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Chapter 10

Chapter 10. The Interference of Light. 10.1 Introduction. Introduction. Interference and diffraction are important properties of waves that occur under certain conditions They have no equivalent in classical particle motion

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Chapter 10

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  1. Chapter 10 The Interference of Light

  2. 10.1 Introduction

  3. Introduction Interference and diffraction are important properties of waves that occur under certain conditions They have no equivalent in classical particle motion Thomas Young first established that light was a wave after demonstrating the two slit interference pattern

  4. Introduction When discussing waves in general, we refer to water waves since they are easy to visualise, and use the same terminology

  5. Introduction The use of crest and trough refers to the points where the electric and magnetic fields are at maximum in either direction

  6. 10.2Diffraction

  7. Diffraction in general Diffraction is the change in direction of propagation of a wave as it passes by an obstacle while remaining in the same medium This is shown below where the lines represent crests of the wave

  8. Diffraction in general This is observable in ocean waves, and is the reason sound can travel around the corner of a building

  9. Diffraction through a single slit When two barriers are used to make a slit, waves passing through will diverge, diffracting around both barriers The spreading out (divergence) of plane waves as they pass through an opening is an example of diffraction

  10. Diffraction through a single slit Why isn’t this phenomenon seen everyday with light waves?

  11. Diffraction through a single slit Diffraction of light is difficult to see due to the short wavelength of light As seen below, the angle of divergence depends on the ratio of the width of the gap to the wavelength of the wave

  12. Diffraction through a single slit As the width of the slit increases, the divergence of the wave decreases As the wavelength of the wave increases, the divergence of the wave increases

  13. Diffraction through a single slit Light passing through a 1cm slit will diffract approximately 0.00003° Effectively the light passes through with no observable divergence To be able to observe diffraction of visible light, it needs to be passed through slits of width between 10-5m to 10-6m

  14. Diffraction through a single slit http://www.youtube.com/watch?v=BH0NfVUTWG4

  15. Diffraction of light by a narrow slit When a plane light wave (parallel beam of light) passes through a narrow slit, it diverges and falls on a screen with the following pattern

  16. Diffraction of light by a narrow slit When diffraction occurs, there is no change in the frequency, velocity or wavelength of the wave The only changes are in the amplitude and direction

  17. Diffraction of light by a narrow slit The pattern consists of a wide band of light, with narrower bands on each side

  18. Diffraction of light by a narrow slit On the right is a graph of intensity, the distance between the centre of the dark regions is approximately equal, and the first dark band is also this distance from the central peak

  19. 10.3coherent wave sources

  20. Phase Two wave sources are in phase with each other if they are emitting waves that are in phase with each other This means that if one source is emitting a crest, the other is emitting a crest; if one is emitting a trough, the other is emitting a trough, etc. Both sources must be producing light of the same frequency, and hence the same wavelength

  21. Coherent Wave Sources The term monochromatic light refers to light of a single frequency Two (or more) sources of waves are coherent if they maintain a constant phase relationship with each other They must, therefore, be emitting light of the same type and frequency

  22. Incandescent Sources of Light • An incandescent solid (or liquid) is one that has been caused to glow through the application of heat • Examples of incandescent solids include: • an iron bar that heated until it glows • the tungsten filament in a light bulb • the glowing coals in a fire • Examples of incandescent liquids include: • molten iron • lava

  23. Incandescent Sources of Light When materials are heated, the molecules and atoms within them vibrate faster Since atoms consist of charged particles (electrons & protons) we have vibrating (accelerating) charged particles The particles don’t all vibrate with the same frequency, but with a range of frequencies

  24. Incandescent Sources of Light The graph below shows the number of particles vibrating at particular frequencies

  25. Incandescent Sources of Light Since the electromagnetic waves emitted have a range of frequencies, light emitted from an incandescent source is not monochromatic Since the E-M waves have different frequencies, they cannot be in phase Thus, light emitted from incandescent sources is not coherent

  26. 10.4Constructive & destructive interference

  27. The Principle of Superposition If 2 or more travelling waves are passing through a medium, the resultant wave is found by adding together vectorially the displacements due to all the individual waves at all points in the medium

  28. The Principle of Superposition In the example to the right, the two waves are travelling in opposite directions As they meet they interact constructively, producing a wave of greater intensity at that point

  29. The Principle of Superposition The waves then continue through one another, emerging unaffected by the interaction

  30. The Principle of Superposition

  31. The Principle of Superposition When two peaks (or troughs) of in phase waves coincide, their displacements are added vectorially to produce constructive interference + =

  32. The Principle of Superposition When the peak of a wave coincides with the trough of another wave out of phase by λ/2, their displacements are added vectorially to produce destructive interference + =

  33. The Principle of Superposition When out of phase or waves of different frequencies waves interact, any combination of constructive or destructive interference can occur

  34. The Principle of Superposition http://www.acs.psu.edu/drussell/demos/superposition/superposition.html

  35. 10.5general two source wave interference

  36. Conditions for Constructive & Destructive Interference • The following are conditions necessary for observing interference of light: • the light from the different sources must overlap • the light must be of the same frequency • the sources must be coherent • the amplitude of the sources must be approximately equal • external light must be excluded

  37. Conditions for Constructive & Destructive Interference Consider two sources of waves emitting identical waves in phase with one another

  38. Conditions for Constructive & Destructive Interference Point P is equidistant from each source, thus the waves from each source will be in phase and constructively interfere

  39. Conditions for Constructive & Destructive Interference At point Q, there will be a path difference between the distances travelled by each wave

  40. Conditions for Constructive & Destructive Interference The path difference between the two waves to Q is = QS2 – QS1

  41. Conditions for Constructive & Destructive Interference If the path difference is one wavelength, then the crests and troughs will constructively interfere

  42. Conditions for Constructive & Destructive Interference If the path difference is half a wavelength, then the crests and troughs will destructively interfere

  43. The Two Source Interference Pattern in Two Dimensions The diagram below shows circles representing crests and troughs of waves emanating from two sources producing waves in phase

  44. The Two Source Interference Pattern in Two Dimensions The purple lines represent crests and the blue lines represent troughs

  45. The Two Source Interference Pattern in Two Dimensions The dotted lines are lines of zero amplitude, where destructive interference is occurring; sometimes referred to as nodal lines

  46. The Two Source Interference Pattern in Two Dimensions Half way between the dotted lines (but not shown) are lines of maximum amplitude; also known as anti-nodal lines

  47. The Two Source Interference Pattern in Two Dimensions This pattern of interference can be seen using water waves, but applies to light, sound, and other waves also

  48. Class Problems Conceptual Questions: 1-2, 5-6 Descriptive Questions: 1-2 Computational Questions: 1-2

  49. 10.6The two slit interference of light

  50. The Two Slit Apparatus The two source interference pattern was first observed by Thomas Young in 1801 Setting up two coherent sources is difficult, Young got around this by setting up a coherent light source that first passed through one slit, which caused diffraction of the wavefront

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