How can light reflections on the surface of water be blocked to see what is on the bottom of the sea?

Transcription

1 How can light reflections on the surface of water be blocked to see what is on the bottom of the sea? Discover the answer to this question in this chapter.

2 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 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 light 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 At first, it was easier to explain polarization with the corpuscular theory. Playing with the shape of light particles, a theory was devised. In this theory, the two refractions obtained in a calcite crystal depended on the orientation of the particles of light when they enter the substance. It was not perfect, but it was much better than the explanation given by the wave theory at that time. For a long time, the proponents of the wave theory were completely 2018 Version 9-Polarization 2

3 unable to explain this phenomenon. Polarization was the only thing keeping the corpuscular theory alive after the successes of the wave theory with Young s experiment (interference) and Fresnel work on diffraction. Supporters of the corpuscular theory could always reply that the corpuscular theory was 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 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 then. 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 new experiments on polarization that will bring the victory of the wave theory. What If Light Waves Were 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 in order for the wave to propagate. This medium was called aether (which has nothing to do with the aether 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 path between the Andromeda Galaxy and the Earth. At the same time, this aether must not exert any frictional force since the Earth is rotating around the Sun without losing any energy because of friction. If aether had exerted only a small frictional 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 had to be rigid. But then, 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 see in a further chapter). However, the weird properties of the aether caused a certain 2018 Version 9-Polarization 3

4 discomfort throughout the 19 th 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 really transverse waves. For about 25 years, physicists continued to try to match Maxwell s equations with the concept of aether with quite extraordinary 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. Here is an animation of the motion of this wave. This is not a mechanical wave since the passage of the wave does not entail any oscillations of a medium. It is said to be 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 Version 9-Polarization 4

5 The Direction of Oscillation of the Electric Field With a transverse wave, there is something more that is impossible for a 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. 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 depending on the direction of the oscillation of the field. For example, in certain substances, a wave that oscillates horizontally (which is said to be horizontally polarized) does not travel at the same speed as a wave that oscillates vertically (which is said to be 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 all these different possibilities be examined? Of course not. It is possible to work with only 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 horizontal polarization and one half of vertical polarization. If the behaviour of each 2018 Version 9-Polarization 5

6 component is known, then the behaviour of any polarization can be known since it is a combination of the behaviour of the two main components. A wave can be easily resolved into its two components along the selected axes. The components are E E = E cosθ 0x 0 = E sinθ 0 y 0 where E 0 is the amplitude of the wave, E 0x is the amplitude of the x-component, E 0y 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 depending on the conditions. However, the two axes must always be perpendicular to each other. Polarized and Unpolarized Light Light is polarized if the electric field oscillates uniquely along one direction. Generally, light is made up of several superimposed waves, and all these waves have the same direction of oscillation in polarized light. 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. This means that the orientation of a rod-shaped antenna must be the same as the direction of the electric field oscillations to get a good reception Version 9-Polarization 6

7 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 Interference 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 interfere at all. This phenomenon was discovered by François Arago and Augustin Fresnel in For example, the interference pattern would look totally different if Young s experiment was performed with polarizers with different orientations for each slit. 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) Version 9-Polarization 7

8 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 slit 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 of the same polarization in 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 2018 Version 9-Polarization 8

9 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 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. I0 I = 2 where I 0 is the intensity of the light before its 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 polarization are parallel, then it is true that all the light passes through the filter. otl.curtin.edu.au/events/conferences/tlf/tlf1997/swan.html 2018 Version 9-Polarization 9

10 If, on the other hand, if the axis is perpendicular to the direction of the polarization, 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 polarization is θ, then the parallel component is A = A cosθ 0 As the intensity is proportional to the square of the amplitude, the intensity is I = I cos 2 θ 0 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, the polarization of the light is always in the same direction as the axis of the last polarizer that the light has passed through Version 9-Polarization 10

11 In summary, we have Polarized Light Passing Through a Polarizing Filter This is Malus s law. The light is polarized in the direction of the polarization axis of the filter. I = I cos 2 θ 0 where I 0 is the intensity of the light before the passage through the filter. Thus, if the angle between the axes is zero, all the light passes. If the angle is 90, no light passes. That s what Grandpa John says and the Department of Physics and Astronomy of the University of California. In this video, a nice magic trick is made. Example Unpolarized light with initial intensity I i 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? Version 9-Polarization 11

12 First Polarizer Unpolarized light arrives on a polarizer. The intensity of the light after its passage through the polarizer is thus I Ii = = 0.5I 2 i The light is now polarized in the direction of the axis of the polarizer, so at 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 = 10. The intensity of the light after its passage through the polarizer is thus I = I 0 cos Ii cos 10 = 0.485I θ = i The light is now polarized in the direction of the axis of the polarizer, so at 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 = 20. The intensity of the light after its passage through the polarizer is thus I I I = I 0 cos Ii cos 20 = 0.428I θ = 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 an observer looks 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 onto the screen. One way to achieve this is to use polarized image. One image is made of vertically polarized light 2018 Version 9-Polarization 12

13 and the other image 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/ 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/ stm 2018 Version 9-Polarization 13

14 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/ A beam of 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 Version 9-Polarization 14

15 Now, let s look at what happens when light is reflected. Let s take a specific example to simplify the reasoning: a beam of light travelling in air reflects and refracts when entering into water. When the electromagnetic wave arrives in 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 particles, there is some reflected light with this polarization. en.wikiversity.org/wiki/file:brewsterangle.jpg 2018 Version 9-Polarization 15

16 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 in water oscillate in the direction shown in the figure. 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 is no light en.wikiversity.org/wiki/file:brewsterangle.jpg 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 2018 Version 9-Polarization 16

17 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 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 a completely polarized reflected light beam. This is the situation shown in the figure. According to Snell s law, we have n sinθ = n sinθ 1 p 2 2 Since there are 90 between the reflected ray and the refracted ray, the angle is θ θ = 180 p 2 2 θ = 90 θ p fr.wikipedia.org/wiki/angle_de_brewster Snell s law then becomes n sinθ = n sinθ 1 p p 2 Since sinθ /cosθ = tanθ, the end result is Brewster s Angle or Polarization Angle 1 p 2 ( θ p ) n sinθ = n sin 90 n sinθ = n cosθ n tanθ p = n 2 1 p 2018 Version 9-Polarization 17

18 Example What is the polarization angle for light travelling in air and reflected from the surface of water? The angle is n tanθ p = n tanθ p = 1 θ = 53.1 p This means that the light polarized in the direction shown in the figure cannot be reflected on water if the angle of incidence is en.wikiversity.org/wiki/file:brewsterangle.jpg If the angle of incidence is not 53.1, then there will be some reflected light. The farther away the angle of polarization is from 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 coming from the bottom of the sea. 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 coming from the bottom of the sea is more intense than the reflected light, and the bottom of the sea can be seen Version 9-Polarization 18

19 The following left image shows reflected light off the car. Using a polarizing filter 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 Reflected light is rarely completely polarized. For this to happen, the angle of incidence must be exactly equal to the polarization angle. But even if the angle is not exactly equal to the angle of polarization, the intensity of the polarization parallel to the surface is often stronger than the other component in the reflected light. There is a partial polarization. A filter can then block 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 Version 9-Polarization 19

20 paraselene.de/cgi/bin?_sid=7e65d76b c35aeec86f67c20bdca7aabd &_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 close to the polarization angle. This strongly polarized reflected light is then almost all blocked by the polarizing filter and no reflected light can be seen. Elsewhere on the lake reflected light can be seen. The reflection seen in these places comes from light having an angle of incidence not that close to the polarization angle. 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 its passage through the glasses, but the human eye is not sensitive to 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 (totally or partially). With glasses having a vertical axis, this polarized reflected light is blocked. The reflected light is thus strongly attenuated with polarized glasses. This is shown in this video Version 9-Polarization 20

21 Scattering occurs when light passes through a gas. Charged particles in the gas molecules start to oscillate and 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 longer 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 Scattered light is also polarized. It comes from the oscillations of the charged particles and it was seen that this light is polarized and is not emitted equally in every direction. Let s look at what happens for light scattered at 90 when unpolarized light passes through a gas Version 9-Polarization 21

22 isites.harvard.edu/fs/docs/icb.topic 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 light scattered at 90 degrees is completely polarized. The direction of polarization is always perpendicular to the initial direction of propagation of the unpolarized light beam. 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 Version 9-Polarization 22

23 paraselene.de/cgi/bin?_sid=7e65d76b c35aeec86f67c20bdca7aabd &_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 light coming from the sky can be used to do some special effects in photography. With a polarizing filter, the intensity of the light coming from the sky, which is often at least partially polarized, can be strongly reduced to increase the contrast between the sky and the clouds (which emit unpolarized light). The picture on the left was made without a filter, and the picture on the right was obtained with a polarizing filter Version 9-Polarization 23

24 forums.steves-digicams.com/newbie-help/ polarizing-filter-necessary.html#b Some crystals are not isotropic (this happens when all the molecules are aligned in the same direction, for example). This often implies that one polarization can go faster in one direction in the crystal. This direction is indicated by the optic (or optical) axis of the crystal. Let s see what this means for light polarized in a direction perpendicular to the optic 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 Version 9-Polarization 24

25 For the other polarization, the wave is propagating faster in the direction of the optic axis. The waves are not circles anymore but ellipses stretched in the direction of the optic 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 follows. This ray goes from the centre 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 Version 9-Polarization 25

26 If unpolarized light pass through such a crystal, then the ordinary ray and the extraordinary ray are present at the same time. Unpolarized 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 rotating the filter, it is possible to switch from one image to the other. The study of the passage of light in anisotropic crystals is quite complex. 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 (as for the extraordinary ray in calcite). These complex cases will not be explored 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. This means that a dextrorotatory enantiomer was used. If the direction turns to the left, a levorotatory enantiomer was used Version 9-Polarization 26

27 /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. The optical activity of some transparent substances depends on the tension forces 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 2018 Version 9-Polarization 27

28 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, light can pass when it arrives at the other polarizer. The light beam 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. 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. This also means that the image that comes out of a liquid crystal display is polarized. This can easily be seen by looking at those screens with polarized glasses. Then, the intensity of the light change depending on the orientation of the glasses. This video shows the light coming out of LCD screens is actually polarized while the light coming out of old CRT screens was not Version 9-Polarization 28

29 Unpolarized Light Passing Through a Polarizing Filter The light is now polarized in the direction of the polarization axis of the filter. I0 I = 2 where I 0 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 cos 2 θ 0 where I 0 is the intensity of the light before the passage through the filter. Brewster s Angle or Polarization Angle n tanθ p = n Version 9-Polarization 29

30 9.3 Polarization by Absorption 1. What is the light intensity after its passage through these two polarizers? 2. What is the light intensity after its passage through these three polarizers if it was not polarized initially? Version 9-Polarization 30

31 3. What should the angle of the second polarizer be to obtain the intensity indicated in the figure if the light is not polarized initially? 4. Polarized light passes through a polarizer. After passing through the polarizer, the intensity of the light is 5 W/m². The intensity decreases to 3 W/m² if the polarizer is rotated by 20. What is the light intensity before its passage through the polarizer? Hint: cos( a + b) = cos a cosb sin asin b 9.4 Polarization by Reflection 5. What should the angle in this figure be in order to have a reflected ray of light totally polarized? Version 9-Polarization 31

32 6. What should the angle in this figure be in order to have a reflected ray of light totally polarized? en.wikipedia.org/wiki/optics 7. 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 8. 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? 2018 Version 9-Polarization 32

33 Challenge (Question more difficult than the exam questions.) 9. The percentage of polarization of a partially polarized beam of light is defined with the following formula. p = I I max max I + I min min where I max and I min are the maximum and minimum intensities obtained when light passes through a polarizer that is rotated slowly. Show that if a beam of partially polarized light passes through a polarizer which makes an angle θ with the position where the intensity is I max, the intensity of the light passing through the polarizer is given by I ( θ ) 1+ p cos 2 = 1+ p Hints: A partially polarized beam can be considered as a superposition of two perpendicularly polarized waves with different intensities and cos( a + b) = cos a cosb sin asin b 9.3 Polarization by Absorption W/m² W/m² or W/m² 9.4 Polarization by Reflection b) 36.6 b) No 2018 Version 9-Polarization 33