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Sight and Wave Phenomena (A) Part 2

Mr. Klapholz Shaker Heights High School. Sight and Wave Phenomena (A) Part 2. Water waves incident on a barrier with a gap. Diffraction. Water waves incident on a barrier with a gap. Diffraction. Huygens’ Theory: Every wave is made of ‘wavelets’ (sources of more waves).

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Sight and Wave Phenomena (A) Part 2

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  1. Mr. Klapholz Shaker Heights High School Sight and Wave Phenomena (A) Part 2

  2. Water waves incident on a barrier with a gap. Diffraction.

  3. Water waves incident on a barrier with a gap. Diffraction.

  4. Huygens’ Theory: Every wave is made of ‘wavelets’ (sources of more waves). http://www.svi.nl/HuygensPrinciple

  5. How would Huygens explain diffraction? http://learn.uci.edu/oo/getOCWPage.php?course=OC0811004&lesson=005&topic=006&page=10

  6. Each wavelet is the source of the next wave. http://www.ux1.eiu.edu/~cfadd/1160/Ch25WO/Huygn.html

  7. Sound waves bend (“diffraction”). How would Huygens explain how sound goes around corners? http://www.pa.op.dlr.de/acoustics/essay1/beugung_en.html

  8. Shine light on a piece of cardboard. If you make a narrow slice in the cardboard, then the light will go through the slit, land on a screen, and look like this….

  9. Light waves incident on a barrier with a slit make this pattern on a screen: http://www.math.ubc.ca/~cass/courses/m309-03a/m309-projects/krzak/index.html

  10. Light waves incident on a barrier with a slit make this pattern: http://electron9.phys.utk.edu/optics421/modules/m5/Diffraction.htm

  11. The pattern of intensity due to single-slit diffraction for any kind of wave always looks like this: http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/sinint.html

  12. Diffraction happens because of interference of waves from the little wavelets in the gap: http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/sinslitd.html

  13. Here is how we label the “minima”.‘Minima’ is the plural of ‘minimum’. q for n = 3 q for n = 2 q for n = 1 q for n = 1 q for n = 2 q for n = 3 http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/sinint.html

  14. Where are the minima? bsinq = nl n = 1,2,3, … b is the size of the opening (meters). q is the angular position of the minima (radians).

  15. If the angle is small, then … sinq≈q So, bsinq = nl becomes: bq = nl For the first minimum only, n = 1, and the approximation is: bq = l Or, • = l / b This is the approximate location of the first minimum.

  16. Two objects, or one? http://electron9.phys.utk.edu/optics421/modules/m5/Diffraction.htm

  17. Basics of resolving two images Consider your teacher holding up two fingers. The two objects are in about the same direction. How ‘close’ can the objects be, while you still can tell that there are two of them? If you walk toward your teacher, then the fingers seem to separate. The fingers are in different directions. Even if you can’t see the difference between objects that are 0.1 degrees apart, for nearby objects it will not matter; the objects look separate. For this reason, nearby objects are easy to resolve.

  18. Resolving Power (Rayleigh Criterion) If you cannot move toward the objects, then what determines if you can tell that there are two of them? In other words, what is qmin? qmin = 1.22 l/ D. A small value of qmin means that objects that are close to each other can be see to be two separate objects. You can resolve things better if the pupil of your eye is greater. For greater D, the smaller qmin. The smaller the wavelength, the smaller qmin.

  19. Light is a wave • To understand what polarized light is, we need to know some basics about light. • Light is made of Electric (E) & Magnetic fields (B) …

  20. Light is an electromagnetic wave: http://www.google.com/imgres?imgurl=http://learn.uci.edu/media/OC08/11004/OC0811004_ElectroWaves.jpg&imgrefurl=http://learn.uci.edu/oo/getOCWPage.php%3Fcourse%3DOC0811004%26lesson%3D005%26topic%3D002%26page%3D21&usg=___6vybCf-mHdTQyGUT0lrBOKoSiA=&h=350&w=350&sz=26&hl=en&start=0&zoom=1&tbnid=dQcKUkHwLMwTaM:&tbnh=117&tbnw=117&prev=/images%3Fq%3Dlight%2Bis%2Ban%2Belectromagnetic%2Bwave%26hl%3Den%26sa%3DX%26biw%3D1280%26bih%3D640%26gbv%3D2%26tbs%3Disch:1,isz:m0%2C12&itbs=1&iact=rc&dur=447&ei=FIaiTPa3AsSqlAeB7dnZAw&oei=mYWiTKyMAoSKlwfA4pSBAw&esq=7&page=1&ndsp=21&ved=1t:429,r:12,s:0&tx=42&ty=48&biw=1280&bih=640

  21. Light is a wave • Light is made of Electric (E) &Magnetic fields (B) … • Light has wavelength (l). • And, most relevant to polarization, light is a transverse wave…

  22. Light is a transverse wave: http://www.sparknotes.com/physics/optics/light/section2.rhtml

  23. Polarization • Without exception, when we are thinking about polarization, we can just think about the electric field (and ignore the magnetic field). • Polarized light has an organization to its electric field vectors. • Ordinary light is not polarized. Light in the room has random orientations of electric field vectors. • Light that passes through polarized sunglasses has very little electric field that oscillates left-right, and it has a lot of electric field that vibrates up and down.

  24. These 2 photos show that reflection can polarize light.(Photos were taken with a polarizing filter) For this reason, people who are fishing prefer polarized sunglasses. They can see fish in the water. http://en.wikipedia.org/wiki/Brewster%27s_angle

  25. Since ice produces ‘glare’, do downhill skiers want polarized sunglasses? http://photo.accuweather.com/photogallery/details/photo/73793/Sun+Glare+on+Ice+Covered+Snow

  26. Polarization by reflection • If you bounce light off of a flat surface, it will be somewhat polarized, and if you get the angle just right, it will be completely polarized. • This is the source of ‘glare’ off of water, roads, and ice. • If light hits a surface at Brewster’s angle, then the reflected light will be completely polarized.

  27. Brewster’s Angle • If light hits a surface at Brewster’s angle (qB), then the reflected light will be completely polarized. • qB = InvTan ( n1 /n2 ). • The incident light and the reflected light are in medium 1, with index of refraction: n1. • Part of the light is transmitted into medium 2, with index of refraction: n2. See picture…

  28. Notice where qB is drawn. http://en.wikipedia.org/wiki/Brewster%27s_angle

  29. A quantitative look at polarizers (1 of 3) • If you shine unpolarized light through a polarizer, what happens to the intensity? • In other words, if light of intensity IO is incident on a polarizing filter, what is the intensity of the light that emerges from the filter? • The answer is ½IO. All of this light is polarized, and we could use it as a source for further exploration.

  30. A quantitative look at polarizers (2 of 3) • Next, let the the light that comes out of the polarizer go through another polarizer. If the two filters are oriented the same way, then how much light comes out of the second filter? • For a perfect polarizer oriented the same way as the incoming light, all of the light that goes in, comes out. So if goes ½IO in, then ½IO comes out. • Now, what if the second polarizer was rotated 90˚ so that its transmission axis was perpendicular to the polarization of the incident light? How much would come out? Nada.

  31. A quantitative look at polarizers(3 of 3) • Take polarized light and send it through a polarizer. If the relative angle in their orientations is 0˚, then all of the light that goes in, comes out. • If the relative angle is 90˚, thennoneof the light comes out. • Hmm, what about in general, if the relative angle was q, what is the equation that tells us how much comes out? ...

  32. If you send an intensity IO onto a polarizer, how much comes out?

  33. I = IO cos2qThis is the law of Malus.

  34. Optically Active Materials • Amazingly, there are some natural materials that will change the polarization of light. • If you transmit polarized light through quartz, or even sugar water, the emitted light will have a different polarization than the incoming light.

  35. Can you feel the stress? http://physics.info/polarization/

  36. Optically Active Materials • Amazingly, there are some natural materials that will change the polarization of light. • If you transmit polarized light through quartz, or even sugar water, the emitted light will have a different polarization than the incoming light.

  37. Quantifying this effect… • How much does the light change polarization? • q = kh, where: • q is the change in polarization (degrees) • k is the constant specific to the material (deg/m) • h is the thickness of the material (meters) • Also, the change in polarization is proportional to the concentration of a solution.

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