Physical Optics

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Physical Optics

• The wave nature of light
• Interference
• Diffraction
• Polarization

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Huygens Principle

• Every point on a propagating wavefront serves as
  the source of spherical wavelets, such that the
  wavelets at sometime later is the envelope of
  these wavelets.
• If a propagating wave has a particular frequency
  and speed, the secondary wavelets have that same
  frequency and speed.

Isotropic
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Diffraction
a

• Diffraction Bending of light into the shadow
  region
• Grimaldi - 17th Century observation of
  diffraction
• Diffraction vs. Refraction?

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Explanation of Snells Law
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Superposition of waves
Constructive Interference
Destructive Interference
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Conditions for Interference

• To observe interference in light waves, the
  following two conditions must be met
• 1) The sources must be coherent
• They must maintain a constant phase with respect
  to each other
• 2) The sources should be monochromatic
• Monochromatic means they have a single wavelength

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Youngs Experiment
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Youngs Experiment
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Youngs Experiment
Maxima occur when
maxima
Minima occur when
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What the pattern looks like
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Intensity Distribution, Electric Fields

• The magnitude of each wave at point P can be
  found
• E1 Eo sin ?t
• E2 Eo sin (?t f)
• Both waves have the same amplitude, Eo

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Intensity Distribution, Resultant Field

• The magnitude of the resultant electric field
  comes from the superposition principle
• EP E1 E2 Eosin ?t sin (?t f)
• This can also be expressed as
• EP has the same frequency as the light at the
  slits
• The magnitude of the field is multiplied by the
  factor 2 cos (f / 2)

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Intensity Distribution, Equation

• The expression for the intensity comes from the
  fact that the intensity of a wave is proportional
  to the square of the resultant electric field
  magnitude at that point
• The intensity therefore is

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Resulting Interference Pattern

• The light from the two slits forms a visible
  pattern on a screen
• The pattern consists of a series of bright and
  dark parallel bands called fringes
• Constructive interference occurs where a bright
  fringe occurs
• Destructive interference results in a dark fringe

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Example

• A He-Ne Laser has a wavelength of 633 nm. Two
  slits are placed immediately in front of the
  laser and an interference pattern is observed on
  a screen 10 m away. If the first bright band is
  observed 1 cm from the central bright fringe, how
  far apart are the two slits?
• At what angle Q is the fourth dark band found?

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Thin Films
Constructive Interference (maxima)
Destructive Interference (minima)
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Chapter 35 - Problem 45
Stealth aircraft are designed to not reflect
radar whose wavelength is 2 cm, by using an
anti-reflecting coating. Ignoring any change in
wavelength in the coating, estimate its thickness.
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Phase shift on reflection
Internal Reflection
External Reflection
Now, If one reflection is internal and one
reflection is external half wavelength path
differences will result in constructive
interference
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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 pulse on a string reflected from a
  rigid support

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Lloyds Mirror

• An arrangement for producing an interference
  pattern with a single light source
• Waves reach point P either by a direct path or by
  reflection
• The reflected ray can be treated as a ray from
  the source S behind the mirror

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Lloyds Mirror
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Interference in Thin Films Again

• Assume the light rays are traveling in air nearly
  normal to the two surfaces of the film
• 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
• For constructive interference
• d2t (m ½)?n (m 0, 1, 2 )
• This takes into account both the difference in
  optical path length for the two rays and the 180
  phase change
• For destructive interference
• d2t m?n (m 0, 1, 2 )

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Newtons Rings
Maxima - bright
Minima - dark
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Chapter 37 Problem 62
Show that the radius of the mth dark Newtons
ring as viewed from directly above is given by
Where R is the radius of curvature of the curved
glass surface and l is the wavelength of the
light used. Assume that the thickness of the air
gap is much less than R at all points and that
xltltR
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Newtons Rings
Minima
Newtons rings are a special case of Fizeau
fringes. They are useful for testing surface
accuracy of a lens.
Maxima
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Wedges Fringes of Equal Thickness
Minima (destructive)
Maxima (constructive)
Fringes of this type are also known as Fizeau
fringes
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Example thin film of air
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Michelson Interferometer

• A lens can be used to form fringes of equal
  inclination (rings)
• Tilting the mirrors can cause fringes of equal
  thickness.
• Accurate length measurements are accomplished by
  fringe counting as one of the mirrors is moved.

Detector
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42. Monochromatic light is beamed into a
Michelson interferometer. The movable mirror is
displaced 0.382 mm, causing the interferometer
pattern to reproduce itself 1 700 times.
Determine the wavelength of the light. What color
is it?
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5. Youngs double-slit experiment is performed
with 589-nm light and a distance of 2.00 m
between the slits and the screen. The tenth
interference minimum is observed 7.26 mm from the
central maximum. Determine the spacing of the
slits.
7. Two narrow, parallel slits separated by 0.250
mm are illuminated by green light (? 546.1 nm).
The interference pattern is observed on a screen
1.20 m away from the plane of the slits.
Calculate the distance (a) from the central
maximum to the first bright region on either side
of the central maximum and (b) between the first
and second dark bands.
17. In Figure 37.5, let L 120 cm and d 0.250
cm. The slits are illuminated with coherent
600-nm light. Calculate the distance y above the
central maximum for which the average intensity
on the screen is 75.0 of the maximum.
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32. A thin film of oil (n 1.25) is located on
a smooth wet pavement. When viewed perpendicular
to the pavement, the film reflects most strongly
red light at 640 nm and reflects no blue light at
512 nm. How thick is the oil film?
33. A possible means for making an airplane
invisible to radar is to coat the plane with an
antireflective polymer. If radar waves have a
wavelength of 3.00 cm and the index of refraction
of the polymer is n 1.50, how thick would you
make the coating?
37. A beam of 580-nm light passes through two
closely spaced glass plates, as shown in Figure
P37.37. For what minimum nonzero value of the
plate separation d is the transmitted light
bright?
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Mach Zehnder Interferometer
Detector

• No compensating plate needed
• Test cell easily inserted in one leg.
• No factor of two as in the Michelson
  interferometer.
• Difficult to align

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Sagnac Interferometer
Detector
Ring laser gyro. The rotation effectively
shortens the path taken by one direction over the
other.
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Phase Angle