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# 4.3

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### 4.3

1. 1. Wave characteristics 4.3
2. 2. Wavefront All the points that started from a source at one time make up the whole of that wavefront, If it was a single point, it will be a circular wavefront If it is a straight line, it will be a straight wave front
3. 3. The wavefronts are by convention found at the crests of the waves. Wavefronts don’t have to be straight. Wavefronts and rays
4. 4. Wavefronts and rays Wavefronts can travel in 3D – consider what happens to the surface of a pond when you skim a stone. Even if a wavefront is curved initially, it will eventually seem planar due to the distance you are from the course.
5. 5. Wavefronts can also change direction due to the medium or an obstacle. Consider, vision correcting lenses, or a telescope, these allow the field of view to be changed. A ray is the direction of a wave and is parallel to the wave velocity. Wavefronts and rays
6. 6. Longitudinal waves also have wavefronts and can be reduced to rays – the wavefronts are due to rarefactions and compressions. Wavefronts and rays
7. 7. Huygen’s Principle Huygen’s principle states that every point on a wavefront may be regarded as a point source of secondary circular wavelets. The new wavefront is formed along the common tangent to these secondary wavelets.
8. 8. I = power / area Amplitude and Intensity Intensity is the rate energy is being transmitted per unit area and is measured in (W m-2). As area is proportional to x2 (where x is amplitude) this results in I α A2
9. 9. Wave superposition is the addition of two or more waves passing simultaneously through a medium. Superposition is also called interference and can be constructive or destructive. Consider, two identical pulses travelling towards each other along a rope. The amplitudes x0 of the two pulses add together, producing a momentary pulse of amplitude 2x0. Superposition 0 x0 2x0 constructive interference
10. 10. Consider,two 180° out-of-phase pulses coming from each end of a taut rope. The amplitudes x0 of the two pulses cancel, producing a momentary pulse of amplitude 0. - x0 0 x0 destructive interference
11. 11. Polarisation Interference and diffraction provides the best evidence that light is wavelike, but neither can describe if the light is, transverse or longitudinal in nature.
12. 12. Nature of light Vibrations in one direction are polarised: Vibrations in all directions are unpolarised:
13. 13. Polarisation A vibrating charge eg. electron, emits an em wave that is plane polarised, in a single plane of vibration. A light source emits unpolarised light waves.
14. 14. Polarisation - charge There is no preferred direction of vibration for the accelerated, oscillating charges. The accelerating charge produces em waves. For every E, there is a B at right angle to it.
15. 15. Polarisation
16. 16. Polarisation – mechanical analogy
17. 17. Polarisation - light Polaroid sheets can be used as an analyser to determine whether, light is polarised or not. By rotating it through 360o, two maxima and two minima will be observed, each separated by 90o.
18. 18. Explain the terms polariser and analyser. Hyperlink
19. 19. Intensity using Malus Law A 'head-on' view of the analyser will help us to find the intensity of the transmitted beam The incident beam has amplitude A0. The component of A0 parallel to the transmission axis of the analyser is A0cos θ So the beam transmitted through the analyser has amplitude A, where A = A0cos θ
20. 20. Intensity using Malus Law The intensity of a beam, measured in W m-2, is proportional to the square of the amplitude. Thus the intensity I0 of the incident beam is proportional to A0 2 the intensity I of the transmitted beam is proportional to A2 = (A0cos θ)2. So the beam transmitted through the analyser has intensity I, where I = I0cos2θ
21. 21. Example 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%?
22. 22. Solution Using Malus law, new I is half original
23. 23. Methods of Producing Polarised Light 1. Selective absorption 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. The energy in the vertical plane is absorbed in exciting the atoms of the vertical crystal.
24. 24. Methods of Producing Polarised Light This sheet is called a polariser as it has turned unpolarised light into, horizontally plane polarised light. If a second sheet of Polaroid is then added perpendicular to the first sheet, no light will be transmitted.
25. 25. Methods of Producing Polarised Light The horizontal vibrations that get through the first sheet, will have their energy absorbed, in vibrating the atoms in the second sheet. This second sheet is called the analyser. It can determine whether the light is polarised, and in what direction.
26. 26. Methods of Producing Polarised Light 2. Reflection Most light reflected of surfaces such as water and glass is polarised. The reflected ray has more vibrations that are parallel to the reflecting surface, than at right angles to it.
27. 27. Methods of Producing Polarised Light
28. 28. Brewsters Law The Scottish physicist Sir David Brewster discovered that for a certain angle of incidence, monochromatic light was 100% polarised upon reflection. The refracted beam was partially polarised, but the reflected beam was completely polarised parallel to the reflecting surface. Furthermore, he noticed that at this angle of incidence, the reflected and refracted beams were perpendicular
29. 29. Brewsters Law Two media of refractive index, n1 n2 respectively. The angle of incidence= angle of polarisation = ip Snells law n1sin ip= n2sinθ
30. 30. Brewsters Law Snells law n1sin ip= n2sinθ According to Brewster ip + θ = 90 So,
31. 31. Brewsters Law At the Brewster’s angle (polarising angle) maximum polarisation for the reflected ray occurs. Brewster angle is the angle of incidence for which the angle between, reflected and transmitted ray is 90o. 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)?
32. 32. Optical activity Optically active materials can change the plane of polarisation of a beam of light. They cause a rotation of the plane They are common in nature
33. 33. Optical activity Some materials can rotate the plane of polarisation of light as it passes through them. The liquid crystals used in calculator displays, digital watches and lap top computer screens are also optically active. The amount of rotation in these crystals can also be altered by applying an electric field between the two faces of the screen and this is how the display is turned from bright to dark.
34. 34. Determining concentration of solutions 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. 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.
35. 35. The polarimeter The specific rotation of a given liquid may be found using a polarimeter as shown in Figure 2. The two polaroids are adjusted to give a minimum light intensity, and the scale reading noted. A measured length of solution of known concentration is then placed in the inner tube and the polaroids readjusted to regain a minimum and the scale is read again. The rotation of the plane of polarization of the light by the solution may then be found from the difference in the two scale readings. Describe the use of polarization in the determination of the concentration of certain solutions.
36. 36. POLARIMETER h polariser analyserr liquid
37. 37. Certain solutions rotate the plane of polarisation of light passing through them. The angle through which the plane of polarisation is rotated depends on the concentration of the solution. Measuring the concentration of solutions
38. 38. Stress analysis 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. 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.
39. 39. Stress analysis Bright and dark fringes appear, with the fringe concentration highest where the stress is greatest. This sort of analysis gives important information in the design of mechanical parts and structures.
40. 40. Outline qualitatively how polarisation may be used in stress analysis. The first photograph below shows a small part of a plastic set square viewed under normal conditions The next photograph shows the same object when placed between crossed polaroids
41. 41. Liquid Crystal Displays Perhaps the most common everyday use of optical activity is in liquid crystal displays (LCDs). 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.
42. 42. Liquid Crystal Displays 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. 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.
43. 43. Liquid crystal displays The screen of an LCD TV is made of millions of liquid crystals. Each crystal is like the shutter of a camera either blocking the light or allowing it to pass through. You can control the amount of light that passes through by applying a voltage to a crystal or pixel. It does this by rotating the plane of polarisation of the light. A much-simplified diagram of this action is shown in Figure 1.