Vern J. Ostdiek
Donald J. Bord
Chapter 9
Optics
(Section 1)
Doggone It!
• When the “dog days” of summer give way to the
“three dog nights” of winter, inhabitants of colder
climates are often treated to spectacular
apparitions like that shown in the accompanying
photo.
•
On brisk days when the Sun is near the horizon and
the sky is filled with thin clouds of ice crystals, one
often sees bright patches of light flanking the Sun at
an angular distance of about 22.
Doggone It!
• These patches frequently exhibit rainbowlike
coloration and are variously called mock suns,
parhelia, or sundogs.
•
Next to rainbows themselves, sundogs are among
the most common atmospheric optics effects seen
at midlatitudes and above.
Doggone It!
• This phenomenon, like that of rainbows and halos,
touches us with its beauty, but it also stirs our
intellectual curiosity about what naturally occurring
circumstances conspire to produce such an
exquisite display.
•
•
What are the underlying physical principles
governing the processes that lead to such striking
visualizations?
How, if at all, might they be related to other optical
phenomena often seen in the sky such as
rainbows?
Doggone It!
• The wonder and fascination afforded to us by
Nature in the form of sundogs can be enhanced by
finding answers to these questions.
•
A primary ingredient in the mix that provides the
answers we seek is the law of refraction.
• By applying this principle and paying close
attention to the relationship between the natural
elements in play, you should be able to frame
responses to the questions posed above.
Doggone It!
• In this chapter, we will investigate the law of
refraction together with its counterpart, the law of
reflection, to discover that they comprise two
important elements in the study of light and its
interaction with matter–the field of optics.
•
These laws also provide the basis for many
practical devices, such as cameras, telescopes,
and liquid-crystal displays, as well as for many of
the most striking natural phenomena, such as
rainbows, soap-bubble iridescence, and, of course,
sundogs.
9.1 Light Waves
• Light generally refers to the narrow band of
electromagnetic (EM) waves that can be seen by
human beings.
•
These are transverse waves with frequencies from
about 4×1014 hertz to 7.5×1014 hertz.
9.1 Light Waves
• The corresponding wavelengths are so small that
we will find it useful to express them in
nanometers (nm).
One nanometer is one billionth of a meter:
-9
1 nanometer =10 meter = 0.000000001 meter
1 nm=10-9 m
9.1 Light Waves
• The wavelengths of visible light (in a vacuum or in
air) range from about 750 nanometers for lowfrequency red light to about 400 nanometers for
high-frequency violet light.
• Keep in mind two important points:
1. different frequencies of light are perceived as
different colors, and
2. white light is typically a combination of all
frequencies in the visible spectrum.
9.1 Light Waves
• As with sound and water ripples, we will use both
wavefronts and rays to represent light waves.
•
Recall that a wavefront shows the location in space
of one particular phase (peak or valley, for
example) of the wave.
9.1 Light Waves
• For a light bulb or other
spherical light source, the
wavefronts are spherical
shells (not unlike balloons)
expanding outward at the
speed of light.
9.1 Light Waves
• A light ray is a line drawn in space representing a
“pencil” of light that is part of a larger beam.
•
Rays are represented as arrows and indicate the
direction the light is traveling.
• A laser beam can often be thought of as a single
light ray.
• The light from a light bulb can be represented by
light rays radiating outward in all directions.
•
Be careful not to confuse these light rays with the
electric and magnetic field lines discussed in the
previous chapters.
9.1 Light Waves
• Some of the general characteristics of wave
propagation, such as reflection, are readily
observed with light waves.
• But other phenomena are more rare in everyday
experience because of two factors:
1. The speed of light is extremely high (3×108 m/s in
a vacuum).
2. The wavelengths of light are extremely short.
9.1 Light Waves
• We must turn to distant galaxies moving away
from us at high speeds to easily observe the
Doppler effect with light.
•
The Doppler effect with sound, on the other hand, is
quite common because the speed of sound is only
about 350 m/s and the wavelengths of sound (in
air) are in the centimeter to meter range.
• In these first two sections, we will describe some
of the phenomena that can occur when light
encounters matter.
•
The remaining sections of the chapter deal with
important things that occur after light has traveled
inside transparent material.
9.1 Light Waves
Reflection
• Reflection of light waves is extremely common:
•
Except for light sources such as the Sun and light
bulbs, everything we see is reflecting light to our
eyes.
• There are two types of reflection:
•
specular and diffuse
9.1 Light Waves
Reflection
• Specular reflection is the familiar type that we
see in a mirror or in the surface of a calm pool of
water.
•
A mirror is a very smooth, shiny surface, usually
made by coating glass with a thin layer of aluminum
or silver.
• Specular reflection occurs when the direction the
light wave is traveling changes.
9.1 Light Waves
Reflection
• By changing the angle of the incident (incoming)
light ray and observing the reflected ray, we see
that the light behaves somewhat like a billiard ball
bouncing off a cushion on a pool table.
9.1 Light Waves
Reflection
• The figure shows an imaginary line drawn
perpendicular to the mirror and touching it at the
point where the incident ray strikes it.
•
This line is called the normal.
• The angle between the incident ray and the
normal is called the angle of incidence, and the
angle between the reflected ray and the normal is
called the angle of reflection.
•
Our observations indicate that these angles are
always equal.
9.1 Light Waves
Reflection
• The following law, first described in a book titled
Catoptrics and thought to have been written by
Euclid in the third century BCE, states this
formally.
Law of Reflection: The angle of incidence equals
the angle of reflection.
•
So specular reflection of light is much like sound
echoing off a cliff.
9.1 Light Waves
Reflection
• The other type of reflection, diffuse reflection,
occurs when light strikes a surface that is not
smooth and polished but uneven like the bottom of
an aluminum pan or the surface of this paper.
•
The light rays reflect off the random bumps and
nicks in the surface and scatter in all directions.
9.1 Light Waves
Reflection
• The law of reflection still applies, but the rays
encounter segments of the irregular surface
oriented at different angles and therefore leave the
surface with different directions.
•
That is why you can shine a flashlight on the
aluminum and see the reflected light from different
angles around the pan.
• With specular reflection from a mirror, you could
see the reflected light from only one direction.
9.1 Light Waves
Reflection
• Except for light sources and smooth, shiny
surfaces such as mirrors, every object we see is
reflecting light diffusely.
•
This diffuse reflection causes light to radiate
outward from each point on a surface.
• You can see every point on your hand as you turn
it in front of your face because each point on your
skin is reflecting light in all directions.
9.1 Light Waves
Reflection
• Things can have color because light actually
penetrates into the material and is partially
reflected and partially absorbed along its way into
and out of the material.
• The reflected light that leaves the surface will have
color if pigments in the material absorb some
frequencies (colors) more efficiently than others.
9.1 Light Waves
Reflection
• A white surface, like this paper, reflects all
frequencies of light nearly uniformly.
•
•
If you shine just red light on it, it will appear red.
With just blue light, it will appear blue.
• A colored surface, like that of a red fire
extinguisher, “removes” some frequencies of the
light.
9.1 Light Waves
Reflection
• A red surface reflects the lower frequency light
(red) most effectively and absorbs much of the
rest.
• If you shine red light on it, it will appear red.
• With blue or any other single color, it will appear
black:
•
very little of the light will be reflected
9.1 Light Waves
Diffraction
• As with all waves, diffraction of light as it passes
through a hole or slit is observable only when the
width of the opening is not too much larger than
the wavelength of the light.
9.1 Light Waves
Diffraction
• This means that light doesn’t spread out after
passing through a window nearly as much as sound
does, but diffraction is observed when a very narrow
slit (about the width of a human hair) is used.
•
The narrower the slit, the more the light spreads out.
9.1 Light Waves
Interference
• Recall that when two identical waves arrive at the
same place, they add together. If the two waves
are “in phase”—peak matches peak—the
resulting amplitude is doubled.
•
This is called constructive interference.
• At any point where the two waves are “out of
phase”—peak matches valley—they cancel each
other.
•
This is destructive interference.
9.1 Light Waves
Interference
• Interference of light waves is an important
phenomenon for two reasons.
•
•
First, in experiments conducted around 1800,
British physician Thomas Young used interference
to prove that light is indeed a wave.
Second, interference is routinely used to measure
the wavelength of light.
• We will consider two types of interference: two-slit
interference and thin-film interference.
9.1 Light Waves
Interference
• When a light wave passes through two narrow slits
that are close together, the two waves emerging
from the slits diffract outward and overlap.
•
If the light consists of a single frequency (color), a
screen placed behind the slits where the two light
waves overlap will show a pattern of bright areas
alternating with dark areas.
9.1 Light Waves
Interference
• At each bright area, the two waves from the slits
are completely in phase and undergo constructive
interference.
9.1 Light Waves
Interference
• Conversely, at each dark area the two waves are
completely out of phase and undergo destructive
interference—they cancel each other.
• There is a bright area at the center of this
interference pattern because the two waves travel
exactly the same distance in getting there, so they
are in phase.
•
At the first bright area to the left of center, the wave
from the slit on the right has to travel a distance
exactly equal to one wavelength farther than the
wave from the slit on the left.
9.1 Light Waves
Interference
• This puts them in phase as well.
•
Similarly, at each successive bright area on the left
side, the wave from the right slit has to travel 2, 3,
4, . . . wavelengths farther than the wave from the
left slit.
• At each bright area on the right side of the pattern,
it is the wave from the left slit that has to travel a
whole number of wavelengths farther.
9.1 Light Waves
Interference
• At the first dark area to the left of the center of the
pattern, the wave from the right slit travels one-half
wavelength farther than the wave from the left slit.
•
The two waves are out of phase and interfere
destructively.
• At the next dark area on the left, the additional
distance is wavelengths, then wavelengths at the
next, and so on.
9.1 Light Waves
Interference
• True constructive and destructive interference
actually occurs only at the centers of the bright
and dark areas.
•
At points in between, the waves are neither exactly
in phase nor exactly out of phase, so they partially
reinforce or partially cancel each other.
9.1 Light Waves
Interference
• The distance between two adjacent bright or dark
areas is determined by the distance between the
two slits, the distance between the screen and the
slits, and the wavelength of the light.
•
Because the first two can be measured easily, their
values can be used to compute the wavelength of
the light.
• The swirling colors you see in oil or gasoline spills
floating on wet pavement are caused by thin-film
interference.
9.1 Light Waves
Interference
• Part of the light striking a thin film of oil is reflected
from it, and part passes through to be reflected off
the water.
9.1 Light Waves
Interference
• The light wave that passes through the film before
being reflected travels a greater distance than the
wave that reflects off the upper surface of oil.
•
If the two waves emerge in step, there is
constructive interference. If they emerge out of
step, there is destructive interference.
9.1 Light Waves
Interference
• The wavelength of the light, the thickness of the
film, and the angle at which the light strikes the
film combine to determine whether the
interference is constructive, destructive, or in
between.
•
With single-color (one wavelength) light, one would
see bright areas and dark areas at various places
on the film.
9.1 Light Waves
Interference
• With white light, one sees different colors at
different places on the film.
•
At some places, the film thickness and angle of
incidence will cause constructive interference for
the wavelength of red light, at other places for the
wavelength of green light, and so on.
9.1 Light Waves
Interference
• Interference in thin films in hummingbird and
peacock feathers is the cause of their iridescent
colors.
•
Soap bubbles are also colored by interference of
light reflecting off the front and back surfaces of the
soap film.
9.1 Light Waves
Polarization
• The fact that light could undergo diffraction and
interference convinced Young and other scientists
of his time that light can behave like a wave.
•
The other model of light elaborated by Newton held
that light is a stream of tiny particles, but this
approach could not account for these distinctively
wavelike phenomena.
• Polarization reveals that light is a transverse
wave rather than a longitudinal wavelike sound.
9.1 Light Waves
Interference
• A rope secured at one end can be used to
demonstrate polarization.
•
•
If you pull the free end tight and move it up and
down, a wave travels on the rope that is vertically
polarized.
Each part of the rope oscillates in a vertical plane.
9.1 Light Waves
Interference
• In a similar manner, moving the free end
horizontally produces a horizontally polarized
wave on the rope.
•
Moving the free end at any other angle with the
vertical will also produce a polarized wave.
• Polarization is possible only with transverse
waves.
9.1 Light Waves
Interference
• The fact that light can be polarized reveals its
transverse nature.
• A Polaroid filter, like the lenses of Polaroid
sunglasses, absorbs light passing through it
unless the light is polarized in a particular
direction.
•
This direction is coincident with the transmission
axis of the filter.
9.1 Light Waves
Interference
• Light polarized in this direction passes through the
Polaroid largely unaffected, light polarized
perpendicular to this direction is blocked
(absorbed), and light polarized in some direction in
between is partially absorbed.
9.1 Light Waves
Interference
• For simplicity, we will assume that our Polaroid
filters are 100-percent efficient in absorbing light
polarized in a direction perpendicular to the
transmission axis.
9.1 Light Waves
Interference
• The light that we get directly from the Sun and
from ordinary light fixtures is a mixture of light
waves polarized in all different directions.
•
The light is said to be “natural” or “unpolarized”
because it has no preferred plane of vibration.
9.1 Light Waves
Interference
• When natural light encounters a Polaroid filter, it
emerges polarized along the transmission axis.
•
The filter allows only that portion of the incident light
that oscillates along this direction to pass through;
the rest of the radiation is absorbed.
9.1 Light Waves
Interference
• Now, if the emergent light encounters a second
Polaroid filter, the amount of light that passes
through will depend on the orientation of the
transmission axis of the second filter.
•
•
•
If the axis of the second filter is aligned with that of
the first, then the light will continue on unimpeded.
If the axis of the second is perpendicular to that of
the first, then all of the light will be blocked by the
second filter.
This is referred to as crossed Polaroids
9.1 Light Waves
Interference
• When the angle between the transmission axes of
the two filters is other than zero or 90, some of
the light will pass through, with the intensity
becoming progressively less for angles closer to
90.
9.1 Light Waves
Interference
•
Polaroid sunglasses are very useful because light
is polarized to some extent when it reflects off a
smooth surface like that of water, asphalt, or the
paint on the hood of a car.
•
In particular, the reflected sunlight is partially
polarized horizontally.
9.1 Light Waves
Interference
• This reflected light, called glare, is usually bright
and annoying.
• Sunglasses using Polaroid lenses with their
transmission axes vertical will block most of this
reflected light, which makes it easier to see the
surface itself.
9.1 Light Waves
Interference
• LCDs used in calculators, digital watches, laptop
computers, and video games also use
polarization.
•
The liquid crystal is sandwiched between crossed
Polaroids, and this assembly is placed in front of a
mirror.
9.1 Light Waves
Interference
• Without the liquid crystal present, the display
would be dark:
•
Light passing through the first Polaroid is polarized
vertically and would be totally absorbed when it
reached the second Polaroid.
• No light would reach the
mirror, so none would be
reflected back from the
display.
9.1 Light Waves
Interference
• The specially chosen liquid-crystal material
between the Polaroids is arranged so that in its
normal state its molecules change the polarization
of the light passing through it.
•
The liquid crystal twists the polarized light 90°.
9.1 Light Waves
Interference
• The polarization is changed from vertical to
horizontal for light passing through from the front
and from horizontal to vertical for light passing
through from the rear.
9.1 Light Waves
Interference
• The light that was vertically polarized by the first
Polaroid is made horizontally polarized by the
liquid crystal, passes through the second Polaroid,
is reflected back through the display, and emerges
polarized vertically.
9.1 Light Waves
Interference
• To make images on the display, segments of it are
darkened.
•
Here is where the liquid crystal property is used.
• An electric field is switched on in the parts of the
display to be darkened.
•
This causes the molecules of the liquid crystal to
rotate and become aligned in one direction.
9.1 Light Waves
Interference
• As a result, they no longer change the polarization
of light passing through.
•
Light going through this segment is absorbed by the
second Polaroid, and that part of the display is
dark.
9.1 Light Waves
Interference
• The transmission axis of the first Polaroid is
oriented vertically so that you can see the display
while wearing Polaroid sunglasses.
•
If you rotate an LCD—say, like that on a digital
watch—and look at it while wearing Polaroid
sunglasses, at one point all of it will be dark.
9.1 Light Waves
Interference
• Some color-blind animals such as squid can sense
the polarization of light.
•
•
This helps squid see plankton, which are
transparent.
Foraging honey bees use their ability to detect
polarized light to help orient their waggle dances,
which are used to communicate the locations of
pollen sources to other bees.
• Even the human eye is weakly sensitive to
polarized light, although to detect polarization
without the use of intervening filters takes practice.