Chapter 22. Wave Optics
Light is an electromagnetic
wave. The interference of
light waves produces the
colors reflected from a CD,
the iridescence of bird
feathers, and the technology
underlying supermarket
checkout scanners and
optical computers.
Chapter Goal: To
understand and apply the
wave model of light.
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Models of Light
• The wave model: under many circumstances, light
exhibits the same behavior as sound or water waves. The
study of light as a wave is called wave optics.
• The ray model: The properties of prisms, mirrors, and
lenses are best understood in terms of light rays. The ray
model is the basis of ray optics.
• The photon model: In the quantum world, light behaves
like neither a wave nor a particle. Instead, light consists of
photons that have both wave-like and particle-like
properties. This is the quantum theory of light.
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Wave propagation
• Diffraction: A
wave passing
through an
aperture spreads
out. The effect is
pronounced if the
aperture size is
comparable to a
wavelength.
http://www.ngsir.netfirms.com/
englishhtm/Diffraction.htm
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Ray model works for
wavelength<<aperture size
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Diffraction of light
Light diffraction is
observed for slits
smaller than a micron
or so. The wavelength
of light (about 0.5
micron = 0.5e-6 m
depending on the
color) can be inferred
from the pattern.
A laser is a source of harmonic (monochromatic) light waves.
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Aperture sources of waves
An aperture with width
small compared to the
wavelength behaves as
a source of circular
waves driven in phase
by the incident wave.
Multiple apertures are
coherent sources.
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Two slit interference of waves
Two coherent wave
sources produce an
interference
pattern.
Two slits driven by
the same incident
wave result in an
interference
pattern.
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Huygen’s Principle
Wave propagation can
be modeled by treating
each element of an
advancing wave front
as a source of spherical
waves and an aperture
as a collection of
elements. In this way,
the diffraction pattern
of any aperture shape
may be computed.
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Diffraction through a slit
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Circular-Aperture Diffraction
Light of wavelength λ passes through a circular aperture of
diameter D, to a screen a distance L behind the aperture,
L>>D. The diffraction pattern has a circular central
maximum, surrounded by a series of secondary rings. The
angle of the first minimum in the intensity is
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Example
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Double slit interference
Double slit interference of light is a simple and important
case.
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Geometry of double slit interference
Constructive interference if path length difference is a multiple of
a wavelength:
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Example of double slit interference
QUESTION:
A laser of wavelength l = 500
nm illuminates a pair of slits
separated by d= 1.0 mm. What
is the angle of the m=1
maximum in radians?
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EXAMPLE:
QUESTION:
A laser of wavelength l = 500
nm illuminates a pair of slits
separated by d= 1.0 mm. What
is the angle of the m=1
maximum in radians?
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Suppose the viewing screen in
the figure is moved closer to
the double slit. What happens
to the interference fringes?
A. They fade out and disappear.
B. They get out of focus.
C. They get brighter and closer together.
D. They get brighter and farther apart.
E.  They get brighter but otherwise do not change.
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Suppose the viewing screen in
the figure is moved closer to
the double slit. What happens
to the interference fringes?
A. They fade out and disappear.
B. They get out of focus.
C. They get brighter and closer together.
D. They get brighter and farther apart.
E.  They get brighter but otherwise do not change.
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The Diffraction Grating
A multi-slit (or multi reflection or refraction) device is
called a diffraction grating. Bright fringes will occur at
angles θm, such that
The y-positions of these fringes will occur at
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Fully constructive
interference at the same
angles as for two slits. But
the amplitude at a
maximum is N times that
of a single slit and the
angular width of the peaks
is much smaller => much
more precise focusing of
the wave energy.
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Figure 22.8 (a) shows the
narrow bright fringes
produced by a grating.
Figure 22.8 (b) shows how
a mix of light of different
wavelength can be
separated into its
components and analyzed
with the aid of a grating.
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Example of use of diffraction grating
QUESTION:
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EXAMPLE 22.3 Measuring wavelengths
emitted by sodium atoms
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Michelson interferometer
A Michelson interferometer
splits light into two beams
which reflect off mirrors and
recombine exhibiting
interference. Moving mirror
M2 and changing the path
length of one beam, or
delaying the light with some
material will change the
interference pattern. To an
observer looking into the
output beam, there are two
coherent sources behind
mirror 1.
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Light of wavelength l1 illuminates a
double slit, and interference fringes are
observed on a screen behind the slits.
When the wavelength is changed to l2,
the fringes get closer together. How large
is l2 relative to l1?
A. l2 is smaller than l1.
B.  l2 is larger than l1.
C.  Cannot be determined from this information.
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Light of wavelength l1 illuminates a
double slit, and interference fringes are
observed on a screen behind the slits.
When the wavelength is changed to l2,
the fringes get closer together. How large
is l2 relative to l1?
A.  l2 is smaller than l1.
B.  l2 is larger than l1.
C.  Cannot be determined from this information.
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White light passes through a diffraction
grating and forms rainbow patterns on a
screen behind the grating. For each
rainbow,
A. the red side is farthest from the center of the
screen, the violet side is closest to the center.
B. the red side is closest to the center of the screen,
the violet side is farthest from the center.
C. the red side is on the left, the violet side on
the right.
D. the red side is on the right, the violet side on
the left.
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White light passes through a diffraction
grating and forms rainbow patterns on a
screen behind the grating. For each
rainbow,
A.  the red side is farthest from the center of the
screen, the violet side is closest to the center.
B.  the red side is closest to the center of the screen,
the violet side is farthest from the center.
C.  the red side is on the left, the violet side on
the right.
D.  the red side is on the right, the violet side on
the left.
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A Michelson interferometer using light of
wavelength l has been adjusted to produce a bright
spot at the center of the interference pattern.
Mirror M1 is then moved distance l toward the
beam splitter while M2 is moved distance l away
from the beam splitter. How many bright-darkbright fringe shifts are seen?
A.  4
B.  3
C.  2
D.  1
E.  0
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A Michelson interferometer using light of
wavelength l has been adjusted to produce a bright
spot at the center of the interference pattern.
Mirror M1 is then moved distance l toward the
beam splitter while M2 is moved distance l away
from the beam splitter. How many bright-darkbright fringe shifts are seen?
A.  4
B.  3
C.  2
D.  1
E.  0
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