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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 2017 Version 9-Polarization 2 Luc Tremblay Collège Mérici, Quebec City 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... 2017 Version 9-Polarization 3 Luc Tremblay Collège Mérici, Quebec City 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. 2017 Version 9-Polarization 4 Luc Tremblay Collège Mérici, Quebec City 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 2017 Version 9-Polarization 5 Luc Tremblay Collège Mérici, Quebec City 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. 2017 Version 9-Polarization 6 Luc Tremblay Collège Mérici, Quebec City 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). 2017 Version 9-Polarization 7 Luc Tremblay Collège Mérici, Quebec City 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 2017 Version 9-Polarization 8 Luc Tremblay Collège Mérici, Quebec City 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 2017 Version 9-Polarization 9 Luc Tremblay Collège Mérici, Quebec City 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. 2017 Version 9-Polarization 10 Luc Tremblay Collège Mérici, Quebec City 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 2017 Version 9-Polarization 11 Luc Tremblay Collège Mérici, Quebec City 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 2017 Version 9-Polarization 12 Luc Tremblay Collège Mérici, Quebec City 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 2017 Version 9-Polarization 13 Luc Tremblay Collège Mérici, Quebec City 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. 2017 Version 9-Polarization 14 Luc Tremblay Collège Mérici, Quebec City 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 2017 Version 9-Polarization 15 Luc Tremblay Collège Mérici, Quebec City 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 2017 Version 9-Polarization 16 Luc Tremblay Collège Mérici, Quebec City 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 = 2017 Version n2 n1 9-Polarization 17 Luc Tremblay Collège Mérici, Quebec City 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. 2017 Version 9-Polarization 18 Luc Tremblay Collège Mérici, Quebec City 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. 2017 Version 9-Polarization 19 Luc Tremblay Collège Mérici, Quebec City 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 2017 Version 9-Polarization 20 Luc Tremblay Collège Mérici, Quebec City 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. 2017 Version 9-Polarization 21 Luc Tremblay Collège Mérici, Quebec City 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. 2017 Version 9-Polarization 22 Luc Tremblay Collège Mérici, Quebec City 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. 2017 Version 9-Polarization 23 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. 2017 Version 9-Polarization 24 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 2017 Version 9-Polarization 25 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. 2017 Version 9-Polarization 26 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 2017 Version 9-Polarization 27 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 2017 Version 9-Polarization 28 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 = 2017 Version n2 n1 9-Polarization 29 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 2017 Version 9-Polarization 30 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 2017 Version 9-Polarization 31 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° 2017 Version b) No 9-Polarization 32