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Chapter 31
Maxwell’s Equations and
Electromagnetic Waves
Copyright © 2009 Pearson Education, Inc.
32-4 Index of Refraction
In general, light slows
somewhat when
traveling through a
medium. The index of
refraction of the
medium is the ratio of
the speed of light in
vacuum to the speed
of light in the medium:
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32-5 Refraction: Snell’s Law
Light changes direction when crossing a
boundary from one medium to another. This is
called refraction, and the angle the outgoing ray
makes with the normal is called the angle of
refraction.
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32-5 Refraction: Snell’s Law
Refraction is what makes objects halfsubmerged in water look odd.
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32-5 Refraction: Snell’s Law
The angle of refraction depends on the
indices of refraction, and is given by
Snell’s law:
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32-5 Refraction: Snell’s Law
Example 32-9: Apparent depth of a pool.
A swimmer has dropped her goggles to the
bottom of a pool at the shallow end, marked
as 1.0 m deep. But the goggles don’t look
that deep. Why? How deep do the goggles
appear to be when you look straight down
into the water?
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ConcepTest 32.4a
Parallel light rays cross interfaces
from air into two different media,
1 and 2, as shown in the figures
below. In which of the media is
the light traveling faster?
Refraction I
1) medium 1
2) medium 2
3) both the same
air
1
air
2
ConcepTest 32.4a
Parallel light rays cross interfaces
from air into two different media,
1 and 2, as shown in the figures
below. In which of the media is
the light traveling faster?
Refraction I
1) medium 1
2) medium 2
3) both the same
The greater the
difference in the speed
air
of light between the two
media, the greater the
bending of the light
1
air
2
rays.
Follow-up: How does the speed in air compare to that in #1 or #2?
ConcepTest 32.5a
To shoot a fish with a gun,
should you aim directly at the
image, slightly above, or slightly
below?
Gone Fishin’ I
1) aim directly at the image
2) aim slightly above
3) aim slightly below
ConcepTest 32.5a
To shoot a fish with a gun,
should you aim directly at the
image, slightly above, or slightly
below?
Due to refraction, the image will
appear higher than the actual
fish, so you have to aim lower to
compensate.
Gone Fishin’ I
1) aim directly at the image
2) aim slightly above
3) aim slightly below
32-6 Visible Spectrum and Dispersion
The visible spectrum contains the full
range of wavelengths of light that are
visible to the human eye.
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32-6 Visible Spectrum and Dispersion
The index of refraction of many transparent
materials, such as glass and water, varies
slightly with wavelength. This is how prisms
and water droplets create rainbows from
sunlight.
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32-6 Visible Spectrum and Dispersion
This spreading of light into the full
spectrum is called dispersion.
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32-7 Total Internal Reflection; Fiber
Optics
If light passes into a medium with a smaller
index of refraction, the angle of refraction is
larger. There is an angle of incidence for which
the angle of refraction will be 90°; this is called
the critical angle:
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32-7 Total Internal Reflection; Fiber
Optics
If the angle of incidence is larger than this,
no transmission occurs. This is called total
internal reflection.
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32-7 Total Internal Reflection; Fiber
Optics
Conceptual Example 32-11: View up from under
water.
Describe what a person would see who looked up
at the world from beneath the perfectly smooth
surface of a lake or swimming pool.
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32-7 Total Internal Reflection; Fiber
Optics
Optical fibers also depend on total
internal reflection; they are therefore
able to transmit light signals with very
small losses.
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32-8 Refraction at a Spherical
Surface
Rays from a single point will be focused
by a convex spherical interface with a
medium of larger index of refraction to a
single point, as long as the angles are not
too large.
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32-8 Refraction at a Spherical
Surface
Geometry gives the relationship
between the indices of refraction, the
object distance, the image distance,
and the radius of curvature:
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32-8 Refraction at a Spherical
Surface
For a concave spherical interface, the rays
will diverge from a virtual image.
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32-8 Refraction at a Spherical
Surface
Example: Apparent depth II.
A person looks vertically down into a 1.0-m-deep
pool. How deep does the water appear to be?
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32-8 Refraction at a Spherical
Surface
Example: A spherical “lens.”
A point source of light is placed at a distance
of 25.0 cm from the center of a glass sphere
of radius 10.0 cm. Find the image of the
source.
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Summary of Chapter 32
• Light paths are called rays.
• Index of refraction:
• Angle of reflection equals angle of incidence.
• Plane mirror: image is virtual, upright, and the
same size as the object.
• Spherical mirror can be concave or convex.
• Focal length of the mirror:
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Summary of Chapter 32
• Mirror equation:
• Magnification:
• Real image: light passes through it.
• Virtual image: light does not pass through.
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Summary of Chapter 32
• Law of refraction (Snell’s law):
• Total internal reflection occurs when angle of
incidence is greater than critical angle:
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Slight Digression
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35-11 Polarization
Light is polarized when
its electric fields
oscillate in a single
plane, rather than in any
direction perpendicular
to the direction of
propagation.
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35-11 Polarization
Polarized light will not
be transmitted through
a polarized film whose
axis is perpendicular
to the polarization
direction.
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35-11 Polarization
When light passes through a polarizer, only the
component parallel to the polarization axis is
transmitted. If the incoming light is planepolarized, the outgoing intensity is:
Remember: I  A2  I  E02
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35-11 Polarization
This means that if initially unpolarized light
passes through crossed polarizers, no light
will get through the second one.
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35-11 Polarization
Example 35-13: Two Polaroids at 60°.
Unpolarized light passes through two
Polaroids; the axis of one is vertical and
that of the other is at 60° to the vertical.
Describe the orientation and intensity of
the transmitted light.
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35-11 Polarization
Conceptual Example
35-14: Three
Polaroids.
When unpolarized
light falls on two
crossed Polaroids
(axes at 90°), no light
passes through.
What happens if a
third Polaroid, with
axis at 45° to each of
the other two, is
placed between
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35-11 Polarization
Light is also partially polarized after reflecting
from a nonmetallic surface. At a special angle,
called the polarizing angle or Brewster’s angle,
the polarization is 100%:
.
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35-11 Polarization
Example 35-15: Polarizing angle.
(a) At what incident angle is sunlight
reflected from a lake plane-polarized? (b)
What is the refraction angle?
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35-12 Liquid Crystal Displays (LCD)
Liquid crystals are unpolarized in the absence
of an external voltage, and will easily transmit
light. When an external voltage is applied, the
crystals become polarized and no longer
transmit; they appear dark.
Liquid crystals can be found in many familiar
applications, such as calculators and digital
watches.
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35-12 Liquid Crystal Displays (LCD)
This particular type of liquid crystal,
called a twisted crystal, shows how the
crystal passes light when the voltage is
off but not when it is on.
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35-13 Scattering of Light by the
Atmosphere
Skylight is partially
polarized due to scattering
from molecules in the air.
The amount of polarization
depends on the angle that
your line of sight makes
with the Sun.
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ConcepTest 35.3
Polarization
If unpolarized light is incident
1) only case 1
from the left, in which case will
2) only case 2
some light get through? Assume
3) only case 3
perfect polarizers.
4) cases 1 and 3
5) all three cases
ConcepTest 35.3
Polarization
If unpolarized light is incident
1) only case 1
from the left, in which case will
2) only case 2
some light get through? Assume
3) only case 3
perfect polarizers.
4) cases 1 and 3
5) all three cases
In cases 1 and 3, light is
blocked by the adjacent
horizontal and vertical
polarizers. However, in case
2, the intermediate 45°
polarizer allows some light
to get through the last
vertical polarizer.
Chapter 33
Lenses and Optical
Instruments
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Units of Chapter 33
• Thin Lenses; Ray Tracing
• The Thin Lens Equation; Magnification
• Combinations of Lenses
• Lensmaker’s Equation
• Cameras: Film and Digital
• The Human Eye; Corrective Lenses
• Magnifying Glass
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Units of Chapter 33
• Telescopes
• Compound Microscope
• Aberrations of Lenses and Mirrors
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33-1 Thin Lenses; Ray Tracing
Thin lenses are those whose thickness is small
compared to their radius of curvature. They
may be either converging (a) or diverging (b).
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33-1 Thin Lenses; Ray Tracing
Parallel rays are
brought to a focus
by a converging lens
(one that is thicker
in the center than it
is at the edge).
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33-1 Thin Lenses; Ray Tracing
A diverging lens (thicker at the edge than in
the center) makes parallel light diverge; the
focal point is that point where the diverging
rays would converge if projected back.
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33-1 Thin Lenses; Ray Tracing
The power of a lens is the inverse of its focal
length:
Lens power is measured in diopters, D:
1 D = 1 m-1.
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33-1 Thin Lenses; Ray Tracing
Ray tracing for thin lenses is similar to that for
mirrors. We have three key rays:
1. This ray comes in parallel to the axis and exits
through the focal point.
2. This ray comes in through the focal point and
exits parallel to the axis.
3. This ray goes through the center of the lens
and is undeflected.
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33-1 Thin Lenses; Ray Tracing
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33-1 Thin Lenses; Ray Tracing
For a diverging lens, we can use the same
three rays; the image is upright and virtual.
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33-2 The Thin Lens Equation;
Magnification
The thin lens equation is similar to the mirror
equation:
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33-2 The Thin Lens Equation;
Magnification
The sign conventions are slightly different:
1. The focal length is positive for converging lenses and
negative for diverging.
2. The object distance is positive when the object is on
the same side as the light entering the lens (not an
issue except in compound systems); otherwise it is
negative.
3. The image distance is positive if the image is on the
opposite side from the light entering the lens;
otherwise it is negative.
4. The height of the image is positive if the image is
upright and negative otherwise.
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33-2 The Thin Lens Equation;
Magnification
The magnification formula is also the same
as that for a mirror:
The power of a lens is positive if it is
converging and negative if it is diverging.
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33-2 The Thin Lens Equation;
Magnification
Problem Solving: Thin Lenses
1. Draw a ray diagram. The image is located
where the key rays intersect.
2. Solve for unknowns.
3. Follow the sign conventions.
4. Check that your answers are consistent with
the ray diagram.
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33-2 The Thin Lens Equation;
Magnification
Example 33-2: Image formed by
converging lens.
What are (a) the position, and (b) the size,
of the image of a 7.6-cm-high leaf placed
1.00 m from a +50.0-mm-focal-length
camera lens?
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33-2 The Thin Lens Equation;
Magnification
Example 33-3: Object close to converging
lens.
An object is placed 10 cm from a 15-cmfocal-length converging lens. Determine
the image position and size (a)
analytically, and (b) using a ray diagram.
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33-2 The Thin Lens Equation;
Magnification
Example 33-4: Diverging lens.
Where must a small insect be placed if
a 25-cm-focal-length diverging lens is
to form a virtual image 20 cm from the
lens, on the same side as the object?
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