After the polarizer
Etransm = E0cosθ j
So the intensity transmitted is
E0cosθ
Itransm = E02 cos2θ = Ι0cos2θ
Long-chain
hydrocarbon
molecules
A polarizer is used to produce
polarized light of intensity I0
and an analyzer rotated at an
angle θ: transmission 100%
when θ = 0 and zero when θ =
90°
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Quick Quiz on MW demo
A polarizer for microwaves can be made as a grid of parallel metal wires
about a centimeter apart. The electric field vector for microwaves
transmitted through this polarizer is _____ to the metal wires.
Quick Quiz on Polarization

(a) parallel

(b) perpendicular


Answer: (b). Electric field vectors parallel to the metal wires cause
electrons in the metal to oscillate parallel to the wires. Thus, the energy
from the waves with these electric field vectors is transferred to the metal
by accelerating these electrons and is eventually transformed to internal
energy through the resistance of the metal. Waves with electric-field
vectors perpendicular to the metal wires pass through because they are
not able to accelerate electrons in the wires.

Unpolarized light (like the light from the sun) passes
through a polarizing sunglass (a linear polarizer). The
intensity of the light when it emerges is:
Zero
1/2
1/3
1/4
I " E 2 # I " cos2 $
$ is varying randomly over fully cycle
1
Therefore, average value is
2
!
Law of Malus Example
Quick Quiz on Polarization
E0
TA
E1
45°
TA
90°
unpolarized
light
I = I0
TA
B1
I1 = 0.5 I0
I2 = I1cos2(45)
I3
2) Light transmitted through first polarizer is vertically
polarized. Angle between it and second polarizer is θ=45º.
I2= I1 cos2 (45º)=0.5I1=0.25 I0
3) Light transmitted through second polarizer is polarized
45º from vertical. Angle between it and third polarizer is θ
=45º. I3= I2 cos2(45º) =0.125 I0
Polarization by scattering
When light hits a material electrons absorb and reradiate part of the light.
The sky appears blue due to scattering of light on air and resulting partially
polarized light.
Short wavelengths (blue) are scattered more intensely than red.
Optically active materials (your lab)!




The light from blue sky is polarized and the direction of polarization at
each point depends on the position of the Sun.
They rotate the plane of polarization of incident light
Solution with sugar: when polarized light passes through the Karo syrup,
the direction of its polarization is changed.
The rotation angle is proportional to depth and concentration of syrup.
The rotation angle depends on the wavelength or color of the light. Blue
light, with its shorter wavelength, rotates more than the longer-wavelength
red light.
Nobel prize to Frisch 1973: bees use the Sun as a compass, orienting their dance angle
to the plane of polarization of the sunlight. Even when the Sun is obscured by clouds,
bees can detect its position from polarization pattern of blue sky.
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