Download How can the reflections of light on the surface of

How can the reflections of light on the surface of water be blocked to see
what is on the bottom of the sea?
www.digital-photography-tips.net/Stay_Focussed-Newsletter-March-2013.html
Discover the answer to this question in this chapter.
Luc Tremblay
Collège Mérici, Quebec City
In 1669, the Danish scientist Rasmus Bartholin discovers a strange phenomenon: when a
calcite crystal is placed over a text, two images of the text are seen!
faculty.kutztown.edu/friehauf/beer/ (oui, oui, c’est le bon site)
The two images of the text have exactly the same intensity. This phenomenon is called
double refraction or birefringence because the image splitting comes from the fact that the
refraction is different for each image when they pass through the crystal. Newton
mentioned that light seems to have two different aspects, like the two poles of a magnet,
which brought the name polarization to this property of light.
A Glorious Victory for the Wave Theory
An Asset for the Corpuscular Theory
At first, it was easier to explain polarization with the corpuscular theory. Playing with the
shape of light particles, a theory explaining how two refractions can be obtained in the
calcite crystal depending on the orientation of the particles of light when they enter the
substance was devised. It was not perfect, but it was much better than the explanation given
by the wave theory at that time. Actually, the proponents of the wave theory were
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completely unable to explain this phenomenon for a long time. Polarization was the only
thing keeping the corpuscular theory alive after the success of the wave theory with
Young’s experiment (interference) and Fresnel’s work on diffraction. Supporters of the
corpuscular theory could always reply that the corpuscular theory is the only theory
providing an explanation for the polarization of light.
New Observations
In 1808, Etienne-Louis Malus discovers something special with birefringence. Up to that
point, it was believed that two images obtained with double refraction always had the same
intensity. Malus discovers that this is not true if the light is reflected on a surface before
passing through the calcite crystal. By observing the reflection of light on the windows of
the Luxembourg Palace in Paris through a crystal of calcite (don’t ask me why he started
to do that!), he noticed that the two images do not have the same intensity. The relative
intensity of these two images can be changed by rotating the crystal and one of the images
can even completely disappear under specific conditions. This discovery was the starting
point of a series of experiments on polarization. Then, the corpuscular theory was still the
only theory able to explain these phenomena. This discovery revived the study of
polarization, which allowed new ideas to be explored.
And If Light Waves Were a Transverse Waves?
In 1816, André-Marie Ampère finally released the wave theory from its deadlocked
position by saying that polarization can be explained if it is assumed that light is a
transverse wave instead of a longitudinal wave. It was a little weird to propose this at the
time. Then, it was believed that light was a mechanical wave, that a medium was needed
so that the wave can propagate. This medium was called aether (which has nothing to do
with the ether functional group in chemistry). This substance had to be present everywhere
in the universe because light can travel throughout the universe. If light can be received
from the Andromeda Galaxy, then aether had to be present everywhere along the way
between the Earth and the Andromeda Galaxy. At the same time, this aether must not exert
any frictional force since the Earth is rotating around the Sun without losing energy because
of friction. If aether had only exerted a small friction force, the Earth would have slowly
lost its energy and would have finished his journey in the Sun. This absence of friction had
initially suggested that the aether must be a fluid and light had to be a longitudinal wave
(because transverse waves cannot propagate in a fluid). By proposing that light is a
transverse wave, Ampère was proposing at the same time that the aether must be rigid. It
only remained to discover how a rigid aether could let the objects travel through it without
exerting any frictional force...
In 1822, Augustin Fresnel further developed this idea of transverse waves. He then got
results in perfect harmony with the observations. The last bastion of the corpuscular theory
was falling, which meant its death and the triumph of the wave theory. After 1822, there
was no longer any significant supporter of the corpuscular theory (until its return in 1905...
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see in a further chapter). However, a certain discomfort remained present throughout the
19th century: how could the aether offer no resistance while being rigid at the same time?
A Transverse Electromagnetic Wave
In 1879, James Clerk Maxwell completed the basic equations of electromagnetism. With
these equations, he confirmed that light is an electromagnetic wave and that these waves
are actually transverse waves.
For about 25 years, the physicists continued to try to match this idea with the concept of
aether with quite dramatic complications sometimes. All of these studies turned out to be
useless since Einstein showed in 1905 that light is not a mechanical wave and that the
aether simply does not exist.
In fact, light does not need a material medium to propagate. Light is a wave of electric and
magnetic fields, which are not material things. In this figure showing a light wave, the
electric field is represented by red arrows and the magnetic field by blue arrows.
www.molphys.leidenuniv.nl/monos/smo/index.html?basics/light_anim.htm
Here is an animation of the motion of this wave.
http://www.youtube.com/watch?v=4CtnUETLIFs
This is not a mechanical wave since the passage of the wave does not entail any oscillations
of a medium. It is said that this is a transverse wave because the direction of the fields is
always perpendicular to the direction of propagation of the wave. Although there are two
fields, only the electric field of the wave will be considered in the sections that follow to
simplify.
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The Direction of Oscillation of the Electric Field
With a transverse wave, we have something that is impossible for longitudinal wave: there
are several possible directions for the electric field. When the direction of oscillation of the
field changes, the polarization of light changes. The following image shows different
possible directions for the direction of the electric field.
www.nikon.com/about/feelnikon/light/chap04/sec01.htm
In each of these cases, the oscillation is perpendicular to the direction of propagation of the
wave, as it must be for a transverse wave.
How did this explain the various observations such as birefringence? Light does not interact
in the same way with a material according to the direction of the oscillation of the field.
For example, in certain substances, a wave that oscillates horizontally (we say that it is
horizontally polarized) does not travel at the same speed as a wave that oscillates vertically
(we say that it is vertically polarized) because the interaction with matter is different. If the
speed is different, then the refractive index is different and the two polarizations are
refracted at different angles.
Principal Components
There is an infinite number of possible directions of oscillation. Should we consider them
all to examine all the possibilities? Of course not. It is possible to work with two main
directions of polarization (e.g. horizontal and vertical) and resolve all the other polarization
with these components. For example, a polarization at 45° can be resolved into one half of
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horizontal polarization and one half of vertical polarization. If the behaviour of the
components is known, the behaviour of any polarization is a combination of the behaviour
of the two main components.
The wave can be easily resolved into its two components along the selected axes. The
components are
E0 x = E0 cos θ
E0 y = E0 sin θ
where E0 is the amplitude of the wave,
E0x
is the amplitude of the xcomponent, E0y is the amplitude of the
y-component and θ is the angle
between the direction of the
polarization and the x-axis. Note that
these axes can be rotated according to
the conditions. However, you should
always have one axis perpendicular to the other.
Polarized and Unpolarized Light
Light is polarized if the oscillation of the electric field is uniquely along one direction.
Generally, light is made up of several superimposed waves and, in polarized light, these
waves all have the same direction of oscillation.
In unpolarized light, the different superimposed waves have different directions of
oscillation. It’s actually a superposition of all possible directions of oscillation with an
equal amount for each direction. Most of the time, light sources around us emit unpolarized
light. For example, the light coming from the Sun and the light coming from light bulbs
are not polarized.
In partially polarized light, all the directions of oscillations are present, but some
polarizations are more intense than the others.
Radio Waves and Microwaves Polarization
All electromagnetic waves can be polarized. The waves used in telecommunications are
very often polarized and, if you want to receive them with a rod-shaped antenna, you must
orient the antenna in the direction of the polarization to get a good reception.
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www.cdt21.com/resources/guide3.asp
With the right orientation, the electric field oscillates in the same direction as the antenna.
The electric field can then move charged particles in the direction of the antenna and
generate a current in the antenna.
Note on Interférence
To have two electromagnetic waves interfering in accordance with the equations given in
Chapter 7, they must have the same polarization. Note that it is always possible for an
observer to receive two electromagnetic waves with the same polarization. This happens
when the direction of polarization is perpendicular to the plane formed by the observer and
the two sources.
However, two waves with perpendicular polarization do not interference at all. This
phenomenon was discovered by François Arago and Augustin Fresnel in 1819. For
example, the interference pattern would look totally different if Young experiment was
performed with polarizers with different orientations before or after the slits. In this case,
the wave coming from one slit would have a polarization in one direction (say, vertical)
and the wave coming from the other slit would have a polarization in the other direction
(say, horizontal).
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With different directions of oscillation, the two waves cannot cancel each other at the
positions where there is destructive interference. In this case, the interference pattern
disappears completely.
An interference pattern appears when the polarization of the light coming from each slot is
the same. It also appears when unpolarized light is used. In this case, there is half and half
of each polarization, and each of these components can cancel the component with the
same polarization from the wave coming from the other slit at the places where there is
destructive interference.
Polarizing Filters
Light can be polarized with a filter that absorbs the light polarized in one direction and let
the light polarized in another direction pass. This is a polarizing filter. For example, in the
following image, unpolarized light arrives on such a filter. Unpolarized light is often
represented by several arrows in directions perpendicular to the direction of propagation of
the wave to show that it is a superposition of every possible direction of transverse
oscillation. This polarizer lets the light
polarized in the vertical direction pass. This
direction is indicated by the big double
arrow on the filter that shows the direction
of polarization that can pass. This direction
is the polarization axis of the polarizing
filter. Then, the light polarized in a direction
perpendicular to the polarization axis of the
polarizing filter is absorbed. When the light
comes out of this polarizing filter, only a
single polarization remains and the light is
now polarized in the direction of the
polarization axis of the filter
hyperphysics.phy-astr.gsu.edu/hbase/phyopt/polabs.html
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Polarizing filters are made of a material composed of very long molecules aligned in the
same direction. These molecules absorb light oscillating in one direction, but they cannot
absorb light that oscillates in the other direction. This kind of filter was invented in 1928.
Unpolarized Light Arriving on a Filter
Light can always be resolved into two principal polarizations components whether or not
it is polarized. For unpolarized light, the two components have exactly the same amplitude.
An axis in the direction of the polarization axis of the filter and an axis perpendicular to
the polarization axis of the filter are then used. When the light passes through the filter, the
perpendicular component disappears and only the parallel component remains. Half of the
light is then lost so that the light intensity is divided by two after the light has passed
through the filter. Therefore
Unpolarized Light Passing Through a Polarizing Filter
The light is now polarized in the direction of the
polarization axis of the filter.
I=
I0
2
where I0 is the intensity of the light before the passage through the filter.
Polarized Light Arriving on a Filter
It’s possible to think that nothing changes when polarized light passes through a polarizing
filter because the light is already polarized. This is not necessarily true because the
direction of the polarization axis of the filter can be different from the direction of
polarization of the light.
If the filter axis and the direction of the oscillation of the light are parallel, then it is true
that all the light passes through the filter.
otl.curtin.edu.au/events/conferences/tlf/tlf1997/swan.html
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If, on the other hand, if the axis is perpendicular to the direction of the oscillation of the
wave, then no light passes through.
otl.curtin.edu.au/events/conferences/tlf/tlf1997/swan.html
Actually, the axis of the polarizer can make any angle with the direction of polarization.
To know the proportion of light that passes then, the light must be resolved into two
components: a component parallel to the axis and a component perpendicular to the axis.
Only the parallel component will pass through.
If the angle between the axis of polarization of the filter and the direction of the oscillation
of the wave is θ, then the parallel component is
A = A0 cos θ
As the intensity is proportional to the square of the amplitude, the intensity is
I = I 0 cos 2 θ
Moreover, as the filter let only pass the component of the light polarized in the direction of
the axis of polarization, the light that comes out of the polarizer is polarized in the direction
of the axis of the polarizer. In the following figure, you can see that the direction of the
polarization of the light is always the same as the direction of the axis of the last polarizer
that the light has passed through.
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www.chegg.com/homework-help/questions-and-answers/suppose-unpolarized-light-intensity-149-w-m2-falls-polarizer-thefigureangle-drawing-is318-q813632
In summary, we have
Polarized Light Passing Through a Polarizing Filter
The light is polarized in the direction of the
polarization axis of the filter.
I = I 0 cos 2 θ
where I0 is the intensity of the light before the passage through the filter.
This is Malus’s law.
Thus, if the angle between the axes is zero, the light passes. If the angle is 90°, no light
passes. That’s what Grandpa John says
http://www.youtube.com/watch?v=QgA6L2n476Y
and the Department of Physics and Astronomy of the University of California.
http://www.youtube.com/watch?v=E9qpbt0v5Hw
In this video, a nice magic trick is made.
http://www.youtube.com/watch?v=9flduws7EsQ
Example 9.3.1
Unpolarized light with initial intensity Ii passes through 3 polarizers whose axes are
oriented as shown in the figure.
What percentage of light is left
after the light has passed through
the three polarizers?
www.chegg.com/homework-help/questions-and-answers/sheets-polarizing-material-shown-drawing-orientationtransmission-axis-labeled-relative-ve-q882361
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First Polarizer
Unpolarized light arrives on a polarizer. The intensity of the light after its passage
through the polarizer is thus
I=
Ii
= 0.5 I i
2
The light is now polarized in the direction of the axis of the polarizer, so in a
direction 20° from the vertical.
Second polarizer
Polarized light arrives on a polarizer. The angle between the axis of the polarizer
(30°) and the direction of polarization of the light (20°) is 30° - 20° = 10°. The
intensity of the light after its passage through the polarizer is thus
I = I 0 cos 2 θ
= 0.5 I i cos 2 10°
= 0.485 I i
The light is now polarized in the direction of the axis of the polarizer, so in a
direction 30° from the vertical.
Third polarizer
Polarized light arrives on a polarizer. The angle between the axis of the polarizer
(50°) and the direction of polarization of the light (30°) is 50° - 30° = 20°. The
intensity of the light after its passage through the polarizer is thus
I = I 0 cos 2 θ
I = 0.485I i cos 2 20°
I = 0.428I i
Only 42.8% of the initial light intensity remains.
Three Dimensional Movies
To have a three-dimensional image, the image received by each eye must be slightly
different. When we look at an image projected onto a screen, both eyes see the same image
and all the elements of the image seem to be at the same distance. For each eye to capture
a different image, two images must be projected on the screen. One is made of vertically
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polarized light and the other is made of horizontally polarized light. Alternating polarizing
filters (vertical and horizontal) in front of the projector polarized these two images.
news.bbc.co.uk/2/hi/entertainment/7976385.stm
To make sure that each eye sees a single image, glasses fitted with polarizing filters are
used. For one eye, the axis of the polarizer is vertical, and only the vertically polarized
image is seen by this eye. For the other eye, the axis of the polarizer is horizontal, and only
the horizontally polarized image is seen by this eye. Each eye then receives a different
image.
news.bbc.co.uk/2/hi/entertainment/7976385.stm
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This way of making 3D movies explained
here actually corresponds to the technology
formerly used. The glasses then looked like
those in the figure to the right.
tpe3d-2013.e-monsite.com/pages/3d-polarisundefinede.html
Now, circularly polarized light is used.
The glasses rather look like those in the
image to the left. Circular polarization
will not be explained here, but the idea is
quite similar.
michaelaisms.wordpress.com/category/3-d-glasses/
The light reflected on a surface can become polarized. To understand why, let’s consider
how light is reflected from a surface.
When light interacts with charged particles, two things happen. First, the oscillating electric
field of the wave exerts an oscillating force on the charged particles. This oscillating force
makes the charged particles oscillate in the direction of the electric field, so in the direction
of the polarization of the wave, with the same frequency as the frequency of the wave.
skullsinthestars.com/2009/06/06/barkla-shows-that-x-rays-have-polarization-1905/
Then, the oscillating charged particle emits an electromagnetic wave with the same
frequency as the frequency of the oscillation of the particle. The emitted wave is polarized
in the direction of the oscillation of the particle. However, the emission in not isotropic.
There is some radiation in the plane perpendicular to the oscillation of the particle, but
there is none in the direction of the oscillation of the particle.
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Now, let’s look at what happens when light is reflected. Let’s take a specific example to
simplify the reasoning: light travelling in air reflects and refracts when entering into water.
When the electromagnetic wave arrives on the water, charged particles in water started
oscillating. In turn, these particles emit an electromagnetic wave. The reflected light comes
from these waves emitted by charged particles while the refracted light is a combination of
the original wave and the wave emitted by the particles.
If the light that comes on the surface
is polarized in a direction parallel to
the surface (i.e. perpendicular to the
sheet), the particles of the medium
will also oscillate in that direction.
As the direction of the reflected
wave is perpendicular to the
direction of the oscillation of the
particle, there is some reflected light
with this polarization.
en.wikiversity.org/wiki/File:BrewsterAngle.jpg
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If the polarization of the light is in
a direction not parallel to the surface
(so along the sheet), then the
situation is quite different. Light
makes particles oscillate in the
direction shown in the figure in
water. This oscillation causes the
emission of light, but it is
impossible for these oscillations to
send light in the direction of the
reflection if the reflected light is in
the same direction as the oscillation
of the particles. In this case, there is
no reflected light because the
particles which oscillate cannot
send light in that direction. As this
oscillation is perpendicular to the
direction of the refracted ray, there
en.wikiversity.org/wiki/File:BrewsterAngle.jpg
is no light reflected with this
polarization if there are 90° between the refracted ray and the reflected ray.
So, if unpolarized light is reflected on a surface, the two polarizations are present. To find
out what happens then, the two figures obtained for each polarization must be added. The
result is
en.wikiversity.org/wiki/File:BrewsterAngle.jpg
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The two components of the polarizations of the light come on the surface. However, as
only one of these polarizations can be reflected, the reflected light is polarized. The two
components of the polarizations can be refracted, and the refracted ray is not so polarized.
It is, however, partially polarized, because one of the polarization components is stronger
than the other. The polarization that can be reflected has lost some of its intensity to the
reflection and less intensity is left for the refracted ray compared to the polarization that is
only refracted. This is how polarized light can be obtained from unpolarized light with a
reflection.
In short, there must be 90° between the reflected ray and the refracted ray to have
completely polarized reflected light. Then we have the situation shown in the figure.
According to Snell’s law, we have
n1 sin θ p = n2 sin θ 2
Since there are 90° between the reflected
ray and the refracted ray, we have
θ p + 90° + θ2 = 180°
θ2 = 90° − θ p
fr.wikipedia.org/wiki/Angle_de_Brewster
Snell’s law then becomes
n1 sin θ p = n2 sin θ 2
n1 sin θ p = n2 sin ( 90° − θ p )
n1 sin θ p = n2 cos θ p
Since sinθ /cosθ = tanθ, the end result is
Brewster’s Angle or Polarization Angle
tan θ p =
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n1
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Example 9.4.1
What is the polarization angle for light travelling in air and reflected from the surface of
water?
The angle is
tan θ p =
n2
n1
1.33
1
θ p = 53.1°
tan θ p =
This means that the light polarized in the direction shown in the figure is not reflected
on water if the angle of incidence is 53.1°.
en.wikiversity.org/wiki/File:BrewsterAngle.jpg
If the angle of incidence is not 53.1°, there will be some reflected light. The farther
away from the angle of polarization is the angle of incidence, the greater is the intensity
of the reflected light.
This effect can be seen in the following images. In this first image, everything is as usual.
The bottom of the sea is hard to see because the light reflected by the surface is brighter
than the light that comes from the bottom. In the picture to the right, a polarizing filter
having a vertical axis is used. As the light reflected on the water is horizontally polarized,
the filter blocks the reflected light. Now, the light that comes from the bottom is more
intense than the reflected light, and the bottom of the sea can be seen.
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www.digital-photography-tips.net/Stay_Focussed-Newsletter-March-2013.html
The following image shows that light is reflected off the car on the left image. Using a
polarizing with a horizontal axis, the light reflected on the vertical surfaces (which is
vertically polarized) is now blocked. The reflected light is now gone (image to the right).
fotografium.com/bw-55mm-polarize-filtre#.UxyRqvl5PTo
In fact, reflected light is rarely completely polarized. For this to happen, the angle of
incidence must be exactly equal to the angle of polarization. But even if the angle is not
exactly equal to the angle of polarization, the polarization of the reflected light parallel to
the surface is often stronger than the other component. There is a partial polarization. A
filter then blocks this strongest polarization and reflected light is less intense with the filter.
This phenomenon can be seen in the following figure. The light reflected off a lake is seen
through a polarizing filter with a vertical axis.
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paraselene.de/cgi/bin?_SID=7e65d76b84105709c35aeec86f67c20bdca7aabd00268925652735&_bereich=artikel&_aktion=detail&ida
rtikel=116150&_sprache=paraselene_englisch
At the bottom of the figure, there is virtually no light reflected on the lake. This is because
the light coming from this place comes on the lake with an angle of incidence near the
angle of polarization. This strongly polarized reflected light is then almost all blocked by
the polarizing filter and there is no reflected light. Elsewhere on the lake, the reflected light
can be seen. The reflection seen in these places comes from light having an angle of
incidence not that close to the angle of polarization. In this case, the reflected light is only
partially polarized. Although the filter blocks the horizontal polarization, the other
polarization remains, and some reflected light can be seen.
Polarized glasses are simply polarizing filters with a vertical axis. The effect is not
spectacular with unpolarized light: they simply absorb half the light. The light is polarized
after the passage through the glasses, but the human eye is not sensitive to the polarization,
which means that there is no difference between light polarized in one direction or another
or between unpolarized light and polarized light. There is, however, a difference with
reflected light. Reflected light is polarized in a direction parallel to the surface so that light
reflected on a lake or on the floor is horizontally polarized. With glasses having a vertical
axis, this polarized reflected light is blocked. The reflected light is thus strongly attenuated
with the polarized glasses. This is what we can see in this video.
http://www.youtube.com/watch?v=MNbg4Go8NR0
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Scattering occurs when light passes through a gas. Charged particles in the molecules of
gas start to oscillate and, in turn, start to emit light. This emitted light is the scattered light.
By the way, the result is not the same for all wavelengths. The scattering is more effective
for smaller wavelength. If white light passes through a gas, there is more scattering for
smaller wavelengths, such as blue light, than for longer wavelengths, such as red light. The
scattered light will then be blue.
This is why the sky is blue. When a person looks at the sky, he sees this blue light scattered
by the gas particles in the atmosphere.
photonicswiki.org/index.php?title=Dispersion_and_Scattering_of_Light
This is also why the Sun becomes redder at sunset. Smaller wavelengths were scattered by
the atmosphere, and only the larger wavelengths remain in the light coming from the Sun.
If the journey of the light through the atmosphere is longer, more blue light is scattered and
red light gains in importance. As the journey through the atmosphere is longer at sunset or
sunrise, the sun is redder at these moments.
photonicswiki.org/index.php?title=Dispersion_and_Scattering_of_Light
The scattered light is also polarized. It comes from the oscillations of the charged particles
and we saw that this light is polarized and is not emitted equally in every direction. Let’s
look at what happens with the light scattered at 90° when unpolarized light passes through
a gas.
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isites.harvard.edu/fs/docs/icb.topic227451.files/images/PolarizationbyScattering002.jpg
Vertically polarized light makes the charged particles oscillate vertically and there is some
light re-emitted in direction A but none in direction B. Horizontally polarized light make
the charged particles oscillate horizontally and there is some light re-emitted in direction
B but none in direction A. Therefore, light is polarized vertically in direction A and light
is polarized horizontally in direction B. All that to say that the light scattered at 90 degrees
is completely polarized. The direction of polarization is always perpendicular to the initial
ray of unpolarized light. The light scattered at other angles is partially polarized. The
polarization gets stronger as the scattering angle gets closer to 90°.
In the following picture, the sky is observed with a polarized filter. This is actually in a
direction perpendicular to the direction of the Sun. In this direction, light scattered at 90°
is seen. By placing the axis of the polarizer in the direction of the Sun, the light polarized
perpendicular to this direction is blocked since it is polarized perpendicularly to the
direction of the initial ray.
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paraselene.de/cgi/bin?_SID=7e65d76b84105709c35aeec86f67c20bdca7aabd00268925652735&_bereich=artikel&_aktion=detail&ida
rtikel=116150&_sprache=paraselene_englisch
The dark band corresponds to the directions where the light of the sky is scattered at 90°.
The polarization of the sky light can be used to do some special effects in photography.
With a polarizing filter, the intensity of the sky light, which is often at least partially
polarized, can be strongly reduced to increase the contrast between the sky and the clouds
(which emits unpolarized light). The picture on the left was made without a filter, and the
picture on the right was obtained with a polarizing filter.
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Luc Tremblay
Collège Mérici, Quebec City
forums.steves-digicams.com/newbie-help/147679-polarizing-filter-necessary.html#b
Some crystals are not isotropic (this happens if the molecules are all aligned in the same
direction, for example). This means one polarization can go faster in one direction in the
crystal. This direction is indicated by the optic axis of the crystal.
Let’s see what this means for light polarized in a direction perpendicular to the optical axis
of the crystal. This polarization creates waves that propagate at the same speed in every
direction (circles in the figure) and so it propagates normally in the substance
(perpendicular to the wavefront). This polarization forms the ordinary ray.
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Luc Tremblay
Collège Mérici, Quebec City
For the other polarization, the wave is propagating faster in the direction of the optical axis.
The waves are not circles anymore but ellipses stretched in the direction of the optical axis
In a previous chapter, it was said that the rays are always perpendicular to the wavefronts.
This is true if the speed of light is the same in every direction but this is no longer true if
the speed is different, as here. The direction is rather as follow.
This ray goes from the center of the ellipse to the point of the ellipse tangent to the
wavefront. This means that ray does not travels in the expected direction (which would
have been directly towards the right here because the angle of incidence was zero). The ray
travelling in this unexpected direction is called the extraordinary ray. For calcite, the angle
between the ordinary ray and the extraordinary ray is 6.2°.
www.a-levelphysicstutor.com/wav-light-polariz.php
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Luc Tremblay
Collège Mérici, Quebec City
If unpolarised light pass through such a crystal, then the ordinary ray and the extraordinary
ray are present at the same time. Unpolarised light is thus separated into two polarized rays
with the same intensity.
theses.ulaval.ca/archimede/fichiers/22342/ch02.html
With a polarizing filter, it is quite easy to see that the two images obtained with a crystal
of calcite are polarized. By turning the filter, we can also switch from one image to the
other.
http://www.youtube.com/watch?v=WdrYRJfiUv0
The study of the passage of light in crystals is quite complex. Be aware that the refractive
index then becomes a 3 x 3 matrix and it is possible to have a refraction with a certain angle
even if the incidence angle is zero (this is the case for the vertically polarized beam in the
last figure). We will not explore these complex cases in these notes.
Certain kinds of molecules in solution can make the direction of polarization of polarized
light rotate. This ability to rotate the polarization direction is called optical activity and the
molecules that can rotate the direction are called enantiomers. In the following figure, a
substance in solution rotates the direction of polarization clockwise when looking at the
beam of light heading towards us. Then, a dextrorotatory enantiomer was used. If the
direction turns to the left, a levorotatory enantiomer was used.
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Luc Tremblay
Collège Mérici, Quebec City
158.64.21.3/chemistry/stuff1/EX1/notions/optique.htm
As the angle of rotation depends on the concentration of the substance, the rotation angle
can be used to determine the enantiomer concentration.
Here is a demonstration with sugar molecules.
http://www.youtube.com/watch?v=GchTURvBz68
The optical activity of some transparent substances depends on the tension in the object
and the wavelength of the light passing through the object. When polarized white light
passes through these objects, the areas of tension in the object can easily be seen if the
object is looked at through a polarizing filter.
en.wikipedia.org/wiki/Photoelasticity
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Luc Tremblay
Collège Mérici, Quebec City
Optical activity is also used in liquid crystal displays. These displays consist of a layer of
liquid crystal inserted between two crossed
polarizers (which have perpendicular axes
relative to each other). When there is no
electric field, the liquid crystals are
optically active. The thickness of the liquid
crystal is exactly chosen so that the
direction of polarization turns by 90°
during its journey through the crystal.
Therefore, the light can pass when it arrives
at the other polarizer. The light is then
reflected on a mirror, passes through the
polarizer again, in the crystal layer that
changes the direction of polarization by
90° again, and through the other polarizer.
Since light can get out, the display is then
white.
https://nothingnerdy.wikispaces.com/11.5+Polarisation
When an electric field is applied, the liquid
crystals lose their optical activity. Thus, the
direction of polarization of the polarized
light that passes through the liquid crystal
layer does not rotate, and the light is
blocked by the polarizer located on the
other side of the layer. Therefore, no light
gets to the mirror and there is no reflected
light. The display is then black.
https://nothingnerdy.wikispaces.com/11.5+Polarisation
This means that the image that comes out of a liquid crystal display is polarized. You can
easily see this by looking at those screens with polarized glasses and turning his head. You
will then see the intensity change depending on the orientation of the glasses.
This video shows the light coming out of LCD screens is actually polarized while that of
old CRT screens was not.
http://www.youtube.com/watch?v=GwzUMEuGZHs
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Luc Tremblay
Collège Mérici, Quebec City
Unpolarized Light Passing Through a Polarizing Filter
The light is now polarized in the direction of the
polarization axis of the filter.
I=
I0
2
where I0 is the intensity of the light before the passage through the filter.
Polarized Light Passing Through a Polarizing Filter
The light is polarized in the direction of the
polarization axis of the filter.
I = I 0 cos2 θ
where I0 is the intensity of the light before the passage through the filter.
Brewster’s Angle or Polarization Angle
tan θ p =
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n2
n1
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Luc Tremblay
Collège Mérici, Quebec City
9.3 Polarization by Absorption
1. What is the intensity of the light after its passage through these two polarizers?
www.chegg.com/homework-help/questions-and-answers/polarization-experiment-shown-incident-beam-light-linearlypolarized-vertical-direction-tr-q1553661
2. What is the intensity of the light after its passage through these three polarizers if
it was not polarized initially?
www.chegg.com/homework-help/questions-and-answers/figure-initially-unpolarized-light-sent-three-polarizing-sheetswhose-polarizing-direction-q1397630
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Luc Tremblay
Collège Mérici, Quebec City
3. What should be the angle of the second polarizer to obtain the intensity indicated
in the figure if the light was not polarized initially?
www.chegg.com/homework-help/questions-and-answers/three-polarizing-plates-whose-planes-parallel-centered-commonaxis-directions-transmission-q2410749
9.4 Polarization by Reflection
4. What should be the angle in this figure so that the reflected ray of light is totally
polarized?
www.rp-photonics.com/brewster_plates.html
5. What should be the angle in this figure so that the reflected ray of light is totally
polarized?
en.wikipedia.org/wiki/Optics
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Luc Tremblay
Collège Mérici, Quebec City
6. Light reflects off a glass surface. The refractive index of the glass is 1.7. What is
the angle between the normal and the refracted ray (θ in the figure) if the reflected
ray is completely polarized?
cnx.org/content/m42522/latest/?collection=col11406/latest
7. Light arrives at an interface between two media (and one of the media is not
necessarily air). The critical angle for internal reflection is 48°.
a) What is the angle of polarization?
b) Is it possible to have a totally polarized total reflection?
9.3 Polarization by Absorption
1. 20.53 W/m²
2. 1.25 W/m²
3. 70.8° or 149.2°
9.4 Polarization by Reflection
4.
5.
6.
7.
57.2°
36.9°
30.5°
b) 36.6°
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b) No
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