Chapter 24:Wave Optics

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Chapter 24Wave Optics

• Conditions for Interference

Homework assignment 10,22,23,33,42,55

• Conditions for interference

Adding two waves wave 1 and wave 2
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Conditions for Interference

• Conditions for interference (contd)

• Two sources producing two traveling waves are
  needed to create
• interference.

• The sources must be coherent, which means the
  waves they emit
• must maintain a constant phase with respect to
  each other.

• The waves must have identical wavelengths.

An old style method to produce two coherent
sources
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Conditions for Interference

• Two slits and interference

Two monochromatic sources of the same frequency
and with any Constant phase relation are said to
be coherent.
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Youngs Double-Slit Experiment

• Youngs double-slit experiment

• Red dots represent spots
• where the two waves are
• in phase and constructive
• interference occurs. This
• produces bright spots.

• Blue circles represent spots
• where the two waves are
• out of phase and destructive
• interference occurs. This
• produces dark spots.

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Youngs Double-Slit Experiment

• Youngs double-slit experiment (contd)

In phase
In phase
Out of phase
Bright image
Bright image
Dark image
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Youngs Double-Slit Experiment

• Youngs double-slit experiment (contd)

Path difference
Constructive interference
m order number m0 zeroth-order, m-1
first-order
Destructive interference
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Youngs Double-Slit Experiment

• Youngs double-slit experiment (contd)

Constructive interference
Destructive interference
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Youngs Double-Slit Experiment

• Example 24.1 Measuring the wavelength of a
  light source

• A screen is separated from a double-slit source
  by 1.20 m. The
• distance between the two slits is 0.0300 mm.
  The second-order
• bright fringe (m2) is measured to be 4.50 cm
  from the centerline.
• Determine
• (a) the wavelength of the light
• (b) the distance between the adjacent bright
  fringes.

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Change of Phase Due to Reflection

• Lloyds mirror

• In the arrangement of a mirror
• and the screen on the right, at
• a point on the screen the light
• waves have two possible paths.

• At point P, the path difference
• of two paths is zero Therefore
• we expect a bright fringe. But we
• see a dark fringe there.

• Similarly on the screen the pattern
• of bright and dark fringes is reversed.

An EM wave undergoes a phase change of 180o or p
upon reflection from a medium that has an index
of refraction higher than the one in which the
wave is traveling.
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Change of Phase Due to Reflection

• Phase change upon reflection

An EM wave undergoes a phase change of 180o upon
reflection from a medium that has an index of
refraction higher than the one in which the wave
is traveling.
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Interference in Thin Film

• Colorful patterns

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Interference in Thin Film

• Interference in thin film

• An EM wave traveling from a medium of index of
  refraction n1
• toward a medium of index of refraction n2
  undergoes a p
• phase change on reflection when n2gtn1.
• There is no phase change in the reflected light
  wave if n1gtn2.

• The wavelength of light ln in a medium with
  index of refraction n is
• lnl/n where l is the wavelength of light in
  vacuum.

Ray 1 A phase change of p at surface A with
respect to the incident wave (ngtnair1)
phase diff. by p due to reflection
Ray 2 No phase change at surface B with
respect to the incident wave (ngtnair1)
Phase difference
Ray 1 p
Ray 2 2p x 2t/ln
constructive
destructive
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Interference in Thin Film

• Interference in thin film (contd)

Interference between ray 1 and ray 2
constructive
destructive
thicker due to gravity
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Interference in Thin Film

• Newtons Rings

• Another example of interference
• A planoconvex lens on top of a flat glass
• surface

Blue ray phase change at the interface
between air and a flat glass.
phase diff. by p due to reflection
Red ray no phase change due to
reflection.
Interference between red and blue ray
constructive
destructive
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Interference in Thin Film

• Non-reflective coating for optical lens

Air, n 1.00
MgF2 n 1.38
?
t
?
Glass, n 1.50
Thin layer of MgF2 with index intermediate
between air and glass there are two phase shifts
of ? in this case, as shown.
Phase shifts of reflected rays Ray 1 ? Ray 2
? (2p/ln)(2t)
For no reflection (2p/ln) (2t) ?
(destructive interference)
Numbers for no reflection at ? 550 nm, t
100 nm.
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Interference in Thin Film

• Interference in a wedge-shaped film

A pair of glass slides 10.0 cm long and with
n1.52 are separated on one end by a hair,
forming a triangular wedge of air as illustrated.
When coherent light from a helium-neon laser with
wavelength 633 nm is incident on the film from
above, 15.0 dark fringes per cm are observed. How
thick is the hair?
For destructive interference with nair1
If d is the distance from one dark band to the
next, the x-coord. of the m-th fringe is
Using similar triangles
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Diffraction

• What is diffraction?

Diffraction is bending of waves around obstacles.
Diffraction also occurs when waves from a large
number of sources interfere.
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Diffraction

• Single slit

Bending on the corner
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• Diffraction at slits

• Single slit

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Diffraction at slits

• Diffraction and Huygens principle

Every point on a wave front acts as a source of
tiny wavelets that move forward.

Light waves originating at different points
within opening travel different distances to
wall, and can interfere!

We will see maxima and minima on the wall.
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• Diffraction at slits

• Single slit

1
1
1?
1?
a
a
path difference
path difference
When a/4 sin q l/2 every ray originating in
top quarter of slit interferes destructively with
the corresponding ray originating in the second
quarter.
When a/2 sin q l/2 every ray originating in
top half of slit interferes destructively with
the corresponding ray originating in bottom half.
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• Diffraction at slits

• Single slit

Condition for halves of slit to destructively
interfere
Condition for quarters of slit to destructively
interfere
Condition for sixths of slit to destructively
interfere
All together
This formula locates minima (for dark fringes)!!
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• Diffraction Grating

• Diffraction grating

• Combination of diffraction and
• interference

• Consists of a large number of
• equally spaced parallel slits.

• Can be made by scratching
• parallel lines on a glass plate
• with a precision machine
• technique.

• Each slit causes diffraction.

• Each slit acts as a source of
• waves in phase.

• Path diff. between two adjacent
• slits at P

• If slits are made to satisfy
• waves from slits are in phase.

dspacing of slits
qbright are the positions of bright maxima.
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• Diffraction Grating

• Diffraction grating (contd)

Pattern of light intensity
Diffraction grating spectrometer
By measuring the positions of maxima, using the
telescope in a diffraction grating spectrometer,
the wavelength of the incident waves can
be determined.
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• Polarization

• EM wave

vector in x-dir.
vector in y-dir.

• Polarization (defined by the direction of
  )

Linear polarization
Circular polarization
If the E-field is in the same direction all the
time, the EM wave is linearly polerized.
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• Polarization (contd)

• Polarization (defined by the direction of
  )

Circular polarization
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• Polarization (contd)

• Polarization by reflection

plane of incidence
When the angle of incident coincides with the
polarizing angle or Brewsters angle, the
reflected light is 100 polarized.
Brewsters law of the polarizing angle
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• Polarization (contd)

• Polarization by absorption and polarizing filters

Polaroid polarizes light through
selective absorption by oriented
molecules
These molecules have a preferred axis
(transmission axis) along which electrons can
move easily. All lights with E parallel (perpendic
ular) to the axis is transmitted (absorbed).
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Maluss Law

• Maluss law

• When linearly polarized light passes through a
  polarizer whose axis
• of transmission make an angle q with the
  direction of the E-field vector (or
  polarization), the intensity of the light follows
  the law

• Unpolarized light (like the light from the sun)
  passes through a polarizing sunglass (a linear
  polarizer). The intensity of the light when it
  emerges is

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• Maluss Law

• Maluss law (contd)

Malus law for polarized light passing through
an analyzer/polarizer
This is true only when the incident light
is linearly polarized.
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Unpolarized light on linear polarizer
Maluss Law

• Most light comes from electrons accelerating in
  random directions and is unpolarized.
• Averaging over all directions, intensity of
  transmitted light reduces due to reduction in E

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ExampleMaluss law
Maluss Law
I1
I I0
I3

1. Intensity of unpolarized light incident on linear
   polarizer is reduced by half . I1 I0 / 2
2. Now ignore the 2nd polarizer for now.

3) Light transmitted through first polarizer is
vertically polarized. Angle between it and 3rd
polarizer is q90º . I3 I1 cos2(90º) 0
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Example Maluss law
Maluss Law
I1 0.5 I0
I1
I2 I1cos2(45)
I2
1) Now put 2nd polarizer in.
2) Light transmitted through first polarizer is
vertically polarized. Angle between it and second
polarizer is q45º. I2 I1 cos2 (45º)0.5I10.25
I0
3) Light transmitted through second polarizer is
polarized 45º from vertical. Angle between it and
third polarizer is q45º. I3 I2 cos2(45º)
0.125 I0
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Example Maluss law
Maluss Law
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Controlled Polarization

• LCD screen

• Electrical voltage on a liquid crystal diode
• Turns on and off polarizing filter effect
• Used in LCD display