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98% porosity aerogel exhibiting frequency
dependent optical birefringence
Polarization
▪ In transverse waves the oscillations are perpendicular to the direction of the
propagation of the traveling wave.
▪ In longitudinal waves the oscillations are parallel to the direction of motion.
▪ Transverse waves can have infinitely many modes of oscillation, each of which is
perpendicular to the propagation, whereas longitudinal can only have a single
mode.
▪ Because of these allowed modes, the phenomenon of polarization only applies to
transverse waves.
▪ We will consider only one type of transverse waves, electromagnetic waves,
particularly light.
▪ We will consider polarization in terms of the electric field, not the magnetic field.
Our eyes are sensitive
to electric field only.
Polarization
▪ Sketching the electric field is simplified even more:
B
View from Point A
View from Point B
A
Polarization
Light emitted by separate atoms and molecules is always polarized
polarized light
(simplified view)
Electric field of (linearly or plane) polarized wave oscillates only in one plane.
Light emitted by the sun, by a lamp in the classroom, or by a candle flame is unpolarized light.
The unpolarized light consists of many different waves from atoms and molecules emitting light
in random directions. An oscillating electric charge produces an electromagnetic wave.
For a light source such as the sun, or a glowing gas, or an incandescent filament, the charges
can oscillate in any direction, thus producing random and continuous orientations of the
electric field. Unpolarized light is a random mixture of light of all polarizations.
If we could view many separate waves in a narrow beam of unpolarized EM wave moving
directly toward our eyes, the vibrations of these waves would look like porcupine. Vibrations
would occur in many directions, but always perpendicular to the direction of propagation.
Unpolarized light
Random orientations of electric fields
in a light source constitute unpolarized light
The process of transforming unpolarized light into
polarized light is known as polarization. There are a variety of methods of polarizing light.
Polarization
To do that we use material known under name Polarizer (polaroid filter – Polaroid sunglasses
for example) that that has the effect of many narrow slits.
When unpolarized light shines on polaroid filter transmitted light is polarized.
Every filter has a transmission/polarization axis which is basically direction in which
vibrations of EM wave will survive. All other components of EM wave will be eaten up
(absorbed) by filter reducing its intensity to half.
Polarizer
Polarization - The Physics Classroom
A Polaroid filter is able to polarize light because of the chemical composition of the filter material.
The filter can be thought of as having long-chain molecules that are aligned within the filter in the
same direction. During the fabrication of the filter, the long-chain molecules are stretched across the
filter so that each molecule is (as much as possible) aligned in say the vertical direction. As
unpolarized light strikes the filter, the portion of the waves vibrating in the vertical direction are
absorbed by the filter. The general rule is that the electromagnetic vibrations that are in a direction
parallel to the alignment of the molecules are absorbed.
The alignment of these molecules gives the filter a polarization axis. This polarization axis extends
across the length of the filter and only allows vibrations of the electromagnetic wave that are
parallel to the axis to pass through. Any vibrations that are perpendicular to the polarization axis are
blocked by the filter. Thus, a Polaroid filter with its long-chain molecules aligned horizontally will
have a polarization axis aligned vertically. Such a filter will block all horizontal vibrations and allow
the vertical vibrations to be transmitted. On the other hand, a Polaroid filter with its long-chain
molecules aligned vertically will have a polarization axis aligned horizontally; this filter will block all
vertical vibrations and allow the horizontal vibrations to be transmitted.
Analyzer
A device which produces plane polarized light is called a polarizer.
Analyzer is a polarizer used to examine, whether light is plane polarized or not. A
polarizer can serve as an analyzer and vice versa.
Is the light polarized
or unpolarized?????
A ray of light is allowed to pass through an analyzer. If the intensity of the emergent
light does not vary, when the analyzer is rotated, then the incident light is
unpolarised; If the intensity of light varies between maximum and zero, when the
analyzer is rotated through 900, then the incident light is plane polarized;
𝜃 𝑖𝑠 𝑡ℎ𝑒 𝑎𝑛𝑔𝑙𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑝𝑜𝑙𝑎𝑟𝑖𝑧𝑒𝑟 𝑎𝑛𝑑 𝑎𝑛𝑎𝑙𝑦𝑧𝑒𝑟
Only 𝐸 cos 𝜃 component will pass through analyzer
𝐸 𝑠𝑖𝑛 𝜃 component will be absorbed by polarizer
Malus’s law
Polarizer
Analyzer
𝐸
𝐸 𝑠𝑖𝑛 𝜃
𝜃
𝐼𝑢𝑛𝑝𝑜𝑙
transmission
axis
𝐼𝑢𝑛𝑝𝑜𝑙
𝐼0 =
2
transmission
axis
𝐸 cos 𝜃
transmitted
beam
𝐼 = 𝐼0 𝑐𝑜𝑠 2 𝜃 =
𝐼𝑢𝑛𝑝𝑜𝑙
𝑐𝑜𝑠 2 𝜃
2
Intensity of a wave is proportional to the square of its amplitude.
Thus the intensity of the light that comes out of the analyzer is proportional to (E cos )2
Malus’s law
𝐼 = 𝐼0 𝑐𝑜𝑠 2 𝜃
Intensity of a beam of plane-polarized light after passing through a rotatable
analyzer varies as the square of the cosine of the angle through which the
analyzerr is rotated from the position that gives maximum intensity
nonpolarized light
vibrates in all
direction
only component parallel to
transmission axis passes through –
intensity cut in half
after passing through the second polarizer
EM wave oscillates in plane parallel to
transmission axis and amplitude is reduced
Light will not pass through a pair of polarizing filters
when their transmission axes are crossed at right
angles.
(REMEMBER: magnetic field would always be
perpendicular to electric)
Solving problems including Malus’s law
The preferred directions of two sheets of Polaroid are initially parallel.
(a) Calculate the angle through which one sheet needs to be turned in order to reduce
the amplitude of the observed E-field to half its original value.
(a) E cos  is the transmitted amplitude:
cos  = 1 / 2   = 60º.
(b) Calculate the effect this rotation has on the intensity.
(b) I = I0 cos2  = I0(1/2)2 = I0 / 4.
(c) Calculate the rotation angle needed to halve the intensity from its original value
(c) I0 / 2 = I0 cos2   cos2  = 1 / 2.
cos  = (1 / 2)1/2   = 45º.
Solving problems including Malus’s law
In general, light sources produce waves having their E-fields oriented in
many random directions.
Polarized light is light whose waves have their E-fields oscillate only
in one plane/ one direction.
 I = I0 cos2 
I = I0 cos2 60º
I = 0.25I0
I0 cos2 0º = I0
I0 cos2 60º = 0.25I0
I0 cos2 90º = 0
I0 cos2 120º = 0.25I0
I0 cos2 180º = I0
In general, light sources produce waves having their E-fields
oriented in many random directions.
Polarizing sunglasses only allow waves in one direction through,
thereby reducing the intensity of the light entering the eye.
Reflecting surfaces also polarize light to a certain extent, thereby
rendering polarizing sunglasses even more effective.
Solving problems including Malus’s law
 I = I0 cos2 .
 I = I0 (1/2)2 = I0 / 4.
Other ways of polarization
There are ways other than Polaroid film to obtain
polarized light.
Some EM radiation is polarized when it is produced.
For example, EM waves used for television are often
polarized either horizontally or vertically,
depending on the arrangement of the aerials.
Circularly polarized light can be
constructed from two polarized rays.
Reflection of unpolarized light from a boundary
between two mediums can polarize light.
Transmission of polarized light through certain
liquids can change the polarization angle.
Circular polarization
At each point (in a plane perpendicular to the
direction), the electric field of the wave has a
constant magnitude but its direction rotates
with time at a steady rate in a plane
perpendicular to the direction of the wave.
The electric field vectors of a traveling
circularly polarized EM wave. This
wave is right-circularly-polarized, since
the direction of rotation of the vector
is related by the right hand rule to the
direction the wave is moving.
quarter-wave plate converts linearly
polarized light into circularly
polarized light and vice versa
Circular polarization is used in those 3D
movies you pay good money to see.
Birefringence is the optical property of a
material having a refractive index that depends
on the polarization and propagation direction
of light. These optically anisotropic materials
are said to be birefringent (or birefractive).
Circular polarization
https://arago.elte.hu/?q=node/12 fever mosquitoes (Aedes aegypti) do not possess
positive polarotaxis, although their larvae develop
in water. Aedes aegypti is the first aquatic insect
species which does not detect water by the
horizontally polarized light reflected from the water
surface. Thus, unfortunately, these dangerous
mosquitoes cannot be exterminated by polarized
light traps.
Figure 8: Photographs of a scarab beetle
(Potosia aeruginosa jousselini) taken through a
left- and a right-handed circular polarizer,
showing that the metallic shiny cuticle reflects
left-handed circularly polarized light.
Polarization by reflection
One way to polarize light is by reflecting light from a surface between two media.
unpolarized light
inc
refl
partially polarized reflected
light
refr
Polarization occurs parallel
to the surface between the
two media and varies with
angle of incidence.
unpolarized refracted light
Brewster’s law
If refl + refr = 900 then the reflected ray
will be completely plane-polarized.
The particular angle of incidence at which this total
polarization occurs is called Brewster’s angle
Polarized
reflected light
Unpolarized
incident light
𝜃1 𝜃1
𝜃2
Partially
polarized
refracted light
Polarization by reflection
Light coming from the Sun can be
polarized horizontally by reflection
from the water or the road or the
snow .... That’s why Polaroid
sunglasses
with
a
vertical
transmission axis reduce this kind of
reflected glare + cuts in half intensity
of direct sunlight.
Polarization – optical activity
A substance is termed optically active if the plane of
polarized light rotates as it passes though the substance.
A sugar solution is an example of such a substance.
So is quartz.
The angle through which the plane rotates depends on
the concentration of the solution (if the substance can be
made into a solution), and the distance through
which the light passes.

Polarization uses – polarimeters
Data for various concentrations of sugar
solution have been gathered for a
sample tube of fixed length.
(a) Plot a suitable graph to represent the data.
C/g cm-3
0.30
0.20
0.10
5
10
15
20
/º
Angle of
rotation /0
Concentration C
/g cm-3
5
0.08
10
0.17
15
0.23
(b) Find the concentration of a sugar solution having  = 18º.
About 0.30 g cm-3.
The above apparatus is called a polarimeter.
Polarization uses – liquid crystal displays (LCD)
Liquid crystals (LC) are optically active substances whose
activity can be controlled by applying a potential
difference across them.
Second polarizer
glass
If there is no p.d. across the LC it will not be optically
active.
Common
electrode
If there is a p.d. across the LC it will
rotate the light through 90º
The light is polarized by the first polarizer.
If there is no p.d. it will continue
through to the second polarizer
at which point it will be completely absorbed
because of the cross polarization.
It is then it will pass to the viewer as black.
Liquid crystal
Shaped electrode
First polarizer
Polarization uses – liquid crystal displays (LCD)
If there is a p.d. across the LC, it will become optically active.
The LC will then rotate the polarized light from
the first polarizer an additional 90º.
Second
polarizer
Glass
This action aligns it with the second polarizer,
which now allows it to pass through unhindered.
Common
electrode
Liquid
crystal
Shaped
electrode
First
polarizer
The image received by the eye will have the shape determined by the shaped electrode.
Polarization uses – stress analyzers
When stressed, glass and plastics develop optical properties that are
dependent on the plane of polarization.
When placed between a polarizer and an analyzer, and illuminated by
white light, the regions of highest stress will appear as colored lines.
Diffraction
When waves pass through a small opening, or pass the edge of a obstacle,
they always spread out to some extent into the region that is not directly in
the path of the waves.
The spreading of a wave into a region behind an obstruction is called
diffraction.
- into the region of the geometrical shadow
Water waves diffracting through two different sized openings..
diffraction effects are small
when slit is much larger
than the incident λ.
The waves are diffracted more
through the narrower opening,
when wavelength is larger than
the opening.
Diffraction by a large object
Almost sharp edges – small
diffraction around obstacle
Diffraction by a small object
Strong diffraction effect behind the obstacle
remember:
big wavelength
big diffraction effects
For example, if two rooms are
connected by an open doorway and a
sound is produced in a remote corner
of one of them, a person in the other
room will hear the sound as if it
originated at the doorway.
Diffraction provides the reason
why we can hear something even if
we can not see it.
Lower-frequency (longer-wavelength) waves can diffract
around larger obstacles, while high-frequency waves are
simply stopped by the same obstacles. This is why AM radio
waves (~1 MHz, 300 m wavelength) signals can diffract around
a building, mountain still producing a usable signal on the
other side, while FM (~100 MHz, 3 m wavelength) signals
essentially require a line-of-sight path between transmitter
and receiver.
Ultrasound is used for echolocation: dolphins, bats, sonar,
sonograms Sonar appeared in the animal kingdom long before it
was developed by human engineers.
But why ultrasound? Because of diffraction!!! Or
should we say because of no difraction!!!
Low frequency sound has longer wavelength, so they will be
diffracted, so not being able to detect the prey. High frequency
sound has smaller wavelength, so it will be reflected back from the
prey. That’s how bat “sees” its prey.
So when ultrasound is emitted toward obstacle it will be
reflected back rather then spread behind the obstacle.
dolphins,
ocras,
whales
Keep in mind that wavelengths of the audible sound are < 1m, of
the visible light ~ 10-7 m, and water waves you can see for yourself.
Now you can understand that diffraction in the case of sound or
water can be very obvious, but for light is not so.
Light waves (red light: λ ~ 500 nm = 0.0005 mm) do not
diffract very much. Obstacle should be very small.
a Shadow!!! (No light behind the obstacle!)
2. Suggest one reason why ships at sea use a very
low frequency sound for their foghorn.
And low frequency sounds do propagate much further
than high-frequency ones – due to diffraction.
Another reason and maybe even better explanation is that
the method of generating the sound involves the
production of a very strong pressure pulse. The fog horn is
loud so that it can be heard far away.
Elephants also use these deep sounds to communicate over
long distance.
Interference - Superposition
two objects can not be at the same place at the same time!
but two waves can be at the same place at the same time!
and when they meet they interfere, superimpose and then carry on living happily ev
after as they never met each other
Property that distinguishes waves from particles: waves can superpose when
overlapping and as the result a lot of possible craziness can happen.
 constructive interference –
increased amplitude,
increased energy
(E ~ A2 ) – increased
intensity – brighter light
or loud sound at point
the waves are in phase
 destructive interference –
decreased amplitude,
decreased energy
– decreased intensity
– no light or no sound
the waves are out of phase
Partially destructive interference.
Principle of superposition:
When two or more waves overlap, the resultant
displacement at any point is the sum of the
displacements of the individual waves at that point.
Two boys playing in a pool make identical waves that travel
towards each other.
The boys are 10 m apart and the waves have a wavelength 2
m. Their little sister is swimming from one boy to the other.
When she is 4 m from the first boy, will she big wave or a
small wave?
The waves from the boys will interfere when they meet, if the girl is 4 m
from the first boy, then she must be 6 m from the other. This is a path
difference of 2 m, one whole wavelength. The waves are therefore in phase
and will add.
d1 - d2 = 2 m = λ constructive interference
X and Y are coherent sources of 2cm waves.
Will they interfere constructively or destructively at:
(a) A
(b) B
(c) C
Real-world examples of interference
So where in this world do we observe two sources interference?
Where can we experience the phenomenon that sound or light taking
two paths from two locations to the same point in space can undergo
constructive and destructive interference?
This is relatively common for homes located near mountain cliffs. Waves
are taking two different paths from the source to the antenna - a direct
path and a reflected path. If the top of the house (antenna) is the point of
destructive interference for some wavelength, that wavelength is not
received. To fix this sell the house.
While the interference is
momentary (the plane does
not remain in a stationary
location), it is nonetheless
observable.
The wavelength of a transverse wave train is 4cm. At some point on the
wave the displacement is -4cm. At the same instant, at another point
50cm away in the direction of propagation of the wave, the
displacement is
A. 0cm
B. 2cm
C. 4cm
D. -4cm