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Chapter 23: Geometric Optics
© 2013 Pearson Education, Inc.
Review Basic Geometry!
Ray Approximation
• The rays are straight
lines perpendicular to
the wave fronts
• With the ray
approximation, we
assume that a wave
moving through a
medium travels in a
straight line in the
direction of its rays
Light Rays: Ignore Diffraction and
Interference of waves!
Diffraction depends on SLIT WIDTH: the smaller the width,
relative to wavelength, the more bending and diffraction.
We will assume that λ<<d , where d is the diameter of the opening.
This approximation is good for the study of mirrors, lenses, prisms, etc.
The Ray Model of Light
 Let us define a light ray as a line in the direction along
which light energy is flowing.
 Any narrow beam of light, such as a laser beam, is
actually a bundle of many parallel light rays.
 You can think of a single light ray as the limiting case
of a laser beam whose diameter approaches zero.
© 2013 Pearson Education, Inc.
Slide 23-19
The Ray Model of Light
 Light travels through a
transparent material in
straight lines called light rays.
 The speed of light is v  c/n,
where n is the index of
refraction of the material.
 Light rays do not interact with
each other.
 Two rays can cross without
either being affected in any
way.
© 2013 Pearson Education, Inc.
Slide 23-20
The Ray Model of Light
 An object is a source of light rays.
 Rays originate from every point on the
object, and each point sends rays in all
directions.
 The eye “sees” an object
when diverging bundles
of rays from each point
on the object enter the
pupil and are focused to
an image on the retina.
© 2013 Pearson Education, Inc.
Slide 23-22
The Ray Model of Light
Light interacts with matter in four different ways:
At an interface between two materials, light can be
either reflected or refracted.
Within a material, light can be either scattered or
absorbed.
© 2013 Pearson Education, Inc.
Slide 23-21
Objects
 Objects can be
either self-luminous,
such as the sun,
flames, and
lightbulbs, or
reflective.
 Most objects are
reflective.
© 2013 Pearson Education, Inc.
Slide 23-23
Objects
 The diverging rays from a point source are emitted in
all directions.
 Each point on an object is a point source of light rays.
 A parallel bundle of rays could be a laser beam, or
light from a distant object.
© 2013 Pearson Education, Inc.
Slide 23-24
Ray Diagrams
 Rays originate from every point on an object and
travel outward in all directions, but a diagram trying to
show all these rays would be messy and confusing.
 To simplify the picture, we use a ray diagram showing
only a few rays.
© 2013 Pearson Education, Inc.
Slide 23-25
Reflection & Refraction
i   r
n1 sin 1  n2 sin  2
Law of Reflection
• The normal is a line
perpendicular to the
surface
i   r
– It is at the point where the
incident ray strikes the
surface
• The incident ray makes an
angle of θ1 with the
normal
• The reflected ray makes
an angle of θ1’ with the
normal
Specular
Reflection
• Specular reflection is
reflection from a
smooth surface
• The reflected rays are
parallel to each other
• All reflection in this
text is assumed to be
specular
Diffuse
Reflection
• Diffuse reflection is
reflection from a rough
surface
• The reflected rays travel in
a variety of directions
• A surface behaves as a
smooth surface as long as
the surface variations are
much smaller than the
wavelength of the light
Following the Reflected and
Refracted Rays
•Ray  is the
incident ray.
•Ray  is the
reflected ray.
•Ray  is refracted
into the lucite.
•Ray  is internally
reflected in the lucite.
•Ray  is refracted as
it enters the air from
the lucite.
Section 35.5
How many times will the
incident beam shown be reflected
by each of the parallel mirrors?
https://www.youtube.com/watch?v=BQNw8HSixGk
Mirror Mirror
QuickCheck 23.3
You are looking at the image of a
pencil in a mirror. What do you see
in the mirror if the top half of the
mirror is covered with a piece of
dark paper?
A. The full image of the
pencil.
B. The top half only of the
pencil.
C. The bottom half only of
the pencil.
D. No pencil, only the paper.
© 2013 Pearson Education, Inc.
Slide 23-41
QuickCheck 23.3
You are looking at the image of a
pencil in a mirror. What do you see
in the mirror if the top half of the
mirror is covered with a piece of
dark paper?
A. The full image of the
pencil.
B. The top half only of the
pencil.
C. The bottom half only of
the pencil.
D. No pencil, only the paper.
© 2013 Pearson Education, Inc.
Slide 23-42
Why are most materials Opaque?
(Opaque – Can’t see through)
They absorb light without re-emitting it. Vibrations given
by the light to their atoms and molecules are turned into
random kinetic energy – they become slightly warmer.
Opacity: Mirrors
Free electrons in opaque reflective surfaces
can vibrate, absorb & re-emit at any frequency.
Transparency
Selective Absorption
Glass resonates strongly with UV and
infrared, absorbing those frequencies
while transmitting visible frequencies.
Refraction:
Bending Light into Focus
Refraction: Bending of Light
Transmitted through Materials
Light Bends because it Slows Down.
Atoms are Optical Tuning Forks
Light slows down as it travels through
glass because it takes time to be
absorbed and re-emitted.
Light Slows Down in Materials
Light Bends Toward the Normal when going from a
medium of lower refractive index to one that has a
higher refractive index and visa versa.
lower n
higher n
Index of Refraction
c
n
v
n 1
Vacuum: 1
Water: 1.33
Glass: 1.46
Diamond: 2.4
The Index of Refraction
• Refraction: Light Bends in
Transmission
• The speed of light in any
material is less than its speed
in vacuum
• The index of refraction, n,
of a medium can be defined
as
• For a vacuum, n = 1
– We assume n = 1 for air
speed of light in a vacuum c
λ
n
 
also
speed of light in a m edium v λn
• For other media, n > 1
λ  λ in vacuum  • n is a dimensionless number
greater than unity, not
n


λn  λ in a medium 
necessarily an integer
Some Indices of Refraction
Variation of Index of Refraction with Wavelength
speed of light in a vacuum c
λ
n
 
speed of light in a m edium v λn
• This dependence of n on λ
is called dispersion
• The index of refraction for
a material generally
decreases with increasing
wavelength
• Violet light bends more
than red light when passing
into a refracting material
Frequency Doesn’t Change!
• As light travels from one
medium to another, its
frequency does not
change
– Both the wave speed and
the wavelength do change
– The wavefronts do not
pile up, nor are created or
destroyed at the
boundary, so ƒ must stay
the same
Snell’s Law of Refraction
Angles are always measured from the normal.
n1 sin 1  n2 sin  2
Snell’s Law of Refraction
In general:
n1 sin 1  n2 sin  2
n11  n22
n1
 2  1
n2
If n2  n1 , then 1  2
measured from the normal!
QuickCheck 23.4
A laser beam passing
from medium 1 to
medium 2 is refracted as
shown. Which is true?
A. n1 < n2.
B. n1 > n2.
C. There’s not enough
information to compare
n1 and n2.
© 2013 Pearson Education, Inc.
Slide 23-53
QuickCheck 23.4
A laser beam passing
from medium 1 to
medium 2 is refracted as
shown. Which is true?
A. n1 < n2.
B. n1 > n2.
C. There’s not enough
information to compare
n1 and n2.
© 2013 Pearson Education, Inc.
Slide 23-54
Prelab for Next Lab:
https://www.youtube.com/watch?v=1-0eQGeWLfY&t=2s
Real and Apparent Depth
Real and apparent depth. The
refraction of light at the surface of
water makes ponds and swimming
pools appear shallower than they
really are. A 1m deep pond would
only appear to be 0.75 m deep
when viewed from directly above.
When light emerges from glass or
water into air it speeds up again.
© 2013 Pearson Education, Inc.
Apparent Depth
© 2013 Pearson Education, Inc.
QuickCheck 23.6
A fish in an aquarium with flat sides looks out at a hungry
cat. To the fish, the distance to the cat appears to be
A. Less than the actual distance.
B. Equal to the actual distance.
C. More than the actual distance.
© 2013 Pearson Education, Inc.
Slide 23-71
QuickCheck 23.6
A fish in an aquarium with flat sides looks out at a hungry
cat. To the fish, the distance to the cat appears to be
A. Less than the actual distance.
B. Equal to the actual distance.
C. More than the actual distance.
© 2013 Pearson Education, Inc.
Slide 23-72
Beam & Refraction Directions
• Possible directions of the
beam are indicated by rays
numbered 1 through 5
• The refracted rays are bent
away from the normal since
n 1 > n2
• An application of internal
reflection
• Plastic or glass rods are used to
“pipe” light from one place to
another
• Applications include:
– medical use of fiber optic
cables for diagnosis and
correction of medical problems
– Telecommunications
• A flexible light pipe is called an
optical fiber
• A bundle of parallel fibers
(shown) can be used to construct
an optical transmission line
Fiber Optics
Construction of an Optical Fiber
• The transparent core is
surrounded by
cladding
– The cladding has a lower n
than the core
– This allows the light in the
core to experience total
internal reflection
• The combination is
surrounded by the
jacket
Total Internal Reflection
 2  90
n1 sin 1  n2 sin  2
n2
sin  C 
n1
The Critical Angle
Critical Angle
• There is a particular angle
of incidence that will
result in an angle of
refraction of 90°
– This angle of incidence is
called the critical angle, θC
n2
sin θC 
(for n1  n 2 )
n1
Critical Angle Sample Problem
A ray of light, emitted by a laser located beneath the surface of an
unknown liquid with air above it, undergoes total internal
refection as shown. What is the index of refraction for the liquid?
What is its likely identification?
QuickCheck 23.5
A laser beam undergoes two
refractions plus total internal
reflection at the interface
between medium 2 and
medium 3. Which is true?
A. n1 < n3.
B. n1 > n3.
C. There’s not enough
information to
compare n1 and n3.
© 2013 Pearson Education, Inc.
Slide 23-62
QuickCheck 23.5
A laser beam undergoes two
refractions plus total internal
reflection at the interface
between medium 2 and
medium 3. Which is true?
A. n1 < n3.
B. n1 > n3.
C. There’s not enough
information to
compare n1 and n3.
© 2013 Pearson Education, Inc.
Slide 23-63
If you pass white light through a prism,
it separates into its component colors.
long wavelengths
short wavelengths
R.O.Y. G. B.I.V
The index of refraction depends on
WAVELENGTH.
long wavelengths
short wavelengths
R.O.Y. G. B.I.V
The speed and wavelength change but
the FREQUENCY does NOT.
Fr
Frequency depends on the oscillating source!
long wavelengths
short wavelengths
R.O.Y. G. B.I.V
Why does Violet Light bend more
than Red Light?
Violet light slows down more because the atoms in the material
are tuned to higher frequencies. As the violet light travels
through glass it takes more time to be absorbed and re-emitted.
Variation of Index of Refraction with Wavelength
speed of light in a vacuum c
λ
n
 
speed of light in a m edium v λn
• This dependence of n on λ
is called dispersion
• The index of refraction for
a material generally
decreases with increasing
wavelength
• Violet light bends more
than red light when passing
into a refracting material
Refraction in a Prism
•Since all the colors have
different angles of deviation,
white light will spread out
into a spectrum.
– Violet deviates the
most.
– Red deviates the least.
– The remaining colors
are in between.
Section 35.7
Compare: Dispersion via
Diffraction and Refraction
Why does Violet Light bend more
than Red Light?
Violet light slows down more because the atoms in the material
are tuned to higher frequencies. As the violet light travels
through glass it takes more time to be absorbed and re-emitted.
Angle of Deviation
• Since all the colors
have different angles
of deviation, white
light will spread out
into a spectrum
– Violet deviates the most
– Red deviates the least
– The remaining colors are
in between
Dispersion Sample Problem
The index of refraction for
violet light in silica flint glass
is 1.66, and that for red light is
1.62. What is the angular
dispersion of visible light
passing through a prism of
apex angle 60.0° if the angle of
incidence is 50.0°? red (660
nm) violet (410 nm)
Use Snell’s Law twice and some
geometry! Angles are always
measured from the normal.
n1 sin 1  n2 sin  2
How are Rainbows Formed?
Dispersion: Raindrops Act like Prisms
• A ray of light strikes a drop
of water in the atmosphere
• It undergoes both reflection
and refraction
– First refraction at the
front of the drop
• Violet light will
deviate the most
• Red light will deviate
the least
The Rainbow
• At the back surface the light is
reflected
• It is refracted again as it
returns to the front surface and
moves into the air
• The rays leave the drop at
various angles
– The angle between the white
light and the most intense violet
ray is 40°
– The angle between the white
light and the most intense red ray
is 42°
Observing the Rainbow
• If a raindrop high in the sky is observed, the red ray is seen
• A drop lower in the sky would direct violet light to the
observer
• The other colors of the spectra lie in between the red and
the violet
The droplets form a circular arc, with each droplet within the arc
dispersing light and reflecting it back towards the observer with
the greatest concentration of outgoing rays found at these 40-42
degree angles of deviation. Every droplet within the arc is
refracting and dispersing the entire visible light spectrum
(ROYGBIV).
Rainbow facts
• an observer is in a position to see only a single color from any
one droplet of water.
• your rainbow is slightly different from the rainbow seen by
others
• your rainbow moves with you
• disk within the bow is brighter because of overlapping of
multiple refractions (which don’t occur outside the disk)
A line drawn from your eye to the top of the rainbow forms a 42degree angle with the imaginary line from the sun through your
eye. (If there is a secondary rainbow, it forms an angle of 51degrees). Because these angles determine the position of the
rainbow in the sky, it will sink as the sun rises and rise as the sun
sinks. At some points, the entire rainbow, not just the bottom half,
will be below the horizon where you can't see it. That's why you'll
never see a summer rainbow at midday.
Double Rainbow
• The secondary rainbow is
fainter than the primary
• The secondary rainbow
arises from light that
makes two reflections
from the interior surface
before exiting the raindrop
• Higher-order rainbows are
possible, but their
intensity is low
•
•
Halos are caused by the light of the sun or moon passing through a very thin layer of
cirruform (ice-crystal) clouds in the upper atmosphere. The ice crystals refract the light
of the moon, similar to the way water droplets in the lower atmosphere can refract
sunlight to produce a rainbow. Just like a rainbow, strong halos can have bands of color
in them, due to slightly different refractive properties of the ice crystals for different
colors. Essentially, halos ARE rainbows caused by primary refraction in ice crystals.
Some interesting facts about halos: Halos always occur exactly 22 degrees away from
the sun or moon. Occasionally, intense halos can be double halos, just as intense
rainbows can be doubled. Intense halos can also produce "moondogs" or "sundogs,"
very bright regions on the halo evenly spaced at 90 degree intervals around the halo.
Colored Filters and Colored Objects
 The figure below shows the absorption curve of
chlorophyll, which is essential for photosynthesis in
green plants.
 The chemical reactions of photosynthesis absorb red
light and blue/violet light from sunlight and puts it to use.
 When you look at
the green leaves
on a tree, you’re
seeing the light that
was reflected
because it wasn’t
needed for
photosynthesis.
© 2013 Pearson Education, Inc.
Slide 23-84
Light Scattering: Blue Skies and Red Sunsets
 Light can scatter
from small particles
that are suspended
in a medium.
 Rayleigh scattering
from atoms and
molecules depends
inversely on the
fourth power of the
wavelength:
Iscattered 4
© 2013 Pearson Education, Inc.
Slide 23-85
Light Scattering: Blue Skies and Red Sunsets
Sunsets are red because all the blue light has scattered as the sunlight passes through the atmosphere.
© 2013 Pearson Education, Inc.
Slide 23-86