Chapter 36 Diffraction Part 1

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Chapter 36 Diffraction Part 1

• Single Slit Diffraction
• Diffraction and the Double Slit apparatus
• Intensity Formula for single and double slit

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Definition and Types of Diffraction

• Diffraction is the bending of a wave around an
  object accompanied by an interference pattern
• Fresnel Diffraction - curved (spherical) wave
  front is diffracted
• Frauenhofer Diffraction - plane wave is diffracted

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Examples of Fresnel Diffraction
Fresnel Diffraction from a sharp edge
Fresnel Diffraction from a circular obstruction
Fresnel bright spot
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Example of Frauenhofer (plane wave) Diffraction
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Diffraction Minima
Flaring of rays greater when silt size is smaller
and small compared to the wavelength of light ?
What is the anlge of the first minima when
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Single Slit Diffraction - Minima

• Slit has width a
• Divide slit into 5 wavelet sources see text
  for a different number of slit divisions
• If the path difference is half a wavelength for
  any pair, they will cancel
• Minimum occurs if all pairs cancel i.e. 1 and 3
  and 5 plus 2 and 4

Dividing the slit in 4 yields
Dividing the slit in 6 yields
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Single Slit Diffraction - Minima
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Phase Construction which allows us to derive the
Intensity at Point P on Screen
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Phase Difference between adjacent points in slit
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Single Slit Diffraction - Intensity Distribution

• Consider next adding the amplitudes of the
  electric field vector, including phase for each
  increment
• The resulting electric field is the vector sum as
  shown in the figure
• Now let N go to infinity

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Single Slit Diffraction - Intensity Distribution

• Divide the slit into small increments Dy
• Determine the phase difference Db

The total phase difference for N increments is
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Single Slit Diffraction - Intensity Distribution
(2)

• Combine and square since intensity is
  proportional to the square of the electric field

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Single Slit Diffraction - Intensity Distribution

• Minima occur when f mp, except
• when f 0 a maximum occurs
• Other maxima occur at solutions of intensity
  equation for sin q 1

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Double Slit and Diffraction
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Recall Intensity by Phasor Method for Double Slit
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Single Slit Diffraction - Envelope for other
interference patterns
Intensity equation for a double slit
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For Exam Study such problems

• Example 36-5

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Resolution Diffraction and Rayleigh Criteria
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Sample Prob. 36-4

• What is distance between peaks on screen?

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Diffraction Grating

• Generalize the double slit in addition to
  diffraction from each slit
• For adjacent slits

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Gratings Instensity

• Intensity plot as a function of angle

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Width of lines and the first minima

• Angle (and thus distance to ) first min from the
  central max

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Distance to the first Minimum

• As in the single slit diffraction pattern, the
  first minimum occurs when the path length
  difference betwn the top and bottom rays equals
• Half-width of any other line depends on location
  relative to central axis is,

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Grating Spectrometer

• S-source, L1-Lens, S1-slit, C-collimator,
  L2-Lens, G-grating
• Light from source focused by L1 on vertical slit
  S1 placed in focal plane of L2. Emerging light
  is a plane wave incident on G-grating diffracted
  into diffraction patter, with m0 order
  diffracted at angle along central axis
  of the grating
• Lens L3 of telescope focuses light diffracted at
  angle onto focal plane FF within
  telescope

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X-ray Diffraction

• Standard optical diff. grating cannot be used to
  discriminate btwn different wavelengths in the
  x-ray wavelength range ie d3000nm shows that
  first max
• If could resolve.
• 1912 Max von Laue, crystal lattice forms a
  natural diffraction gratting for x-rays.Nobel
  Prize

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Geometry of X-ray diffraction
Braggs Law 1915
X-ray diffraction powerful tool for studying
x-ray spectra and the arrangement of atoms in
crystals. Spectra a set of crystal planes
having known spacing, d, are chosen. They
reflect different wavelengths at different
angles. A detector that can discriminate one
angle from another can be used to determine the
wavelength l of radiation reaching it. The
crystal itself can be studied with a
monochromatic x-ray beam, to determine not only
the spacing btwn various crystal planes but also
the structure of the unit cell.