Wave Properties

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Wave Properties
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Coherent sources
Two sources of light are said to be coherent if
the waves emitted from them have the same
frequency and are 'phase-linked' that is, they
have a zero or constant phase difference.
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Path Difference

• Suppose we go along the centre line between the
  two sources.
• At all points we are the same distance from
  either of the sources.
• There is zero path difference. Since the waves
  are in phase and produced at the same frequency
  and travelling at the same speed, they must still
  be in phase.
• So they must reinforce.

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Path Difference

• We also see regions of constructive interference
  symmetrically on either side of the centre line.
  Thus the waves must be in phase.
• This is because the waves have a path difference
  of one or more whole wavelengths.
• We often describe this in terms of half
  wavelengths, so for there to be constructive
  interference, there must be a path difference of
  an even number of half wavelengths.
• The reverse side of the argument applies to odd
  numbers of half wavelengths. If the path
  difference is ½ a wavelength or 1 ½ and so on, we
  get regions of cancellation.
• This is because the waves are in antiphase.

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Single Slit Diffraction

? - is the diffraction angle l - is the
wavelength a is the width of the slit.
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Diffraction

• If the slit is narrow, the diffraction is more
  marked.
• The wavelength remains the same.
• Diffraction does not need a slit. Waves can bend
  round a barrier by diffraction. Radio signals
  can be picked up behind hills for this reason.
• The longer the wavelength, the more the waves
  will diffract.
• All waves diffract.

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One wide slit
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One Narrow slit
We can explain the effect of diffraction using
the idea of secondary wavelets. In the middle
these form a plane wave-front. At the edges,
circular wave-fronts move into the shadow region.
The maxima and minima are caused respectively by
constructive and destructive interference.
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Secondary wavelets
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INTERFERENCE
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where ? - is the wavelength (m) w - is the
fringe spacing (m) s - is the slit spacing (m) D
- is the distance from the slits to the screen
(m).
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Can you derive this!!!!
? - is the angle, ??- is the wavelength, d - is
the slit width n - the spectrum order

d sin ? n?
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• Parallel rays of a monochromatic light of
  wavelength l are incident on a diffraction
  grating in which the slit separation is d. If
  the grating has N lines per metre, the grating
  spacing is given by d 1
• N
• Constructive interference only occurs along a few
  precise lines, one of which is shown in the
  diagram. Light from A must be in phase with
  light from B, and this can only happen when the
  path difference is a whole number of complete
  wavelengths.
• AC nl, where n 0, 1, 2, 3...
•   s o AC d sin q
•   where q is the angle of diffraction.
•   So d sin q nl
•  
• The term n is called the spectrum order. If n
  1, we have the first diffraction maximum.
•  
• Sin q can never be greater than 1, so there is a
  limit to the number of spectra that can be
  obtained.

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The Diffraction Grating

• The diffraction grating has the advantage over
  the double slit method of measuring wavelength in
  that
• the maxima are more sharply defined
• the beam passes through more slits than two, so
  the intensity is brighter
• the angles are larger so that they can be
  measured with greater precision.

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Double Slit Interference
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Remember
Double slits the pattern is due to
interference.  Single slit, its due to
diffraction.