Announcements

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• Announcements
• HW set 10 due this week covers Ch 24.5-9 (skip
  24.8) and 25.1-3
• Office hours
• Prof. Kumars Tea and Cookies 5-6 pm today
• My office hours Th 2 -3 pm
• or make an appointment
• Final exam Saturday 4/23, 3 5 pm, CUMULATIVE
  EXAM
• Make-up exam, Wednesday 4/20, 510 700 pm,
  NPB 1220, CUMULATIVE EXAM
• Always check out http//www.phys.ufl.edu/courses/
  phy2054/spring11/ for more announcements
• QUESTIONS? PLEASE ASK!

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From last time

• Constructive and Destructive Interference
• Youngs double slit experiment
• Bright fringe d sin ?bright m ?
• Dark fringe d sin ?bright (m1/2) ?
• Thin film interference
• Three different media
• Constructive and destructive interference
  equations depend on indices of refraction for
  each media

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Interference in Thin Films

• Interference is due to the interaction of the
  waves reflected from both surfaces of the film
• Ray 1 - phase change of 180 with respect to the
  incident ray
• Ray 2 - no phase change with respect to the
  incident wave
• Ray 2 travels an additional physical distance of
  2t in the film
• The wavelength ? is reduced by n in the film ?
  the optical path length is 2 n t
• Constructive interference
• 2 n t (m ½ ) ? m 0, 1, 2
• takes into account both the difference in optical
  path length for the two rays and the 180 phase
  change
• Destructive interference
• 2 n t m ? m 0, 1, 2

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Anti-reflection coatings

• Two phase shifts
• Constructive interference
• 2 n t m ?
• m 0, 1, 2
• takes into account both the difference in optical
  path length for the two rays and both 180 phase
  changes
• Destructive interference
• 2 n t (m ½ ) ?
• m 0, 1, 2

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Handling thin films problems

• Identify the thin film causing the interference
• Determine the indices of refraction in the film
  and the media on either side of it
• Determine the number of phase reversals zero,
  one or two
• Interference is constructive if the path
  difference is an integral multiple of ? and
  destructive if the path difference is an odd half
  multiple of ?
• NOTE The conditions are reversed if one of the
  waves undergoes a phase change on reflection

Equation 1 phase reversal 0 or 2 phase reversals
2nt (m ½) l constructive destructive
2nt m l destructive constructive
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Diffraction

• Huygens principle light waves spread out after
  they pass through slits
• ? diffraction
• Diffraction occurs when waves pass through small
  openings, around obstacles or by sharp edges
• A good example was Youngs double slit experiment
• A single slit placed between a distant light
  source and a screen produces a diffraction
  pattern
• broad, intense central band
• a series of narrower, less intense secondary
  bands ? secondary maxima
• In between the secondary maxima are a series of
  dark bands ? minima
• Cannot be explained by geometric optics!!

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Single Slit Diffraction
DEMO

• Huygens principle - each portion of the slit
  acts as a source
• Light from one side of the slit interferes with
  light from the other side
• The resultant intensity on the screen depends on
  the direction ?
• Wave 1 travels farther than wave 3 by a path
  length difference d (a/2) sin ?
• If d l/2, the two waves cancel each other and
  destructive interference results

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Single Slit Diffraction, 2

• Divide slit into 1/4, 1/6,
• In general, destructive interference occurs for a
  single slit of width for
• m ?1, ?2, ?3,
• Note doesnt give any information about the
  variations in intensity along the screen

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Single Slit Diffraction, 3

• Broad central bright fringe flanked by much
  weaker bright fringes alternating with dark
  fringes
• Points of constructive interference lie
  approximately halfway between the dark fringes

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Problem 24.36, p 819

• A screen is placed 50 cm from a single slit that
  is illuminated with light of wavelength 680 nm
  wavelength. If the distance between the first
  and third minima is 3.0 mm, what is the width of
  the slit?

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Polarization of Light Waves

• Each electron in an atom produces a wave with its
  own orientation of E
• Electrons in oscillating sinusoidal motion
• Unpolarized light - all directions of the
  electric field vector are equally possible and
  lie in a plane perpendicular to the direction of
  propagation of the light
• A wave is said to be linearly polarized if the
  resultant electric field vibrates in the same
  direction at all times at a particular point
• Polarization can be obtained from an unpolarized
  beam by
• Selective absorption
• Reflection
• Scattering
• In Lasers

unpolarized
polarized
E
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Polarization by Selective Absorption

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

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Selective Absorption

• ET Eo cos q
• I E2
• ? IT Io cos2 ?
• Io is the intensity of the polarized wave
  incident on the analyzer
• This is known as Malus Law and applies to any
  two polarizing materials whose transmission axes
  are at an angle of ? to each other

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Problem 24.58, p 821

• 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 the intensity of the light is reduced
  by a factor of (a) 2, (b) 4, and (c) 6?

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Polarization by Reflection
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Polarization by Reflection II

• The angle of incidence for which the reflected
  beam is completely polarized is called the
  polarizing angle, ?p
• Brewsters Law relates the polarizing angle to
  the index of refraction for the material
• ?p may also be called Brewsters Angle

Brewsters Angle
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Polarization by Scattering
Why is the sky blue?

• When light is incident on a system of particles,
  the electrons in the medium can absorb and
  reradiate part of the light
• This process is called scattering
• An example of scattering is the sunlight reaching
  an observer on the earth becoming polarized
• 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
• Horizontally and vertically polarized waves are
  emitted

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Optical Activity

• Certain materials display the property of optical
  activity
• A substance is optically active if it rotates the
  plane of polarization of transmitted light
• Also called birefringence
• Optical activity occurs in a material because of
  an asymmetry in the shape of its constituent
  materials

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Answer to 23.36
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Answer to 23.58