Leica Polarization brochure

Leica Polarization brochure
Polarization
of Light
Leica Microsystems is a world leader of microscopes that
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Leica DM E
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Infinity-corrected optics provide superb, color accuracy and
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Leica BF200
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Polarization of Light
Contents
1.0 Introduction
2.0 Theories of Light
............................................................................................2
............................................................................................3
2.1 The Corpuscular Theory.........................................2
2.2 Huygens’ Wave Hypothesis...................................4
2.3 Transverse Wave Theory .......................................6
2.4 Summary ...................................................................9
3.0 Demonstration Methods.....................................................................................10
4.0 Natural Polarizers ..........................................................................................12
5.0 Synthetic Polarizers ..........................................................................................17
5.1 Demonstration III...................................................18
5.2 Demonstration IV...................................................19
5.3 Demonstration V ....................................................19
5.4 Polarization by Reflection ....................................21
5.5 Demonstration VI...................................................22
5.6 Polarization by Scattered ........................................
Reflection................................................................23
5.7 Demonstration VII .................................................24
5.8 Retardation Effects ...............................................26
5.9 Demonstration VIII ................................................26
5.10 Demonstration IX...................................................27
5.11 Demonstration X ....................................................28
5.12 Demonstration XI...................................................28
5.13 Demonstration XII .................................................29
5.14 Summary .................................................................30
6.0 Experiments
..........................................................................................31
6.1 Experiement I: Calcite...........................................32
6.2 Experiement II: Sheet Polarizers ........................32
6.3 Experiement III: Polarization by Reflection.......33
6.4 Experiement IV: Polarization by Scattering ......35
6.5 Experiement V: Reflection of Polarized Light ...35
6.6 Experiement VI: Crystals ......................................36
6.7 Experiement VII: Fibers ........................................38
6.8 Experiement VIII: Plastics....................................38
7.0 Appendix
..........................................................................................39
1
Polarization of Light
1.0 Introduction
Although most of man’s information about his environment
normally comes to him through his sense of vision, the study of
light is often neglected in basic science courses. This situation
is perhaps due to the lack of suitable equipment and text
material. The Leica Table Top Polarization Demonstrator and
this companion booklet are designed to introduce teachers
and students to a special, but extremely interesting, aspect of
light — that of polarization.
A knowledge of polarization contributes to a fuller
understanding of the theory of light in general. It helps to correct
overemphasis on the geometrical treatment of light and is thus
useful in educational science programs. The phenomena
associated with polarization are both easy to demonstrate and
beautiful to observe. In addition to its academic value, a study of
polarization explains many practical applications which are
being developed to use polarized light.
This booklet consists of three parts: 1) a brief review of the
major theories of light; 2) a discussion of the basic phenomena
of polarized light, with suggestions for class demonstrations; 3)
further experiments for individual pupil use. The demonstrations
and experiments are based on the equipment found in the
Polarization Demonstrator.
2
2.0 Theories of Light
One of the earliest attempts to account for the process of
vision involved the supposition that one’s eyes emit invisible
streamers. When these streamers reached an object, they
transmitted the sensation back to the viewer who then
“saw” the object. This naive explanation has been replaced
by several concepts which are still current.
2.1 The Corpuscular Theory
Whenever we conceive of light as traveling in a straightline motion, we are supposing that it behaves like a stream
of small particles moving in straight lines as do the balls on
a billiard table. The old name given to these supposed
particles was “corpuscles.” Now we speak of the assumed
light particles as “photons.”
This concept is useful describing many optical phenomena.
We use it in showing the reflection of light from a mirror
(figure 1), or in the focusing of light by lenses, for example.
The light is represented by rays, which are ideal straight
lines. It should be emphasized that this treatment is purely
descriptive, not explanatory. Geometrical constructions
show only what happens, not why the event occurs.
The corpuscular theory is inapplicable to the processes
involved in the polarization of light. In its modern or
3
a. Path of light reflected from
mirror.
b. Path of ball bouncing from rail of a
billiard table.
Figure 1. Corpuscular Theory. List may behave as if it consisted of particles.
“photon” form, it does, however, provide an explanation for
the events that occur when energy changes are produced
as the result of light absorption by some object. For
example, photoelectricity such as that in the exposure
meters used by photographers can be explained only by
assuming that a beam of light consists of indivisible
particles. These bombard the sensitive surface of the meter,
causing it to eject electrons which comprise a weak, but
measurable, electrical current. The changes which occur
when a photographic film is exposed in a camera are also
best explained by the corpuscular theory.
2.2 Huygens’ Wave Hypothesis
This concept, evolved by the 17th Century Dutch scientist
Christian Huygens, supposes that light behaves as sound
does — that it is a wave motion carried by some medium.
We think of a sounding object, a bell for example, as
producing spherical shells of disturbance in the
surrounding air. These shells rapidly expand and are
4
succeeded by further spheres of disturbance as the sound
continues. Using this analogy, we may think of a light source
as producing similar swelling spherical waves (figure 2).
Huygens’ theory is useful in explaining the refraction which
occurs whenever light passes from one medium to another.
The observed change in the direction of light beam, which
is associated with refraction in general, is best understood
by explaining it as a change in the speed of the wave. That
part of the front of the wave shell, which enters the new
medium, is the first to change in velocity. Hence, the whole
front takes up a new direction. In this situation, Huygens’
wave hypothesis is superior to the corpuscular theory.
The wave hypothesis is, however, inadequate as an
explanation for many of the facts of light behavior, including
a. Longitudinal waves
produced by a sounding
bell. Arrows indicate
motion of the medium
carrying the waves.
b. Assumed longitudinal
waves produced by an
operating lamp.
Figure 2. Huygens’ Wave Hypothesis. Light may behave as if it consisted of
spherical longitudinal waves.
5
those of polarization. This inadequacy is associated with
the behavior of the medium carrying the wave-like
disturbances. In sound waves, the air particles vibrate in a
direction parallel with the direction in which the wave is
moving. Such waves are called “longitudinal.” Polarization
of light, we shall see, can be explained only by supposing
that light waves behave differently from those of sound in
this respect.
2.3 Transverse Wave Theory
This theory likens light to water ripples. Seen from above,
they are spreading, circular disturbances of the water
surface, from the side, they are seen as waves in which the
water moves in a direction approximately at right angles to
the direction of the wave movement. The transverse wave
theory conceives of light was similar to such ripples, with
the added notion that for an ordinary horizontal light beam,
the motion of the (hypothetical) medium may be vertical,
horizontal or at any angle to these, as long as the motion
crosses the direction of the light path perpendicular to it
(figure 3).
A mechanical analogy to this theory may be found
(demonstration 1) in the waves produced when a 6-8 foot
length of laboratory rubber tubing is laid in approximately a
straight line on the floor. When one end of the tubing is
grasped and shaken in a random fashion — horizontally,
vertically, and at other angles in between, a complex wave
6
motion can be seen to travel from the hand along the tubing
until it disappears at the free end. If the far end of the tubing
is fastened, reflected waves occur at that point, and return
to the hand. This increases the complexity of the wave
pattern.
Such complex waves are not to be found in water ripples.
There the motion of the water is nearly always substantially
vertical. It is difficult to visualize the behavior of the
“medium” carrying the transverse waves of light. The
phenomena of polarization strongly indicate that light
waves must nevertheless have a transverse motion.
There was a period during which the nature of the medium
carrying light waves was seriously considered. The
a. Water ripples from above.
b. Water ripples from side. Arrows
show water motion.
c. Perspective view of light waves. Three of the infinitely
large number of transverse motions are shown.
Figure 3. Transverse Wave Theory. Light may behave as if it consisted of a
mixture of transverse waves similar to water ripples.
7
medium was first postulated and named the “aether.” More
recently, the conclusions of the famous Michelson-Morley
experiment were taken as evidence that the postulated
aether was non-existent. It was concluded that no medium
was necessary to carry light waves. For a time, this seemed
to contradict the wave theory of light. More recently still,
Einstein’s Theory of Relativity is held to indicate that there is
no method by which we can determine the absolute velocity
of the aether. Most physicists now believe that there is no
possible way to test experimentally the existence or the
non-existence of the aether. The questions has, in effect,
been set aside until more fruitful questions are answered.
Light is now considered to have aspects similar to the
electrical and magnetic “fields” in the space near a wire
carrying an alternating electrical current. Hence light is
grouped with other similar kinds of radiant energy in the
“electro-magnetic spectrum.” The reader is referred to any
reasonably advanced text book in physics for a discussion
of these matters.*
The transverse wave theory of light is particularly useful
whenever questions of color arise. One may associate
different hues with different lengths of the assumed waves.
The hue “red” is associated with the longest visible waves,
the hue “green” with the medium-sized waves, and the hue
“blue” with the shortest waves. Because of a quirk of color
vision, the hue “yellow” may be observed either for waves
8
just longer than those which elicit the perceived hue
“green,” or for a mixture of the waves associated
separately with the hues “green” and “red.” Reference will
be made to these relationships in the following discussion.
2.4 Summary
For purposes of “explaining” the behavior of light, several
different and, in a sense, contradictory concepts are useful.
For some purposes it is sufficient, and sometimes it is
necessary, to think of light as a stream of particles; for other
purposes, it is useful to liken light to the waves of sound.
Probably the most sophisticated and generally most
applicable theory requires that light be treated as if it were
a complex transverse wave motion. The polarization of light
can be understood only by the application of the last theory.
* Fundamentals of Optics by FRANCIS A. JENKINS and HARVEY E. WHITE.
McGraw-Hill.
Introduction to Modern Physics by F.K. RICHTMYER. McGraw-Hill.
Principals of Physics, Vol. III, Optics, by FRANCIS WESTON SEARS.
Addison-Wesley Press.
The Principals of Optics by ARTHUR C. HARDY and FRED H. PERRIN.
McGraw-Hill.
9
3.0 Demonstration Methods
Projection is the most convenient and effective way of
showing a group the demonstrations which follow. Here are
a few different techniques that may be used.
Many old style 3 1/4” x 4 1/4” slide projectors have easilyremovable bellows. Often the bellows may be slipped out if
the projection lens is racked outward from the lamphouse.
The resulting space between the light source and the
projection lens is large enough to insert the specimens to be
shown. The specimens should be supported by clamps held
by a ringstand or other similar device. The items could be
held manually, but the resulting image motion would be
distracting. The 2” specimens may be conveniently held in a
simple lens holder. The 4-cm size (manufactured by various
companies) works well if the prongs of the holder are
spread apart a little. The specimens should be placed as
close to the light source as possible. The illumination is
better here and it is easier to focus the images on the
screen. If the projector has no cooling fan, the specimens
may become quite warm. They are not likely to be damaged,
however. Warping does not destroy the effectiveness of the
sheet polarizers. The images of the specimens will be
inverted on the screen, but this is of little consequence,
since they are usually symmetrical.
10
Vertical projectors are equally useful. The specimens may
be placed on the stage, which should be masked down with
a piece of opaque card having a central aperture of
appropriate size.
The screen illumination level possible with these two
projection methods is usually great enough so that the
classroom need only partially be darkened. A reduction in
stray light, however, enhances the effects. The less
“uninvited” light, the clearer your image will be. Placing the
projector close to the screen is helpful in the presence of
high general illumination, but the images will then be small.
A third method involves the use of a lens bench and easily
obtainable optical devices, as shown in figure 4. If the lens
has a focal length of 6”, it will give a magnification of about
three times when placed 8” from the specimen. The image
quality and light level will be poor as compared with the
preceding suggested methods, but will be adequate for
small groups.
If equipment is available for none of the preceding methods,
many of the demonstrations can be performed merely by
holding the specimens in front of a suitable light source. A
student’s desk lamp, for instance, is satisfactory if it is
masked to avoid glare.
11
4.0 Natural Polarizers
The effects on light produced by certain crystals offer a
logical starting point for the study of polarization.
4.1 DEMONSTRATION II
Place on opaque card in the projector slide holder. This
card should have a small pin hole (approximately 1 mm in
diameter) near its center. Focus the image of the hole on the
screen, or hold a similar card over a light source.
a. Place a piece of glass over the hole. Observe that the
single image is slightly reduced in brightness because of
light lost by reflection from the glass surfaces. Notice
how the image is shifted slightly in position when the
glass is held so that the light falls on it at angles other
than the perpendicular.
Figure 4. Projection method using optical bench apparatus.
b. Place the calcite crystal over the hole. Calcite is a
naturally-occurring form of calcium carbonate, allied to
12
limestone. The flat surfaces are not artificial, but are
formed during the process of crystallization. Observe the
double image, each part of which is about half as bright
as the original spot. The images may be slightly fuzzy, due
to small defects in the crystal. This fuzziness is
inconsequential. Observe that the two spots appear with
any orientation of the crystal. Observe, when the crystal
is rotated about an axis parallel to the light beam, that
one of the spots remains relatively still, and that the
second spot rotates about the first.
These observations lead to the following conclusions:
1. When a beam of light is refracted by glass, only a single
path is followed by the light.
2. When a beam of light is refracted by a calcite crystal, the
light is somehow divided into two parts, each part
containing substantially half the energy of the original
beam. That part of the light forming the nearly stationary
spot is the “ordinary” ray; the rest is the “extra-ordinary”
ray.
Figure 5 shows by ray diagram what must be occurring in
these two different situations. We explain the refraction of
light on the basis of a change in velocity of the light on
entering a new medium. That there is only a single path for
the light in glass implies that the light, ignoring wavelength
considerations, has only a single velocity in the glass.
13
Glass, therefore has a single index of refraction. The fact
that there are two paths for the light in calcite implies that
calcite must have two different velocities for light, and,
therefore, two different indexes of refraction. We use the
term “double refraction” to describe this behavior of calcite
and similar crystals.
The difference between glass and calcite just demonstrated
is associated with the different arrangements of molecules
composing the substances. Glass is believed to consist of
molecules randomly positioned. Calcite, on the other hand,
has a precise molecular orientation in which the molecules
and atoms are arranged in a strict pattern. This is indicated
by the flat cleavage which bound the crystal and form
definite angles which are characteristic of this substance.
One may think of the crystal as having a “grain.” Just as
wood splits easily with the grain, but not against it, so light
a. Refraction of light by
glass at two different
angles of incidence. A
single path.
a. Refraction of light by calcite at two
different angles of incidence. Two
light paths. “a” represents the
ordinary ray; “b” represents the
extra-ordinary ray.
Figure 5. Single Refraction of Light by Glass; Double Refraction of Light by
Calcite.
14
travels more easily “with the grain” of the crystal, than
against it.
Although the two beams of light produced by double
refraction show no visible difference other than position, it
can be shown (Demonstration III below) that they are
fundamentally unlike in one significant respect. The beam
of light which enters the crystal contains traverse waves
whose vibrations lie in many different directions, as in
figure 3c. Each of the two emergent beams, however,
contains light vibrating only in a single direction. Those
waves of the original beam vibrating only vertically or
horizontally appear in the correct emergent beam. Waves
vibrating at other angles have both vertical and horizontal
components. The crystal separates each component into
its appropriate beam. Each of the waves is a part of the
initial beam containing random vibrations and will have a
vertical and a horizontal component. Each of these
components appears in the appropriate beam. Hence, there
is practically no loss of energy. Thus, we speak of both
beams as consisting of plane polarized light, with the two
vibration directions at right angles to each other. See
figure 6.
Plane polarized light may be imitated by the tubing used in
Demonstration I if the hand is moved only vertically, or only
horizontally, or in some other consistent direction. Water
waves are polarized: the vibration is always consistently
vertical or practically so.
15
Many crystals other than calcite are doubly refracting. The
difference between the two indices of refraction may be
small (in ice the indices are 1.309 and 1.313) or quite large (in
calcite they are 1.486 and 1.658).
Figure 6. Double Refraction (Schematic). Unpolarized light is converted into
two beams of polarized light, with mutually perpendicular vibration
directions.
For experiments with polarized light, it is necessary to
separate the two beams of polarized light. One difficult
technique, used in the Nicol prism, is to saw through a
calcite crystal at a precise angle, and then to reassemble
the two pieces with a special cement. When this is done
correctly, the ordinary ray is reflected to one side at the
cement layer, and only the extra-ordinary ray emerges from
the front of the crystal. Light which is totally polarized in one
plane is thus obtained. Nicol prisms are very expensive and
usually of comparatively small aperture, since it is difficult
to find large calcite crystals of sufficiently good quality.
Other naturally-occurring crystals, such as tourmaline,
16
have been discovered which are not only doubly refracting,
but also have the property (unlike calcite) of absorbing
strongly only one of the two rays. The light which emerges
from such a crystal is, therefore, plane polarized.
Tourmaline crystals sufficiently clear and free from color
are, however, difficult to obtain.
5.0 Synthetic Polarizers
Artificial crystals that would serve as polarizers have been
known for over a century. Only recently, however, has it
been possible to use such crystals, and other materials as
well, to make polarizers of high quality and very large
aperture.
The first polarizing sheet film was made of a multitude of
very small synthetic crystals, all lying in the same
orientation in a sheet of plastic. They were sub-microscopic
needles, about a micron (a millionth of a meter) long. There
were about 10” crystals in a square centimeter of film. Each
crystal acted as the tourmaline: it caused the incident light
to be doubly refracted, but permitted only one of the two
beams of light to emerge.
The sheet polarizers in your Leica Table Top Polarization
Demonstrator consist of a special plastic (polyvinyl alcohol)
chemically treated with iodine. The long molecules of the
plastic are aligned by stretching the material during
17
manufacture, and serve as the polarizing agents. Compared
with the previously available polarizers (Nicol prisms and
tourmaline crystals), sheet polarizers are less expensive
and obtainable in much larger sizes.
5.1 Demonstration III
Use the same arrangement as in Demonstration II. Slip the
5” diameter sheet polarizer into the slot which held the
forward edge of the bellows in the 3 1/4” x 4 1/4” slide
projector. It may be necessary to cut a narrow piece of stiff
cardboard to fit the bottom of the slot so that it holds the
polarizer high enough to cover the projection lens.
Hold the calcite crystal over the hole in the card and rotate
the polarizer. Observe the images of the spots of light on the
screen. As the polarizer is rotated, each spot appears and
disappears.
Explanation: The polarizer will transmit only light waves
vibrating in a single plane. Since the calcite causes the
initial beam of light to be divided into waves having two
mutually perpendicular vibration planes, the orientation of
the polarizer determines which will pass. At some positions
of the polarizer, two images of reduced intensity will appear.
In this case, the axis of the polarizer lies in a direction
between the vibration planes of the two beams. It permits
only a component of each of them to emerge.
18
Note: This demonstration is a crucial one. It confirms the
validity of the concept of light as a transverse wave motion.
It is impossible to conceive of a longitudinal wave motion,
like sound, behaving as in the demonstration. Though sound
waves may be refracted, they can never be double
refracted — they can never be divided into two waves
vibrating in different planes. Only under the assumption of
transverse vibrations in light waves can this demonstration
be explained.
5.2 Demonstration IV
Remove the card from the slide holder and remove the
calcite. Compare the appearance of the unobstructed light
on the screen with that which was transmitted by the single
polarizer. Observe that the light is about half as bright with
the polarizer, and that it is substantially uncolored. There
may be a very slight yellowish appearance, indicating that
the transmittance of the polarizer is slightly deficient for
blue light. The theoretical maximum transmittance of a
polarizer is 50%. Sheet polarizers approach 40% over most
of the wavelengths in the visible spectrum.
5.3 Demonstration V
Add a second sheet polarizer to the projection system. The
5” square sheet may be put in the rear bellows slot of the
projector. Rotate the 5” diam. polarizer through a complete
circle. Observe that there are two positions for which the
light on the screen is substantially as bright as with a single
19
polarizer, and that there are two other positions for which
almost no light reaches the screen.
Explanation: The first polarizer transmits only light vibrating
in a single direction. This light will pass through the second
polarizer almost undiminished if the second is properly
oriented with the first. That is, there is little loss of light if the
“axes” of the two polarizers are parallel. As the second
polarizer is rotated, the light diminishes since only a portion
of the polarized light can now pass. When the two polarizers
are “crossed,” that is, when their axes are perpendicular,
practically none of the light which emerges from the first
polarizer can pass through the second. Continued rotation
of the second polarizer will cause a bright light on the
screen when the relative angle of rotation is 180o, since the
axes will again be parallel. Rotating the second polarizer
through the remaining 180o will produce one more extinction
and reappearance of the light.
Applications: Two polarizers may be used to control the
intensity of the light in viewing apparatus, such as
telescopes and microscopes. Since there is a strict
mathematical relationship between the light intensity and
the angle between the axes of the polarizers (the intensity
varies directly as the square of the cosine of the angle), the
intensity of the light may be controlled accurately.
It has been proposed to equip automobiles with sheet
polarizers over headlights and windshield. The polarizers
20
would have their axes parallel, but at 45o to the vertical.
Since the axes are parallel, the driver would be able to see
by means of his own headlights. Oncoming cars, similarly
equipped, would have the axes of the polarizers over their
headlights crossed with respect to the driver of the other
car. In this way, the glare from oncoming headlights would
practically be eliminated. Such a system would necessitate
doubling the candlepower of the bulbs in the headlights.
Most automobiles would need to be fitted with polarizers
for the method to be generally effective.
Stereoscopic pictures, still or moving, may be seen
simultaneously by a large group of persons through the use
of polarized light. Two projectors are used, each fitted with
a polarizer. The viewers wear polarizing spectacles. The
axes of the projection and viewing polarizers are arranged
so that each eye of the observers receives only a single
image. These images are combined visually and seen as a
single relief image.
5.4 Polarization by Reflection.
Many kinds of reflecting surfaces partially polarize the light
they reflect.
Figure 7. Apparatus for Demonstrating Polarization by Reflection (top view).
21
5.5 Demonstration VI
Aim the projector (a flashlight, or other source producing a
fairly narrow beam of light) across the room. Support the
square of black plastic or a piece of plain glass in front of
the projector to reflect a path of light to the front wall of the
room. Make the angle between the light path and the plastic
surface about 40o, (See figure 7.) Rotate a sheet polarizer in
the reflected beam. Observe how the intensity of the path of
light changes. It becomes nearly zero with some
orientations of the polarizer. Change the angle between the
plastic surface and the light path from the projector.
Observe that the rotation of the polarizer now causes much
less change in the intensity of the patch of light on the wall.
Repeat the demonstration with a metallic reflecting surface,
such as a small metal mirror or a flat piece of aluminum foil.
Observe that there is no angle at which the metallic surface
can be held where the polarizer makes a significant change
in the intensity of the reflected spot.
Explanation: Non-metallic glossy surfaces polarize light by
reflection. The polarization is a maximum at some particular
angle. The best angle is that whose tangent is equal to the
index of refraction of the material. The angle is measured
between the incident light and a perpendicular to the
surface. Glossy metallic surfaces do not polarize reflected
light to the degree that glass does.
22
Applications: Polarizing filters used by photographers
effectively absorb about half of the light they receive. In
addition, polarizing filters suppress much of the glossy
reflection from water, store windows, painted or varnished
surfaces, or glossy plastics, when they lie at an angle of 30
to 40 degrees to the line of sight. Since this reflection often
occurs out of doors, the use of polarizing filters permits
seeing “through” the dazzling reflections.
5.6 Polarization by Scattered Reflection
Light which is reflected from very small particles is, in
general, partially polarized.
5.7 Demonstration VII
Add two or three drops of milk or a little soap or starch
solution to a battery jar of water. A square-sided quart
bottle is a good substitute for the battery jar (Figure 8a.) The
mixture should have a faint bluish appearance. Shine the
light from the projector, or equivalent illuminator,
horizontally through the mixture. Observe that the path of
the light is seen easily. This is because the small particles
Figure 8a. Polarization by Scattered Reflection.
Top view of apparatus. Polarized light is seen in direction “b.” Mostly
unpolarized light is seen in the directions “a” and “c.”
23
suspended in the water scatter the entering light. The light
is bluish because the particles scatter short wavelengths
more effectively than they do long waves. A corresponding
effect in the atmosphere makes the sky look blue. Place a
sheet polarizer between the jar of water and the observers
and rotate the polarizer. Observe a variation in the
brightness of the reflected light. The variation is most
noticeable when the observer looks in a direction
perpendicular to the light beam. Little variation is seen at
angles nearly parallel to the beam.
Explanation: A mixture of waves having various vibration
directions falls on the particles causing them to move, and
to cause secondary waves. Any of the original waves which
has a vibration direction parallel to the observer’s line of
sight would cause a motion of the particle to and fro with
reference to the observer. But light is a transverse wave
motion. This kind of particle movement would be ineffective
in producing secondary waves. Only a crosswise
movement of the particle could give rise to transverse
waves, and these would vibrate in a vertical direction.
Hence, the light which is polarized vertically, is that which
is observed. From a direction nearly parallel to the light
beam, almost any motion of the particle would be
approximately transverse to the line of sight. There is,
therefore, no effective polarization in this direction. (See
figure 8b.)
24
Application: Light reflected by scattering from the particles
in the atmosphere is partially polarized. The effect is most
noticeable when seen from a direction about perpendicular
to the direct rays of the sun.
mixture of
waves
Figure 8b. Polarization by Scattered Reflection
Polarized light reflected to observer “b”; a mixture of waves passes to
observer “c.” (The lines “m-n” and “o-p” represent two possible vibrations of
the particle. Only the “m-n” vibration can produce transverse waves in the
direction “b.”)
This phenomenon may be used in landscape photography to
produce a pictorial effect. A polarizing filter is placed over
the camera lens with the filter oriented to produce a subtle
variation in the tone of the sky from horizon to zenith. The
result is especially pleasing in color photography. Clouds
are not affected by a polarizing filter, since the water
droplets are too large.
Some scientists believe that birds may be able to find their
way on their migrations because they can detect
atmospheric polarization, and thus determine their direction
by a polarization “compass.”
25
5.8 Retardation Effects
The most beautiful and useful phenomena connected with
polarized light are based on the following principle: many
doubly refracting substances separate polarized light into
two components. The two components have different
velocities in the substance. When the two beams of light
emerge from the substance, they re-combine. Since,
however, one beam has traveled faster than the other, the
two are generally “out of step” or out of phase with each
other. The extent to which the two components are out of
phase depends upon the nature of the doubly refracting
substance, its thickness, and the wavelength of the light
involved. (See appendix.)
5.9 Demonstration VIII
Superimpose one 1/4 - wave plate on the other so that their
axes are parallel. Place them between crossed polarizers.
Observe that the screen becomes bright. Also observe that
as the pair of wave plates is rotated, the brightness of the
screen is modulated. Note that in a complete rotation of
360o, the screen becomes dark four times and that the
brightness is at a maximum four times — this is twice as
many cycles as one obtains by rotating one of the
polarizers through 360o.
Explanation: The two superimposed quarter-wave plates
constitute a half-wave plate as long as their axes are
parallel. The effect of the two quarter-wave plates is to
26
rotate the plane of polarization of the first polarizer thru an
angle which is twice the angle between the first polarizer
and the axis of the wave plate. You will note that the screen
brightness is at maximum when the angle between the
polarizer axis and the wave plate axis is 45o (also 135o, 225o,
315o); i.e., when this angle is 45o, the plane of polarization of
the first polarizer is rotated through 2 x 45o = 90o, and
consequently the light is transmitted by the second
polarizer.
5.10 Demonstration IX
Rotate the full wave retarder between crossed polarizers.
Observe that this retarder has little effect on the screen
brightness, but that distinct colors are seen.
Explanation: A full wave retarder produces a 360o out-ofphase relationship between the two retarded beams. A 360o
shift represents a full cycle and should bring the two beams
back together to their original relationship. There is,
however, a variation in wavelength for different hues of
light. Some wavelengths are shifted by a precise full wave,
and other wavelengths are shifted by more or less than a
full wave. Different wavelengths therefore have different
orientations with respect to the second polarizers and fall
on the screen with greater or lesser intensity. Thus we may
account for the colors which are seen.
27
5.11 Demonstration X
Place the sheet of mica in the projector. Focus the image of
the mica on the screen, and observe this image. First
observe with no polarizer, then with one, then with two.
Observe the effect of rotating one polarizer, and of rotating
the specimen. Repeat the demonstration with the Benzoic
Acid Crystal specimen. If a micro-projector is available,
crystals prepared as in Experiment VI may be projected.
Beautiful images are produced.
Explanation: Many natural crystals like mica and artificial
ones like benzoic acid are double refracting and retarding.
Since the crystals vary in thickness, they have different
effects on different wavelengths of light.
Application: In the visual examination and photography of
crystals, polarized light is frequently used to study their
form and structure. Small differences in pattern which are
almost impossible to detect with ordinary light are
discovered easily with polarized light.
In the microscopic examination of living things, polarized
light helps in studying crystalline structures since it is
unnecessary to use stains. Standard microscope stains
usually kill the specimens.
5.12 Demonstration XI
Form a pattern by sticking various numbers of layers of
pressure-sensitive transparent tape (such as “Scotch”
28
brand tape) on a glass plate. The simplest pattern is a
stepped wedge formed of one, two, three, etc., layers.
Project this as in Demonstration X. Observe the intense
colors. Note that any thickness of tape exhibits two
complementary hues. Which hues are seen depends on the
setting of the polarizers. The colors seen between crossed
and parallel polarizers are complementary. When the
specimen is rotated between fixed polarizers, the intensity
changes but the hue is constant. For instance, one
thickness will show either blue or orange; two layers, either
magenta or green. The effective limit is about five layers.
5.13 Demonstration XII
Place the photoelastic specimen in the projector as in
Demonstration XI. Observe that the specimen has no effect
on the light under any circumstances. Cross the polarizers,
and apply pressure to the specimen. Observe the colored
patterns at certain spots within the specimen.
Explanation: The material used in making this specimen is
not normally doubly refracting. When stress is applied to the
specimen, however, its molecular conformation is changed.
This specimen, as a result of the applied stress, now
exhibits artificial double refraction as do the specimens
used in Demonstrations XI and XII.
Application: The patterns seen in the image of the specimen
are, in effect, a map of the strains produced. A study of
these patterns is exceptionally useful in analyzing expected
29
performance of machine parts, bridges, and other
structures which must resist breaking under stresses. The
design of these structures may be improved by examining
with polarized light models made of plastic and altering
their designs to cause the least strain.
Many manufactured items, particularly those of optical
glass, must be strain-free in order to work properly. This is
especially true, for instance, of glass lenses. They are
inspected with polarized light which clearly shows the
strains.
In the photography of rapidly occurring events, like
explosions, a very fast shutter is required for the camera. A
cylinder of glass or quartz or a selected liquid in a glass
cylinder is placed between crossed polarizers. Almost no
light passes the system. The glass or liquid is then
subjected to a sudden, very intense, electrical or magnetic
field. The glass or liquid becomes doubly-refracting almost
instantaneously, and thereby permits light to pass to the
film. Since the field immediately collapses, the light passes
for only a very short time. Pictures may thus be made with
exposure times as short as a hundredth of a millionth of a
second.
5.14 Summary
The fundamentals of polarized light, which have been
discussed and demonstrated, offer confirmation of one of
30
the theories of light: it must be considered as having the
characteristics of a transverse wave motion. Only this
theory can explain the phenomena which have been shown.
Polarized light is an effective tool for: (1) the scientist in the
fields of light measurement and the study of the structures
of crystals; (2) the engineer in the study of mechanical
structures and in specialized types of photography; (3) the
amateur and professional photographer in the control of
reflected
light;
(4)
the
theatre-goer
or
amateur
photographer who enjoys viewing 3-Dimensional pictures.
6.0 Experiments
The following experiments are intended for individual work by
students who would like to study polarized light more
intensively than in the preceding demonstrations. The
experiments are especially suitable for the members of a
science club. With some modifications, they would serve as
interesting exhibits for a science fair.
In addition to the equipment included in the Demonstrators,
only materials commonly found in school laboratories (or
easily available elsewhere) are required. It is assumed that
the students are familiar with the theory and demonstrations
in the preceding portions of this booklet. Since the results of
these experiments are not given here, students are urged to
make a notebook record of their observations.
31
6.1 Experiment I: Calcite
1. Lay the calcite crystal over a small dot on a piece of white
paper. Observe the two images of the dot. Particularly
note that one image seems closer to you than the other.
Sketch the two light paths from the dot. Observe that one
light path is necessarily longer than the other. Relate this
fact to the apparent distances of the images from you.
2. Place the crystal so that different faces lie over the dot.
Look through the crystal at the dot at angles other than
perpendicular. Describe any differences in the images.
3. Use a sheet polarizer having the polarization axis marked
on it to determine the plane of vibration of the light
forming the two dot images. Place the polarizer over the
crystal, and rotate the polarizer. When the image
disappears, the axis of the polarizer is at right angles to
the direction of the vibration of the light forming the
image.
6.2 Experiment II: Sheet Polarizers
1. Look at a bright source of light through two superimposed
sheet polarizers. Describe the changes in the transmitted
light as one polarizer is rotated through successive small
angles.
2. Note the hue seen when the two polarizers are crossed.
Determine from this observation for which wavelengths
of light the polarizers are most effective. Any light seen
32
when the polarizers are crossed must be only partially
polarized. Recall that short wavelengths of light are blue
in hue, middle wavelengths are green, and long
wavelengths are red.
3. Obtain a photoelectric “exposure” meter with a linear
scale. If the scale is logarithmic, simply paste on a piece
of paper with linear markings. Place two sheet polarizers
with parallel axes over the sensitive cell. Illuminate the
polarizers with the light from a tungsten lamp. Place the
lamp so that the meter gives the largest reading possible.
Record this reading. Rotate the first polarizer 5o as
measured by a protractor. Record the new meter reading.
Repeat the rotation of the polarizer and the light
measurement, and thus obtain information. Look up in a
table the cosines of the angles of rotation. Square these
numbers, and plot a new graph showing the relationship
between the squares of the cosines of the angles of
rotation and the original light measurements.
6.3 Experiment III: Polarization by Reflection
1. Draw a straight line on a sheet of plain white paper.
Support the black plastic so that its front surface is
vertical, and rests on the line you have drawn. Place a
vertical pin 1/2” from the plastic. Examine the reflected
image of the pin at various angles through a rotating
polarizer. Observe the change in the brightness of the
reflected image as you change the angle of view.
33
2. Find the angle from which the image of the pin appears to
dim most as the polarizer is rotated. Place a second pin so
that its image lines up with the first (See figure 9.) Remove
the plastic, and draw a straight line through the pinholes
in the paper to the line marking the position of the
reflecting surface. Construct a perpendicular to the
reflecting surface at the intersection of the two lines.
Measure the angle between the perpendicular and the
line through the pinholes. This is the polarizing angle for
this material.
3. Repeat the experiment for a piece of glass (backed by
black paper) and for a shiny metallic surface.
Figure 9. Method of Determining Polarizing Angle for a Reflecting Surface.
34
6.4 Experiment IV: Polarization by Scattering
1. Look through a polarizer at the blue of the sky and rotate
the polarizer. Any change in the brightness of the sky
indicates that the light is partially polarized. Try different
positions of the sky from the horizon upward and
different directions of the compass.
2. Determine by the same method whether light reflected
from clouds is polarized.
3. Determine by the same method whether light reflected
from a hazy sky is more or less polarized as compared
with that from a clear blue sky.
4. Add a very dense photographic negative to protect your
eyes. Determine by the same method whether direct light
from the sun is polarized.
5. Carefully record your observations.
6.5 Experiment V: Reflection of Polarized Light
1. Provide a narrow beam of light. You may use a card with
a small hole in it placed in the slide carrier of a projector
or a similar card taped over a flashlight. Shine a light
beam through a second polarizer onto the black plastic.
2. Determine whether the light reflected from the plastic is
polarized by examining the direct reflected beam through
a second polarizer which you rotate.
35
3. Determine whether a difference in the polarization of the
reflected light is caused by a change in the angle which
the light makes falling on the plastic.
4. Repeat the experiment with other materials such as glass
and metal. Repeat the experiment also with non-glossy
reflections like dull white paper, flat painted surfaces,
brick, or concrete.
6.6 Experiment VI: Crystals
Note: For the following experiment you will need a
microscope fitted with two polarizers, one under the stage
(below the slide) and one in or over the eyepiece. Sets are
available especially for this purpose. Polarizing sheets may
be fastened temporarily in place with tape. If you have no
microscope, a magnifier may be improvised. A 10x
magnifier will be reasonably satisfactory, though somewhat
higher power is better.
1. On glass plates (microscope slides or other small, thin
pieces of glass), prepare crystals in the following manner:
dissolve as much of the substance as possible in one or
two milliters (a half-teaspoonful) of warm water. Place a
drop of the clear solution on the glass plate. Do not use a
cover glass. Observe the growth of the crystals through
crossed polarizers, using the low power of the
microscope. (Note: since you have no cover glass, be
especially careful in the operation of the microscope. The
36
bottom lens of the microscope must never touch the liquid
on the slide). Look especially for crystals growing free
from interference with other crystals. Suitable
substances to use for this experiment are: epsom salts
(magnesium sulfate); cream of tartar (sodium potassium
tartrate); washing soda (sodium carbonate); baking soda
(sodium bicarbonate); aspirin (sodium acetyl salicylate).
Some crystals grow rapidly — some slowly. Be patient.
2. Sketch some of the crystal forms, labeling them with the
name of the substance.
3. Observe the color changes that occur with some of the
crystals. Such changes accompany an increase in the
thickness of the crystal. If the color remains constant, you
can conclude that the crystal is growing only laterally.
4. Try dissolving mixtures of substances. Observe whether
you can distinguish the different substances by their
crystal forms.
5. Similarly, grow crystals of common salt (sodium chloride)
and table sugar (sucrose). Observe their appearance with
polarized light. State the relationship between the shape
of the crystal and its effect on polarized light.
6. Examine a few grains of very fine sand in the same
manner. No water need be used.
37
6.7 Experiment VII: Fibers
1. Secure samples of white cotton, wool, rayon, nylon, and
other fibers. Fray the end of a thread so that the fibers are
separated.
2. Examine the fibers microscopically with crossed
polarizers. Make sketches of the appearance of the
fibers.
3. From your observations make a key for the identification
of fibers by this method. Test your key on an unidentified
sample supplied to you by your teacher or a fellow
student.
6.8 Experiment VIII: Plastics
1. Use clear plastic tape to make designs by using different
numbers of layers of tape pressed to a glass plate.
Examine the results with two polarizers, one on each side
of the specimen. The tape may be cut with a sharp knife
or razor blade to make letters or other simple designs. Try
to approximate your school colors. (Hint; changing the
direction in which the tape lies produces more colors
with a single orientation of the polarizers.)
2. Examine single and double layers of transparent
wrapping materials between two polarizers. Observe the
effects when the material are crumpled. Similarly,
observe the results when the materials are stretched.
38
3. Secure 1/8” thick Lucite plastic sheets. Cut (preferably
with a fine-toothed saw) the plastic into simple shapes:
bars, U-shapes, hooks, hollow triangles. Examine the
pieces between two polarizers. Bend, twist, and
otherwise apply pressure to the samples. Sketch the
patterns that appear.
Appendix
The retardation effects discussed on page 26 can be
explained when light is described as “circularly” or
“elliptically” polarized. A mechanical analogy may be found
in the behavior of the length of rubber tubing used in
Demonstration I. The end of the tube is moved rapidly in a
circle instead of laterally. The tube forms a wave which
moves as a spiral or helix resembling the thread of a screw.
Such a wave may be mathematically described as a rotating
vector. A vertical polarized transverse wave may be
represented by a double-headed vertical arrow — a line
vector. In the same terms, circularly polarized light would be
represented by such an arrow which changes direction
from vertical to horizontal, then moves back to vertical in the
opposite direction. The direction of rotation may be
clockwise or counterclockwise. Thus, there are two
different kinds of circularly polarized light. Elliptically
39
polarized light would be represented by a similar vector
which not only rotates but changes in length.
Linearly polarized light may be converted to circularly
polarized light by passing it through a 1/4-wave retarder.
The retarder has two axes along which the light has two
different velocities. The light is therefore divided into two
parts traveling in the retarder at different speeds. If the two
axes are perpendicular to each other, and if the retarder is
oriented so that these axes are at 45o to the original plane of
vibration, the light is split into two equal vibrations at right
angles to each other. Since there is a speed difference,
there will be a phase difference. In this case, there will be a
1/4-wave difference, which is equivalent to 90o.
The vector sum of the two beams will no longer be a line,
but a rotating line, which produces a helical pattern. Since
the two beams are equal, the vector sum will always have
the same magnitude. Hence, circularly polarized light is
formed. By using different materials, or different
thicknesses of the same material, any desired phase
difference may be produced. Thus, we have 1/2-wave and
full-wave retarders, as well as other out-of-phase
relationships. The effect of a 1/2-wave retarder is merely to
change the direction of the plane of polarization. Color
effects are usually observed because the extent of
retardation varies with the wavelength of the light involved.
40
Bibliography
FUNDAMENTALS OF POLARIZED LIGHT
DITCHBURN, R.W.
“Light”, Interscience Publ., Inc., New York, 1953, 680pp.
JENKINS, F.A. and WHITE, H.E.
“Fundamentals of Optics,” McGraw-Hill Book Co., New York,
1957, 3rd Ed., 637pp.
PARTINGTON, J.R.
“An Advanced Treatise on Physical Chemistry: Vol.IV: PhysicoChemical Optics,” Longmans, Green & Co., 1953, 688pp.
LAND, E.H.
“Some Aspects of the Development of Sheet Polarizers,” J.
Optical Soc. Am. 41, 1951, P.957.
WEST, C.D. and JONES, R.C.
“On the Properties of Polarization Elements as Used in Optical
Instruments I. Fundamental considerations,” J. Optical Soc. Am
41, 1951, P. 976.
SURCLIFF, W.A.
“Polarized Light,” a section of Encyclopedia Americana, 1957
ed.
41
GRAY, D.E.
“American Institute of Physics Handbook,” McGraw-Hill
Book Co., New York, 1957, of Section 6 on the numerical
constants of commercial polarizers.
APPLICATIONS
GRABAU, M.
“Polarized Light Enters the Work of Everyday Life,” J. Appl.
Phys. 2, P.215.
WATERMAN, T.H.
“Polarized Light and Animal Navigation,” Scientific
American, July, 1955, P. 88.
LAND, E.H. and CHUBB, L.W., JR.
“Polarized Light for Auto Headlights,” Traffic Eng’g.
Magazine, April and July, 1950, 8pp.
BILLINGS, B.H. and LAND, E.H.
“A comparative Survey of Some Possible Systems of
Polarized Headlights,” J. Optical Soc. Am. 38, 1948, P. 819.
COKER, E.G. and FILON, L.N.G. and JESSOP, H.T.
“A Treatise on Photo-Elasticity,” Cambridge, Univ. Press,
New York, 1957, 2nd rev. Ed. 720pp.
MARTHSHORNE, N.H. and STUART, A.
“Crystals and the Polarizing Microscope,” Arnold Press,
London, 1950, 2nd ed.
42
JOHANNSEN, A.
“A Manual of Petrographic Methods,” McGraw-Hill Book
Co., New York, 1918.
HILTNER, W.A.
“Polarization of Stellar Radiation. III. The Polarization of
841 Stars,” Astrophysical J. 114, 1951, P. 241.
JAFFS, L.
“Effect of Polarized Light on Polarity of Focus,” Science,
123, 1956, P. 1081.
43
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