Wave Optics

1
Chapter 24

• Wave Optics

Conceptual questions 3, 4, 13, 14, 17, 18 Quick
Quizzes 1, 2, 3, 4 Problems 10, 17, 34
2
Interference

• Light waves interfere with each other much like
  mechanical waves do
• Two conditions which must be met
• The sources must be coherent. They must maintain
  a constant phase with respect to each other
• The waves must have identical wavelengths

3
Producing Coherent Sources

• Old method
• Light from a monochromatic source is allowed to
  pass through a narrow slit
• The light from the single slit is allowed to fall
  on a screen containing two narrow slits
• The first slit is needed to insure the light
  comes from a tiny region of the source which is
  coherent
• New method use a laser

4
Youngs Double Slit Experiment

• The narrow slits, S1 and S2 act as sources of
  waves
• The waves emerging from the slits originate from
  the same wave front and therefore are always in
  phase

5
Interference Patterns

• Constructive interference occurs at the center
  point
• The two waves travel the same distance and they
  arrive in phase

6
Interference Patterns, 2

• The upper wave travels one wavelength farther
• Therefore, the waves arrive in phase
• A bright fringe occurs

7
Interference Patterns, 3

• The upper wave travels one-half of a wavelength
  farther than the lower wave
• The trough of the bottom wave overlaps the crest
  of the upper wave
• This is destructive interference
• A dark fringe occurs

8
Interference Equations

• The path difference, d, is found from the tan
  triangle
• d r2 r1 d sin ?
• This assumes the paths are parallel

9
Interference Equations, 2

• For a bright fringe, produced by constructive
  interference, the path difference must be
• d m ?
• m 0, 1, 2,
• d d sin ?bright m ?
• m is called the order number
• When m 0, it is the zeroth order maximum
• When m 1, it is called the first order maximum

10
Interference Equations, 3

• When destructive interference occurs, a dark
  fringe is observed
• This needs a path difference of an odd half
  wavelength d (m ½) ?
• d d sin ?dark (m ½) ?
• m 0, 1, 2,

11
Interference Equations, 4

• The positions of the fringes can be measured
  vertically from the zeroth order maximum
• y L tan ? L sin ?
• Approximation
• ? is small and therefore tan? sin ?
• For bright fringes
• For dark fringes

12
Quick quiz 24-1

• In a two slit interference pattern projected on a
  screen the fringes are equally spaced on the
  screen
• A. everywhere
• B. only for large angles
• C. only for small angles

13
Problem 24.10

• A pair of slits, separated by 0.150 mm, is
  illuminated by light having a wavelength of ?
  643 nm. An interference pattern is observed on a
  screen 140 cm from the slits. Consider a point on
  the screen located at y 1.80 cm from the
  central maximum of this pattern.
• What is the path difference d for the two slits
  at the location y?
• (b) Express this path difference in terms of the
  wavelength.
• (c) Will the interference correspond to a
  maximum, a minimum, or an intermediate condition?

14
Phase Changes Due To Reflection

• An electromagnetic wave undergoes a phase change
  of 180 upon reflection from a medium of higher
  index of refraction than the one in which it was
  traveling
• Analogous to a reflected pulse on a string

15
Phase Changes Due To Reflection, cont

• There is no phase change when the wave is
  reflected from a boundary leading to a medium of
  lower index of refraction
• Analogous to a pulse in a string reflecting from
  a free support

16
Interference in Thin Films

• Rules to remember
• An electromagnetic wave traveling from a medium
  of index of refraction n1 toward a medium of
  index of refraction n2 undergoes a 180 phase
  change on reflection when n2 gt n1
• There is no phase change in the reflected wave if
  n2 lt n1
• The wavelength of light ?n in a medium with
  index of refraction n is ?n ?/n where ? is the
  wavelength of light in vacuum

17
Interference in Thin Films, 2

• Ray 1 undergoes a phase change of 180 with
  respect to the incident ray
• Ray 2, which is reflected from the lower surface,
  undergoes no phase change with respect to the
  incident wave
• Ray 2 also travels an additional distance of 2t
  before the waves recombine

18
Interference in Thin Films, 3

• For constructive interference
• 2 n t (m ½ ) ? m 0, 1, 2
• This takes into account both the difference in
  optical path length (2t) for the two rays and the
  180 phase change (1/2 ?)
• For destruction interference
• 2 n t m ? m 0, 1, 2

19
Interference in Thin Films, 4

• An example of different indices of refraction
• A coating on a solar cell

20
Quick quiz 24-2

• Supposed Youngs experiment is carried out in
  air, and then, in a second experiment, the
  apparatus is immersed in water. In what way does
  the distance between bright fringes change?
• A. they move further apart
• B. they move closer together
• C. no change

21
Problem 24.17
A coating is applied to a lens to minimize
reflections. The index of refraction of the
coating is 1.55, and that of the lens is 1.48. If
the coating is 177.4 nm thick, what wavelength is
minimally reflected for normal incidence in the
lowest order?
22
Newtons rings
23
Conceptual questions

• 3. Consider a dark fringe in an interference
  pattern, at which almost no light energy is
  arriving. Light from both slits is arriving at
  this point, but the waves are canceling. Where
  does the energy go?
• 4. If Youngs double slit experiment were
  performed under water, how would the observed
  interference pattern be affected?
• 13.Would it be possible to place a nonreflective
  coating on an airplane to cancel radar waves of
  wavelength 3 cm?

24
Reading a CD

• As the disk rotates, the laser reflects off the
  sequence of lands and pits into a photodector
• The photodector converts the fluctuating
  reflected light intensity into an electrical
  string of zeros and ones
• The pit depth is made equal to one-quarter of the
  wavelength of the light

land
25
Diffraction

• Huygens principle requires that the waves spread
  out after they pass through slits
• This spreading out of light from its initial line
  of travel is called diffraction

26
Fraunhofer Diffraction

• Fraunhofer Diffraction occurs when the rays leave
  the diffracting object in parallel directions
• A bright fringe is seen along the axis (? 0)
  with alternating bright and dark fringes on each
  side

27
Single Slit Diffraction

• According to Huygens principle, each portion of
  the slit acts as a source of waves
• The light from one portion of the slit can
  interfere with light from another portion
• The resultant intensity on the screen depends on
  the direction ?
• Wave 1 travels farther than wave 3 by an amount
  equal to the path difference (a/2) sin ?

destructive interference occurs when sin ?dark
m? / a
28
Single Slit Diffraction, 2

• A broad central bright fringe is flanked by much
  weaker bright fringes alternating with dark
  fringes
• The points of constructive interference lie
  approximately halfway between the dark fringes

29
Problem 34
A screen is placed 50.0 cm from a single slit,
which is illuminated with light of wavelength 680
nm. If the distance between the first and third
minima in the diffraction pattern is 3.00 mm,
what is the width of the slit?
30
Quick quiz 24.3
In a single-slit diffraction experiment, as the
width of the slit is made smaller, the width of
the central maximum of the diffraction pattern
becomes (a) smaller, (b) larger, (c) remains
the same.
31
Diffraction Grating

• The condition for maxima is
• d sin ?bright m ?
• m 0, 1, 2,
• The integer m is the order number of the
  diffraction pattern
• If the incident radiation contains several
  wavelengths, each wavelength deviates through a
  specific angle

32
QUICK QUIZ 24.4
If laser light is reflected from a phonograph
record or a compact disc, a diffraction pattern
appears. This occurs because both devices contain
parallel tracks of information that act as a
reflection diffraction grating. Which device,
record or compact disc, results in diffraction
maxima that are farther apart?
33
Diffraction Grating in CD Tracking

• A diffraction grating can be used in a three-beam
  method to keep the beam on a CD on track
• The central maximum of the diffraction pattern is
  used to read the information on the CD
• The two first-order maxima are used for steering

34
Polarization of Light Waves

• Each atom produces a wave with its own
  orientation of E
• This is an unpolarized wave

35
Polarization of Light, cont

• 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

36
Polarization by Selective Absorption

• The most common technique for polarizing light
• Uses a material that transmits waves whose
  electric field vectors in the plane parallel to a
  certain direction and absorbs waves whose
  electric field vectors are perpendicular to that
  direction
• Malus law I Io cos2 ?

37
Polarization by Reflection

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

38
Polarization by 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
• Horizontally and vertically polarized waves are
  emitted

39
Conceptual question

• 14. Certain sunglasses use a polarizing material
  to reduce intensity of light reflected from shiny
  surfaces, such as water or a hood of a car. What
  orientation of the transmission axis should the
  material have to be most effective?
• 18. Can a sound wave be polarized?
• 17. When you receive a chest x-ray at a hospital,
  the ex-ray passes through a series of parallel
  ribs in your chest. Do the ribs act as a
  diffraction grating for x-rays?

40
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

41
Liquid Crystals

• Rotation of a polarized light beam by a liquid
  crystal when the applied voltage is zero
• Light passes through the polarizer on the right
  and is reflected back to the observer, who sees
  the segment as being bright

42
Liquid Crystals

• When a voltage is applied, the liquid crystal
  does not rotate the plane of polarization
• The light is absorbed by the polarizer on the
  right and none is reflected back to the observer
• The segment is dark

43
MCAD

• Two light sources produce light with wavelength
  l. The sources are placed 22.5 l and 45 l away
  from point P. When both sources are turned on
  and their intensities, I, at point P are equal,
  the resultant intensity at point P will be
• A. 0
• B. 0.5 I
• C. I
• D. 2I

44

• The process discussed in the previous question is
  called
• Diffraction b. Refraction
• Interference d. Dispersion
• Which of the following would result in greatest
  diffraction?
• Small wavelengths moving through a small opening
• Large wavelengths moving through a small opening
• Small wavelengths moving through a large opening
• Large wavelengths moving through a large opening