Diffraction vs. Interference

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Diffraction vs. Interference

• Both involve superposition of coherent light
• Custom
• Interference only a few waves
• Diffraction large number of waves
• Fresnel correction to Huygens Principle
• Every unobstructed point of of a wavefront, at a
  given instant, serves as a source of spherical
  secondary wavelets (with the same frequency of
  that of the primary wave). The amplitude of the
  optical field is the superposition of all these
  wavelets (considering their amplitudes and
  relative phases)

2
Fraunhofer vs. Fresnel

• Fresnel Diffraction is occurring near the
  aperture. a.k.a near field diffraction
• Initially the fringe pattern looks like the
  aperture but then the pattern changes as the
  distance from the aperture increases.
• Fraunhofer Diffraction occurs far from the
  aperture. a.k.a far field diffraction
• In this region the fringe pattern remains
  constant, changing only in size as distance from
  the aperture increases.

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Diffraction by edges
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Fig 38-2, p.1207
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Single-Slit Diffraction

• The finite width of slits is the basis for
  understanding Fraunhofer diffraction
• According to Huygenss principle, each portion of
  the slit acts as a source of light waves
• Therefore, light from one portion of the slit can
  interfere with light from another portion

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Diffraction by a single slit
Minima
m 1,2,3,
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Diffraction Pattern, Single Slit

• The diffraction pattern consists of the central
  maximum and a series of secondary maxima and
  minima
• The pattern is similar to an interference pattern

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Intensity

• The light intensity at a point on the screen is
  proportional to the square of ER
• Imax is the intensity at ? 0
• This is the central maximum

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Combination of interference and diffraction for 2
slits
Diffraction
Interference
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Final Exam Problem 48

• Light of wavelength 632 nm is incident on a
  single slit. The distance from the slit to a
  screen is 3 m. If the distance from the first
  minimum on one side of the center of the
  diffraction pattern to the first minimum on the
  other side is 8 mm, the width of the slit is
  closest to
• 0.22 mm
• 0.31 mm
• 0.47 mm
• 0.59 mm
• 0.66 mm

screen
3 m
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The Square Aperture
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Circular Aperture
Airy Pattern
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Circular apertures
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Rayleigh resolution criteria
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Rayleigh Criteria for Resolving Two Objects

• Overlapping images from two apertures are just
  resolved when the center of one Airy disk falls
  on the first minimum of the other.

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Rayleigh resolution criteria
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Resolution, Example

• Pluto and its moon, Charon
• Left Earth-based telescope is blurred
• Right Hubble Space Telescope clearly resolves
  the two objects

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Final Exam Problem 49

• A boat has lights on a mast that are 1 m apart.
  The dominant wavelength in the lights is 600 nm.
  The pupil in a persons eye has an opening of 1
  mm. For simplicity, we assume that the eye has a
  refractive index of 1. If the boat is closer,
  the person sees two lights on the mast. If the
  boat is farther away, the person sees only one
  light on the mast. The best value for the
  distance from the person to the boat is
• 1.4 km
• 1.2 km
• 2.0 km
• 1.6 km
• 1.8 km

1 m
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Diffraction Grating
Two slits
Grating
Maxima
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Final Exam Problem 50

• A beam of light is incident on a diffraction
  grating that has 600 lines/mm. The second order
  maximum occurs at a distance 0.7 m from the
  center of a screen that is 1.0 m from the
  grating. The wavelength of light is closest to
• 478 nm
• 613 nm
• 574 nm
• 589 nm
• 542 nm

grating
0.7 m
1.0 m
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Polarization
Linear or plane polarization
Vertically polarized

• Processes for accomplishing polarization
• selective absorption
• reflection
• double refraction
• scattering

Unpolarized?
Horizontally polarized
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Polarization by Selective Absorption

• The most common technique for polarizing light
• Uses a material that transmits waves whose
  electric field vectors lie in the plane parallel
  to a certain direction and absorbs waves whose
  electric field vectors are perpendicular to that
  direction

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Polarizing Sheets Selective absorption
Law of Malus
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Polarization by reflection
Brewsters Angle
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Polarization by Double Refraction

• Unpolarized light splits into two plane-polarized
  rays
• The two rays are in mutual perpendicular
  directions
• Indicated by the dots and arrows

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Polarization by Scattering, Rayleigh Scattering

• The horizontal part of the electric field vector
  in the incident wave causes the charges to
  vibrate horizontally
• The vertical part of the vector simultaneously
  causes them to vibrate vertically
• If the observer looks straight up, he sees light
  that is completely polarized in the horizontal
  direction

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Final Exam Problem 37

• When unpolarized light is passed through two
  polarizing filters in succession, its intensity
  is decreased by 80. The angle, q, between the
  transmission axis of the filters is
• 78.5 degrees
• 63.4 degrees
• 26.6 degrees
• 36.9 degrees
• 50.8 degrees

q
I0.2Io
Polaroids
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3. A screen is placed 50.0 cm from a single
slit, which is illuminated with 690-nm light. If
the distance between the first and third minima
in the diffraction pattern is 3.00 mm, what is
the width of the slit?
6. Light of wavelength 587.5 nm illuminates a
single slit 0.750 mm in width. (a) At what
distance from the slit should a screen be located
if the first minimum in the diffraction pattern
is to be 0.850 mm from the center of the
principal maximum? (b) What is the width of the
central maximum?
18. A binary star system in the constellation
Orion has an angular interstellar separation of
1.00 105 rad. If ? 500 nm, what is the
smallest diameter the telescope can have to just
resolve the two stars?
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41. Plane-polarized light is incident on a
single polarizing disk with the direction of E0
parallel to the direction of the transmission
axis. Through what angle should the disk be
rotated so that the intensity in the transmitted
beam is reduced by a factor of (a) 3.00, (b)
5.00, (c) 10.0?
45. The critical angle for total internal
reflection for sapphire surrounded by air is
34.4. Calculate the polarizing angle for
sapphire.