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Topic 11: Wave phenomena 11.5 Polarization

11.5.1 Describe what is meant by polarized light. 11.5.2 Describe polarization by reflection. 11.5.3 State and apply Brewster’s law. 11.5.4 Explain the terms polarizer and analyzer. 11.5.5 Calculate the intensity of a transmitted beam of polarized light using Malus law.

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Topic 11: Wave phenomena 11.5 Polarization

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  1. 11.5.1 Describe what is meant by polarized light. 11.5.2 Describe polarization by reflection. 11.5.3 State and apply Brewster’s law. 11.5.4 Explain the terms polarizer and analyzer. 11.5.5 Calculate the intensity of a transmitted beam of polarized light using Malus law. Topic 11: Wave phenomena11.5 Polarization

  2. Describe what is meant by polarized light. Recall that in transverse waves the oscillations are perpendicular to the direction of the propagation of the traveling wave. On the other hand, longitudinal waves oscillate parallel to the direction of motion. Thus, transverse waves can have infinitely many modes of oscillation, each of which is perpendicular to the propagation, whereas longitudinal can only have a single mode. Because of these allowed modes, as we will see, the phenomenon of polarization only applies to transverse waves. In this subtopic we will consider only one transverse wave, namely light. Topic 11: Wave phenomena11.5 Polarization

  3. Describe what is meant by polarized light. Light is a transverse wave having two types of oscillation perpendicular to the direction of propagation of the wave. Note that electro- magnetic radiation consists of mutually perpendicular oscillating electric and magnetic fields. Topic 11: Wave phenomena11.5 Polarization FYI In this subtopic we will consider polarization in terms of the electric field, not the magnetic field.

  4. B A Describe what is meant by polarized light. Sketching the electric field itself is simplified even more: If we look at the ray diagram from the edge of its plane (at edge A) this is what we draw: If we look at the ray diagram from the edge of a perpendicular plane (at edge B) this is what we draw: Topic 11: Wave phenomena11.5 Polarization View from Point A View from Point B

  5. Describe what is meant by polarized light. In general electromagnetic (EM) waves are produced in random orientations. Thus the beam consists of electric fields (all perpendicular to the wave direction, of course) in many orientations. Topic 11: Wave phenomena11.5 Polarization EXAMPLE: This is what the light from an incandescent bulb might look like. Note the random orientations of the E-field. Unpolarized light (simplified view) Unpolarized light

  6. Describe what is meant by polarized light. A manmade film call Polaroid can take unpolarized light, and absorb all rays of light whose electric fields are not oriented in a certain line. Topic 11: Wave phenomena11.5 Polarization EXAMPLE: If unpolarized light is passed through the Polaroid film it will absorb all the rays not oriented with the film. Polaroid is not the only way to polarize light. In general, the object used to polarize unpolarized light is called a polarizer. Polaroid film Linearly-polarized light Unpolarized light POLARIZER

  7. Describe what is meant by polarized light. EXAMPLE: Polaroid is made of very long, parallel molecules. A simple model is a slotted disk. Only electric fields oriented in the proper manner are allow to pass. The rest are absorbed. Topic 11: Wave phenomena11.5 Polarization FYI Although one would think that the electric field would be allowed to pass through the “slots” only if parallel to them, in reality only perpendicular E-fields can pass through. Just live with it! Thus the light that makes it through Polaroid looks like this:

  8. Describe what is meant by polarized light. EXAMPLE: This is a view of unpolarized light passing through a linear polarizer. (The light is traveling from right to left.) Topic 11: Wave phenomena11.5 Polarization FYI Linear-polarized is also called plane-polarized.

  9. Describe what is meant by polarized light. EXAMPLE: In addition to plane-polarization there is also elliptical or circular polarization. Topic 11: Wave phenomena11.5 Polarization FYI Circular polarization is used in those 3D movies you pay good money to see.

  10. Describe what is meant by polarized light. EXAMPLE: Regardless of the polarization type, a projection of the E-field into any plane will reveal a perfect sine wave. The blue plane and the green plane are mutually perpendicular. Note that the blue and green projections are in-phase for linearly polarized light. The blue and green projections are 90º out-of-phase for circularly polarized light. Topic 11: Wave phenomena11.5 Polarization FYI Anything in between will produce elliptical polarization.

  11. Describe what is meant by polarized light. EXAMPLE: An animation of circularly-polarized light shows that in any plane perpendicular to the polarized light, the E-field rotates over time. Topic 11: Wave phenomena11.5 Polarization

  12. Describe what is meant by polarized light. We know we can obtain polarized light using Polaroid. There are, however, other ways to obtain polarized light. Some EM radiation is polarized when it is produced. For example, EM waves used for television are often polarized either horizontally or vertically, depending on the arrangement of the aerials. Some polarized light, for example circularly polarized light, can be constructed from two polarized rays. Some polarized light comes from the reflection of unpolarized light from a boundary in two mediums. We will learn about this in the next few slides. Topic 11: Wave phenomena11.5 Polarization

  13. Describe polarization by reflection. EXAMPLE: Besides a Polaroid filter, there are other ways to polarize light. One way is by reflecting light from a surface between two media where you get reflection and refraction. Topic 11: Wave phenomena11.5 Polarization Unpolarized light Partially polarized reflected light inc refl FYI Polarization occurs parallel to the surface between the two media and varies with angle of incidence. refr Unpolarized refracted light

  14. Ifrefl + refr = 90º then the reflected ray will be completely plane-polarized. Brewster’s law State and apply Brewster’s law. It turns out that if the refracted and reflected rays make a 90º angle then the reflected ray will be totally linearly polarized. The particular angle of incidence at which this total polarization occurs is called Brewster’s angle. Topic 11: Wave phenomena11.5 Polarization ( Or inc + refr = 90º ) PRACTICE: Use the simplified method to draw an unpolarized incident ray becoming completely polarized by reflection. inc refl FYI Also, recall that inc = refl. refr

  15. Ifrefl + refr = 90º then the reflected ray will be completely plane-polarized. Brewster’s law inc refl n = tan index of refraction ( Or inc + refr = 90º ) where  is Brewster’s angle refr State and apply Brewster’s law. Topic 11: Wave phenomena11.5 Polarization EXAMPLE: Show that the refractive index n of the medium is given by SOLUTION: Recall that n2/n1 = sin1 /sin2. Thus n/1 = sininc /sinrefr = sin /sinrefr. Recall the identity sin(90º - ) = cos. Then sinrefr = sin(90º-inc) = cosinc = cos. Thus n/1 = sin /sinrefr = sin/cos = tan. 1 = inc =  n1 = 1 n2 = n 2 = refr

  16. State and apply Brewster’s law. PRACTICE: Unpolarized light in air is reflected from a glass surface in such a way that it is completely polarized. The angle of incidence is is 51º. (a) What is the index of refraction of the glass? (b) What is the angle of refraction? (c) What is the speed of light in the glass? SOLUTION:  = inc = 51º. (a) n = tan = n = tan51º = 1.2. (b)The law of reflection says that inc = refl so refl + refr = 90º 51º+ refr = 90º refr = 39º (c) v2/v1 = sin2 /sin1 v/c = sin39º/sin51º v = 3.0108(sin39º/sin51º) = 2.4108 ms-1. Topic 11: Wave phenomena11.5 Polarization

  17. First filter LIGHT Explain the terms polarizer and analyzer. EXAMPLE: Two Polaroid filters are placed in a beam of light as shown. Explain why when one of the filters is rotated through 90º, the inten- sity of the light pass- ing through the pair decreases to zero. The first filter plane- polarizes the incoming light. The second filter, originally oriented to allow passage, is now oriented to completely block the polarized beam. Topic 11: Wave phenomena11.5 Polarization Second filter Analyzer Polarizer FYI The first filter is called the polarizer, and the second filter is called the analyzer.

  18. Observe the light intensity through two polarizing filters as the top one is rotated through 180º. Which filter is the analyzer? Which filter is the polarizer? BLACK FILTER RED FILTER

  19. A P  E Ecos Calculate the intensity of a transmitted beam of polarized light using Malus law. In general, polarizing filters are sketched with lines showing the orientation of the E-field allowed through: Note that the analyzer is rotated (rather than the polarizer).  is the angle between the polarizer P and the analyzer A. Topic 11: Wave phenomena11.5 Polarization  Polarized light E (from polarizer) Direction of allowed E-field (by analyzer)  Angle through which analyzer has been turned E-field allowed to pass

  20. I = I0 cos2 Malus’s law Where I0 is the original intensity of the light and  is the angle of the analyzer.  E Ecos Calculate the intensity of a transmitted beam of polarized light using Malus law. Recall that the intensity of a wave is proportional to the square of its amplitude. Thus the intensity of the light that comes out of the analyzer is proportional to (E cos )2. Topic 11: Wave phenomena11.5 Polarization Polarized light E (from polarizer) Direction of allowed E-field (by analyzer)  Angle through which analyzer has been turned E-field allowed to pass

  21. Calculate the intensity of a transmitted beam of polarized light using Malus law. PRACTICE: The preferred directions of two sheets of Polaroid are initially parallel. (a) Calculate the angle through which one sheet needs to be turned in order to reduce the amplitude of the observed E-field to half its original value. (b) Calculate the effect this rotation has on the intensity. (c) Calculate the rotation angle needed to halve the intensity from its original value. SOLUTION: (a) Solve cos  = ½   = 60º. (b) I = I0 cos2 = I0(1/2)2 = I0/4. (c) I0/2 = I0 cos2  cos2 = ½. Thus cos = (½)1/2   = 45º. Topic 11: Wave phenomena11.5 Polarization

  22. 11.5.6 Describe what is meant by an optically active substance. 11.5.7 Describe the use of polarization in the determination of the concentration of certain solutions. 11.5.8 Outline qualitatively how polarization may be used in stress analysis. 11.5.9 Outline qualitatively the action of liquid-crystal displays (LCDs). 11.5.10 Solve problems involving the polarization of light. Topic 11: Wave phenomena11.5 Polarization

  23. Describe what is meant by an optically active substance. A substance is termed optically active if the plane of polarized light rotates as it passes though the substance. A sugar solution is an example of such a substance. So is quartz. The angle through which the plane rotates depends on the concentration of the solution (if the substance can be made into a solution), and the distance through which the light passes. Topic 11: Wave phenomena11.5 Polarization 

  24. C/gcm-3 0.30 0.20 0.10 /º 5 10 15 20 Describe the use of polarization in the determination of the concentration of certain solutions. Topic 11: Wave phenomena11.5 Polarization PRACTICE: Data for various concentrations of sugar solution have been gathered for a sample tube of fixed length. (a) Plot a suitable graph to represent the data. SOLUTION:

  25. C/gcm-3 0.30 0.20 0.10 /º 5 10 15 20 Describe the use of polarization in the determination of the concentration of certain solutions. Topic 11: Wave phenomena11.5 Polarization PRACTICE: Data for various concentrations of sugar solution have been gathered for a sample tube of fixed length. (b) Find the concentration of a sugar solution having  = 18º. SOLUTION: Polarimeter About 0.30 g cm-3. FYI The above apparatus is called a polarimeter.

  26. Outline qualitatively how polarization may be used in stress analysis. When stressed, glass and plastics develop optical properties that are dependent on the plane of polarization. When placed between a polarizer and an analyzer, and illuminated by white light, the regions of highest stress will appear as colored lines. Topic 11: Wave phenomena11.5 Polarization

  27. Outline qualitatively the action of liquid-crystal displays (LCDs). Liquid crystals (LC) are optically active substances whose activity can be controlled by applying a potential difference across them. If there is no p.d. across the LC it will not be optically active. If there is a p.d. across the LC it will rotate light through 90º. Reflector Second polarizer Topic 11: Wave phenomena11.5 Polarization Common electrode Liquid crystal Shaped electrode First polarizer FYI The LCD is illuminated by ambient unpolarized light from the external environment.

  28. Outline qualitatively the action of liquid-crystal displays (LCDs). The light is polarized by the first polarizer. If there is no p.d. it will continue through to the second polarizer at which point it will be completely absorbed because of the cross polarization. It is then reflected back to the viewer as black. Reflector Second polarizer Topic 11: Wave phenomena11.5 Polarization Common electrode Liquid crystal Shaped electrode First polarizer FYI An LCD projector replaces the reflector with a light source.

  29. Outline qualitatively the action of liquid-crystal displays (LCDs). If there is a p.d. across the LC, it will become optically active. The LC will then rotate the polarized light from the first polarizer an additional 90º. This action aligns it with the second polarizer, which now allows it to pass through unhindered. Reflector Second polarizer Topic 11: Wave phenomena11.5 Polarization Common electrode Liquid crystal Shaped electrode First polarizer FYI The image received by the eye will have the shape determined by the shaped electrode. You will perceive your number shapes.

  30. Solve problems involving the polarization of light. Topic 11: Wave phenomena11.5 Polarization In general, light sources produce waves having their E-fields oriented in many random directions. Polarized light is light whose waves have their E-fields oriented in one direction.

  31. Solve problems involving the polarization of light. Topic 11: Wave phenomena11.5 Polarization Use I = I0 cos2. Then I = I0 cos260º I = 0.25I0

  32. Solve problems involving the polarization of light. I0 cos20º = I0 I0 cos260º = 0.25I0 Topic 11: Wave phenomena11.5 Polarization I0 cos290º = 0 I0 cos2120º = 0.25I0 I0 cos2180º = I0

  33. Solve problems involving the polarization of light. Topic 11: Wave phenomena11.5 Polarization In general, light sources produce waves having their E-fields oriented in many random directions. Polarizing sunglasses only allow waves in one direction through, thereby reducing the intensity of the light entering the eye. Reflecting surfaces also polarize light to a certain extent, thereby rendering polarizing sunglasses even more effective.

  34. Solve problems involving the polarization of light. Topic 11: Wave phenomena11.5 Polarization Use I = I0 cos2. Then I = I0 (1/2)2 = I0/4.

  35. Solve problems involving the polarization of light. Topic 11: Wave phenomena11.5 Polarization If plane-polarized light (say horizontal) passes through an optically active substance (say LC), the plane will be rotated as the polarized light passes through (no longer horizontal, but still plane-polarized).

  36. Solve problems involving the polarization of light. Topic 11: Wave phenomena11.5 Polarization Light polarized at P1 would not be transmitted at P2 because it is oriented at 90º to P1so the observer would see black reflected.

  37. The p.d. across the LC makes it optically active. The LC then rotates the P1 ray by 90º. Solve problems involving the polarization of light. Topic 11: Wave phenomena11.5 Polarization The ray is now parallel to P2 and transmitted. It thus reflects to eye in shape of electrode.

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