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  1. 1. Polarisation 11.5
  2. 2. Polarisation <ul><li>Interference and diffraction </li></ul><ul><ul><li>provides the best evidence that light is wavelike, but neither can describe if the light is, transverse or longitudinal in nature. </li></ul></ul>
  3. 3. Nature of light <ul><li>Vibrations in one direction are polarised: </li></ul><ul><li>Vibrations in all directions are unpolarised: </li></ul>
  4. 4. Polarisation <ul><li>A vibrating charge eg. Electron, </li></ul><ul><ul><li>emits an em wave that is plane polarised, in a single plane of vibration. </li></ul></ul><ul><li>A light source emits unpolarised light waves. </li></ul>
  5. 5. Polarisation - charge <ul><li>There is no preferred direction of vibration for the accelerated, oscillating charges. </li></ul><ul><li>The accelerating charge produces em waves. </li></ul><ul><li>For every E , </li></ul><ul><li>there is a B at </li></ul><ul><li>right angle to it. </li></ul>
  6. 6. Polarisation
  7. 7. Polarisation – mechanical analogy
  8. 8. Polarisation - light <ul><li>Polaroid sheets can be used as an analyser to determine whether, light is polarised or not. </li></ul><ul><li>By rotating it through 360 o , two maxima and two minima will be observed, each separated by 90 o . </li></ul>
  9. 9. Animation
  10. 10. Intensity using Malus Law <ul><li>A 'head-on' view of the analyser </li></ul><ul><li>will help us to find the intensity </li></ul><ul><li>of the transmitted beam </li></ul><ul><li>The incident beam has amplitude A 0 . </li></ul><ul><li>The component of A 0 parallel to the transmission axis of the analyser is A 0 cos θ </li></ul><ul><li>So the beam transmitted through the analyser has amplitude A , where </li></ul><ul><li>A = A 0 cos θ </li></ul>
  11. 11. Intensity using Malus Law <ul><li>The intensity of a beam, measured in W m -2 , is proportional to the square of the amplitude. </li></ul><ul><li>Thus the intensity I 0 of the incident beam is proportional to A 0 2 </li></ul><ul><li>the intensity I of the transmitted beam is proportional to A 2 = ( A 0 cos θ ) 2. </li></ul><ul><li>So the beam transmitted through the analyser has intensity I, where </li></ul><ul><li>I = I 0 cos 2 θ </li></ul>
  12. 12. Example <ul><li>A sheet of Polaroid is being used to reduce the intensity of a beam of polarised light. What angle should the transmission axis of the Polaroid make with the plane of polarisation of the beam in order to reduce the intensity of the beam by 50%? </li></ul>
  13. 13. Solution <ul><li>Using Malus law, new I is half original </li></ul>
  14. 14. Methods of Producing Polarised Light <ul><li>1. Selective absorption </li></ul><ul><li>Unpolarised light falls on a sheet of Polaroid with the polarising crystals in the vertical direction, i.e. polarisation axis is vertical, only horizontal planes of vibration are transmitted. </li></ul><ul><li>The energy in the vertical plane is absorbed in exciting the atoms of the vertical crystal. </li></ul>
  15. 15. Methods of Producing Polarised Light <ul><li>This sheet is called a polariser as it has turned unpolarised light into, horizontally plane polarised light. </li></ul><ul><li>If a second sheet of Polaroid is then added perpendicular to the first sheet, no light will be transmitted. </li></ul>
  16. 16. Methods of Producing Polarised Light <ul><li>The horizontal vibrations that get through the first sheet, will have their energy absorbed, in vibrating the atoms in the second sheet. </li></ul><ul><li>This second sheet is called the analyser . It can determine whether the light is polarised, and in what direction. </li></ul>
  17. 17. Methods of Producing Polarised Light <ul><li>2. Reflection </li></ul><ul><li>Most light reflected of surfaces such as water and glass is polarised. </li></ul><ul><li>The reflected ray has more vibrations that are parallel to the reflecting surface, than at right angles to it. </li></ul>
  18. 18. Methods of Producing Polarised Light
  19. 19. Brewsters Law <ul><li>The Scottish physicist Sir David Brewster discovered that for a certain angle of incidence, monochromatic light was 100% polarised upon reflection. </li></ul><ul><li>The refracted beam was partially polarised, but the reflected beam was completely polarised parallel to the reflecting surface. </li></ul><ul><li>Furthermore, he noticed that at this angle of incidence, the reflected and refracted beams were perpendicular </li></ul>
  20. 20. Brewsters Law <ul><li>Two media of refractive index, n 1 n 2 respectively. </li></ul><ul><li>The angle of incidence= angle of polarisation = i p </li></ul><ul><li>Snells law n 1 sin i p = n 2 sin θ </li></ul>
  21. 21. Brewsters Law <ul><li>Snells law n 1 sin i p = n 2 sin θ </li></ul><ul><li>According to Brewster </li></ul><ul><li>i p + θ = 90 </li></ul><ul><li>So, </li></ul>
  22. 22. Brewsters Law <ul><li>At the Brewster’s angle (polarising angle) maximum polarisation for the reflected ray occurs. </li></ul><ul><li>Brewster angle is the angle of incidence for which the angle between, reflected and transmitted ray is 90 o . </li></ul><ul><li>What is the polarising angle for a beam of light travelling in air when it is reflected by a pool of water ( n = 1.33)? </li></ul>
  23. 23. Optical activity <ul><li>Optically active materials can change the plane of polarisation of a beam of light. </li></ul><ul><li>They cause a rotation of the plane </li></ul><ul><li>Common in nature </li></ul>
  24. 24. Determining concentration of solutions <ul><li>This process comes about because of the molecular structure of these materials, and has been observed in crystalline materials such as quartz and organic (liquid) compounds such as sugar solutions. </li></ul><ul><li>Polarised light is passed through an empty tube, and an analyser on the other side of the tube is adjusted until no light is transmitted through it. The tube is then filled with the solution, and the analyser is adjusted until the transmission through it is again zero. The adjustment needed to return to zero transmission is the angle of rotation. </li></ul>
  25. 25. Stress analysis <ul><li>Polarised light can be used to measure strain in photoelastic materials, such as glass and celluloid. These are materials that become birefringent when placed under mechanical stress. </li></ul><ul><li>A celluloid model of a machine part, for example, is placed between a crossed polariser and analyser. The model is then placed under stress to simulate working conditions. </li></ul>
  26. 26. Stress analysis <ul><li>Bright and dark fringes appear, with the fringe concentration highest where the stress is greatest. </li></ul><ul><li>This sort of analysis gives important information in the design of mechanical parts and structures. </li></ul>
  27. 27. Liquid Crystal Displays <ul><li>Perhaps the most common everyday use of optical activity is in liquid crystal displays (LCDs). </li></ul><ul><li>A typical LCD on a digital watch or electronic calculator consists of a small cell of aligned crystals sandwiched between two transparent plates between a crossed polariser and analyser. </li></ul>
  28. 28. Liquid Crystal Displays <ul><li>Using liquid crystal's inherent polarizing characteristics, the liquid crystal of the front panel redirects the entering polarized light, according to degree of the liquid crystal twist. </li></ul><ul><li>To control the liquid crystal twist, an electrical field is applied. Varying the electric field, sub-pixel by sub-pixel, results in polarization angle changes for each sub-pixel. </li></ul>