CLASS 39. ARGUMENTS FOR THE WAVE NATURE
DIFFRACTION AND POLARIZATION
OF
LIGHT:
INTERFERENCE,
39.1. INTRODUCTION
As we begin our story in the mid 1600’s, Newton’s particle theory is the dominant theory of the
nature of light. This is due in part to his stature in the scientific community, but also to the lack of
experiments that could be explained by a wave theory but not a particle theory. The next two
chapters examine the experiments that support light as being a wave or a particle.
39.2. MAIN CONCEPTS
• Waves behave in characteristic ways that differ from the ways that particles behave.
• Waves can reflect from surfaces and interfere with each other. They can reinforce each other
(interfere constructively) or destroy each other (interfere destructively).
• Wavefronts are used to represent waves.
• Waves can bend around objects (diffraction)
• Young’s two-slit experiment showed that two beams of light could diffract through small slits
and then interfere with each other, causing alternating regions of dark and light spots.
• Materials can be used to shape waves so that the oscillations of the wave go in only one direction
(polarization)
• These three experiments (interference, diffraction and polarization) are experiments that can only
be explained if we assume that light is a wave.
39.3. REFLECTION AND INTERFERENCE OF
WAVES
If you are on campus on a football day, you might
notice that the sound appears to come from places
other than the stadium. Outside the physics
building, it sounds like the noise is coming from
the Lied Center. This is because waves can reflect
from surfaces. We can investigate reflection by
looking at a wave on a string and what happens to
the pulse when it hits a surface, like the wall. The
pulse reflects from the wall, as we might expect,
but it reflects upside down. When the pulse
reaches the end of the support, it is pushing
upward, just as it would if it were hitting another
part of the string and trying to cause that part of
the string to move up. Because the wall is fixed,
the support exerts an equal and opposite force
down, causing the reflection. Note that some of
the energy of the wave is absorbed by the wall or
transformed into thermal energy, which is why the
amplitude of the wave decreases after it hits the
wall.
Waves obey the principle of linear superposition.
That is, if two waves are in the same region of
space at the same time, they will interact with
each other. Linear superposition allows us to
y1
t
y2
t
y 1+2
t
Figure 39.1: Constructive interference.
y1
t
y2
t
y 1+ y 2
t
Figure 39.2: Destructive interference.
describe how they interact fairly easily. If we were to plot the two waves as a function of time, they
might look like the top two waves in Figure 39.1. Linear superposition means that we just add the
value of each wave and plot that as the sum. So the result of this combination of waves is another
wave that has the same frequency, but an amplitude that is the sum of the amplitudes of the two
starting waves. Figure 39.2 repeats this process, but before we add, one of the wave has been shifted
by 180°. This time, the maximum of the first wave is at the minimum of the second and vice-versa,
so when you add them up, you get zero.
Anytime two waves interact, we say that they undergo interference. When the waves interact so that
the sum is larger than the original waves, we call that constructive interference. When they interact
so that the sum is smaller, we call that destructive interference. You can have everything in between
– partially destructive and partially constructive interference.
One of the reasons we care about how the waves interact with each other is because there are a
number of places where waves travel into an object – like an organ pipe – and travel out again. Use
the rope as an example. If I shake the rope, a pulse traveling down the rope will reach the fixed end
and will reflect back inverted. If I keep shaking the rope, I set up a wave train such that, when one
pulse reaches the end of the line and turns around, it will interfere with one of the pulses still heading
toward the wall. There will be some points along the rope where the waves interact constructively
and some points where they interact destructively. The result is that there are some points on the
rope that are always standing still. We call these nodes. There are other points at which the wave
has maximum values, which we call anti-nodes. The waves that result from this are called standing
waves. Interference is unique to waves. Particles cannot interact with each other in this way.
Interference is the first argument for the wave nature of light.
39.4. REPRESENTING WAVES
39.4.1. Point Sources. If you drop a pebble in water, it will make
a series of ripples. The ripples are the nodes and antinodes of the
wave that is produced. Figure 39.3 shows a wave produced by
bobbing something up and down repeatedly in the water. The
dark areas represent crests and the light areas represent troughs.
We call the source of a wave like this a point source because the
waves emanate from a point. Each circle is called a wave front.
In three dimensions, the wave fronts would be spheres.
Figure 39.3: A circular wave
39.4.2. Wavefronts from Point Sources. An array of point produced by dropping
sources can be used to represent any type of wave. Huygens’ something in the water.2
principle is that every point on a wave front can be considered to
behave as a point source for waves generated in the direction of
the wave’s propagation. Figure 39.4 shows the case of a circular
wave front. Each small dot represents a point source along the
wave front. If you draw around the maxima of each source’s
wave fronts, you will see the circle that represents the next
wavefront (which is shown as a dashed line). We thus can
represent the behavior of waves by picturing them as wave fronts.
Figure 39.4: Wavefronts on a
circular wave
2
This
is
a
still
taken
from
http://www.slcc.edu/schools/hum_sci/physics/tutor/2220/interference/
the
movie
at
39.4.3. Plane Waves. If you stand far back from a point source, the
curvature of the wave front is so small that it can be neglected and
represented by a straight line instead. This is called a plane wave, and is
shown in Figure 39.5. We use plane waves because they are easier to think
about than other geometries. We may represent these waves by a straight
line or by the curved line just to the left of the straight line in Figure 39.5.
39.4.4. Interference of Circular Waves. If we take two sources of circular
waves, separate them by some distance and then start the sources bobbing
at the same rate and with the same frequency and amplitude, we will obtain
an interference pattern, as shown in Figure 39.6. The waves will interfere
with each other, as we saw in the one-dimensional case. Wherever two
maxima overlap, the resultant wave will be larger due to constructive
interference, and wherever a maximum and a minimum overlap, the wave
will be essentially zero due to destructive interference. This is no different
than the earlier explanation with one-dimensional waves: we have merely Figure 39.5: Plane
extended the description to two dimensions. This is important because waves
sound and light waves exist in three dimensions (two dimensions make it easier to visualize them).
Figure 39.6: Interference between two
circular waves.3
A
B
B
C
A
Figure 39.7: Interference between two
circular waves
3
From the text ‘Trefil and Hazen’.
An applet that lets you adjust the parameters for
interferences can be found at:
http://id.mind.net/~zona/mstm/physics/waves/interferen
ce/twoSource/TwoSourceInterference1.html
Figure 39.7 shows a schematic of what is happening.
The dark lines represent crests and the dotted lines
represent troughs. When the two waves interact, the
points at which the two crests touch will have
maximum interference and produce a much larger crest.
(points A). The points where a crest and a trough come
together will create a node because the two will cancel
each other ought (points B). Finally, when two troughs
come together, there will be a larger trough because
they will add constructively.
39.5. DIFFRACTION
Francesco Maria Grimaldi (1618-1663) was an
Italian physicist and Jesuit priest.4 In 1648, he
shone light through a very small pinhole (shown in
Figure 39.8a). Grimaldi expected that light would
behave like a stream of particles, so he expected to
see a shadow exactly the size as the pinhole with
sharp edges. Grimaldi’s experiment, however,
looked more like Figure 39.8b. The results of the
experiment are:
1. The light beam on the screen is larger than the
pinhole through which the light travels.
2. The edges of the light beam are fuzzy, not sharp
as expected.
3. There are one, two or sometimes three colored
bands that border the cone of light when it hits the
screen.
These results could not be explained by a particle
theory of light.
Grimaldi referred to this
phenomenon as diffraction, which is the
phenomenon in which light bends around objects
such as the edges of the pinhole. The first reference
to diffraction appears in the work of Leonardo da
Vinci, but Grimaldi was the first to do a more
thorough investigation. Unfortunately, Grimaldi
died of a sudden illness just after finishing his paper
on diffraction.
Although it was published
posthumously, it did not receive as much attention
as it would have if he had been alive to be a
proponent for it.
Christian Huygens (1629–1695) proposed a theory
around the same time as Grimaldi’s experiments.
Huygens suggested that light propagated as a
longitudinal wave that undulated in the direction of
its motion. Huygens’ theory suffered from being
much more complicated to understand than
Newton’s particle theory of light. Even though
Newton’s particle theory of light could not explain
diffraction, it remained the dominant theory.
4
shadow
light
shadow
Figure 39.8a: Grimaldi’s experiment. What
you would expect if light were particles. The
slit is larger than in the picture below to
show the sharp edges and straight path.
shadow
light
shadow
Figure 39.8b: Grimaldi’s experiment. The
straight lines show where the beam of light
would be expected to go.
Grimaldi was also an ardent astronomer. Francesco Grimaldi is responsible for the practice of naming lunar regions
after astronomers and physicists, rather than after ideas such as "tranquility"
39.6. YOUNG’S EXPERIMENTS: DIFFRACTION AND INTERFERENCE
39.6.1. The Single-Slit Experiment. The wave
theory of light was revived by Thomas Young
(1773–1829) in 1803.6 Young was trained as a
medical doctor and his interest in light was due to
his interest in vision. Young repeated Grimaldi’s
experiment, but used an even smaller pinhole
than Grimaldi had used. Young found that
distinct bands of light appeared, as in Figure 39.9.
A pattern of light and dark alternated across the
screen. This was an extension of what Grimaldi
had learned about diffraction and cast even more
doubt on the particle theory of light.
39.6.2. The Two-Slit Experiment. This result
was strange enough; however, when Young used
two holes instead of one, he found something
totally unexpected.
If light were made of
particles, when you shine light through two small Figure 539.9: Young’s diffraction experiment
holes, you expect to see two small spots of light, results.
as shown in the left side of Figure 39.10.
Grimaldi’s results might make you expect two slightly spread beams of light with fuzzy edges.
Young saw a much more complex pattern, as shown in the right side of Figure 39.10.
light
light
Figure 39.10: Young’s two-slit diffraction experiment. Left: what you expect to see if you
believe light is a particle and right, what he actually saw.7 The white areas indicate areas of
high intensity and the black areas indicate areas of low intensity
5
http://micro.magnet.fsu.edu/primer/java/diffraction/basicdiffraction/
In the latter part of Young’s career, he studied Egyptology. He was one of the first to interpret the writings on the
Rosetta stone, which was found near the Nile in 1799. He also provided the foundation for the theory of sight.
6
39.6.3. The Interpretation. In Figure 39.10, the
white areas indicate areas of high intensity light
and the black areas indicate areas of low intensity.
It is difficult to explain this pattern using particles;
however, waves can provide a satisfactory
experiment for both single-slit diffraction and
double-slit diffraction.
Recall the interference of water waves from the
earlier section. This also produced alternating
bands of light and dark. When wavelets come from
two slits, the waves from the first slit interfere with
the waves of the second slit. We know that waves
can constructively and destructively interfere. Figure 39.11: diffraction of a wave through a
Some places on the screen have complete single slit
destructive interference (the black areas), while
other have complete constructive interference (the
white areas).
Young interpreted this phenomenon as the effect of
light waves being diffracted around the corners
formed by the edges of the apertures. The image
on the screen was an interference pattern: The
bright bands were the result of the peaks of some
light waves coinciding; the dark bands were caused
by the trough of one wave canceling out the peak of
another wave.
Young was able to use his
diffraction experiments to calculate the wavelength
of light. Figure 39.11 shows how a wave might Figure 39.12: A wave explanation of the
diffract through a slit, changing the nature of the pattern from the two-slit experiment
wave from a plane wave to a circular wave.
Figure 39.12 shows how destructive and constructive interference can explain the observed patterns.
Figure 39.13 a) diffraction from a small slit and b) diffraction from a large slit
39.6.4. The Importance of the Slit Size. Diffraction only occurs through small apertures. This can
be understood by looking at the diffraction in two differently size slits, as shown in Figure 39.13.
The left diagram shows that the small slit produces more rounding of the wave front as it passes
through, whereas the wave fronts are less rounded when passing through the large slit, as shown in b.
7
http://www.anu.edu.au/physics/courses/Physics2000/applets/twoslitsa.html
Only if the slit size is comparable to the wavelength of light will diffraction occur. This is why the
phenomenon wasn’t noticed prior to Grimaldi’s experiments.
Young’s findings made the failure of the particle theory to explain diffraction that much more
troubling to scientists, as they was no way for the particle theory to explain the results of his two-slit
experiment either.
39.7. POLARIZATION
39.7.1. The Experiment. If light is passed through a piece of tourmaline, a greenish light passes
through. If you place a second piece of tourmaline after the first piece, the amount of light that gets
through depends on the relative orientations of the two pieces of mineral. When the two pieces are
approximately at 90° with respect to each other, no light passes. When the two pieces are in the
same orientation, the maximum amount of light passes through them. Newton suggested that this
behavior had something to do with ‘sides’ or ‘poles’ of the light and called the phenomenon
polarization. Although tourmaline was the first material found to have this effect on light, there are
many other materials that do the same thing.
y
x
Figure 39.14: a) Looking at a transverse wave coming out of the page. Since the direction of
oscillation is perpendicular to the direction of propagation, the oscillation can be in any direction
within the plane of the page. b) shows the wide sideways (it is propagating to the right.)
39.7.2. Transverse Waves in 3D. Although Huygens’ theory suggested that light was a longitudinal
wave, explaining polarization in terms of longitudinal waves is difficult. Young realized by 1817
that light waves propagated transversely instead of longitudinally. We’ve been looking at onedimensional waves, so now we need to consider a three-dimensional case. Figure 39.14a shows a
transverse wave in one dimension. Rotate the wave so that it is coming straight out of the page at
you. Now realize that the wave can oscillate in any direction and still be transverse to the direction
of the page. Figure 39.14b shows three different directions for the wave to oscillate.
Young communicated his idea that light was a transverse wave in letters that eventually made it to
Augustin Jean Fresnel (1788– 1827), who was able to refine and better develop the wave-based
theory of light. This was an important fundamental contribution to science, but also had practical
consequences, as Fresnel was able to apply his theory to the design of highly efficient lenses for
lighthouses. In 1821, Fresnel developed a mathematically rigorous theory to explain diffraction.
The realization that light was a transverse wave made explaining polarization easier. Think of the
tourmaline as a mask, or filter, that allows only one orientation of wave through can explain the
observed results. A wave that is simultaneously oscillating in all allowed directions is called
‘unpolarized’ and a wave oscillating in one particular direction is called ‘polarized’ or ‘planepolarized’.
A polarizing material (such as tourmaline) has a microscopic structure such that only one orientation
of wave is allowed to pass. If the direction of oscillation is along the preferred direction, the wave
gets through. If it is partially aligned, some of the light gets through and some doesn’t. Figure 39.15
explains the observations with tourmaline. When light passes through the first piece, only one
orientation of light is allowed through. If the second piece of tourmaline is 90° to the first, none of
the light that passed through the first tourmaline will pass through the second tourmaline.
Figure 39.15: Viewing tourmaline as a slit to explain how polarized light is blocked when the
second tourmaline is rotated by 90°.
Why would a tourmaline behave this way? The tourmaline selectively passes light that is polarized
(i.e. oscillates in the direction of) in a certain orientation. All other light is absorbed. If you put long
chains of polymers together so that they all point in the same direction, they absorb light waves that
are parallel to the long direction of the molecules. Light can also be polarized due to reflections
from some types of materials. Scattering can also select out particular orientations of polarization.
You
can
view
a
polarization
animation
at:
http://www.anu.edu.au/physics/courses/Physics2000/applets/lens.html. If you rotate a polarizer, you
see that the intensity of the light changes according to the relative angles between the two slits.
Polaroid film uses this concept to selectively develop some areas of film. Sunglasses use
polarization to block out the sun while still letting some light through.
39.8. CONCLUSION
Newton’s particle theory of light was not capable of explain diffraction, interference or polarization.
These three experiments proved to be strong evidence against the idea that light is a particle. The
next major advances were due to Faraday and Maxwell, who developed a complete wave theory of
light. In 1846 Faraday gave a lecture at the Royal Institution in which he put suggested that there is
a unity in the forces of nature. He proposed that the lines of electric and magnetic force associated
with atoms could provide the medium by which light waves were propagated. Maxwell followed
this with a mathematically rigorous theory of light as electromagnetic waves that addressed how
waves propagated. He developed four partial differential equations, now known as Maxwell's
equations, which completely describe classical electromagnetic theory; however, the idea of the
aether persisted. Michelson and Morely developed an experiment that was suggested by Maxwell to
measure the speed of the aether, but they found no evidence for aether. The idea of aether was
abandoned, but the idea of light as a wave persisted. By the early 1900’s the idea that light was a
wave was taken for granted.
39.9. SUMMARIZE
39.9.1. Definitions: Define the following in your own words. Write the symbol used to represent
the quantity where appropriate.
1. Nodes and anti-nodes
2.
Point source
3.
Huygens’ Principle
4.
Wave front
5.
Diffraction
6.
Polarization
7.
Interference
39.9.2. Equations: None.
39.9.3. Concepts: Answer the following briefly in your own words.
1. Light moving through a small pinhole does not make a shadow with a distinct, sharp edge
because of a) refraction; b) diffraction; c) polarization; d) interference.
2.
Explain the difference between constructive interference and destructive interference.
3.
Explain the principle of linear superposition in your own words.
4.
You are at the store and find a pair of sunglasses. How can you tell whether a pair of
sunglasses is polarizing or not? You may assume that the store has more than one pair.
5.
Explain, in your own words (and pictures if that helps) why diffraction occurs from small
apertures and not large ones.
6.
Explain polarization in your own words.
7.
Is it possible to explain reflection and refraction in terms of a particle model of light? Why or
why not? Why can’t you explain interference in terms of particles of light?
8.
Explain in your own words (and pictures) why diffraction occurs from small slits, but not from
large slits.
9.
Explain how Young’s experiments with diffraction through two slits provided strong evidence
in favor of the idea that light is a wave.
10. Explain Young’s two-slit experiment in your own words, and show how a wave theory could
explain the results. Was this experiment an example of diffraction, interference or something
else?
39.9.4. Your Understanding
1. What are the three most important points in this chapter?
2.
Write three questions you have about the material in this chapter.
39.9.5. Questions to Think About
1. Explain why the intensity of light changes if you tilt your head from side to side while wearing
polarized sunglasses.
PHYS 261 Spring 2007
HW 40
HW Covers Class 39 and is due April 20st, 2007
1.
2.
3.
You are at the store and find a pair of sunglasses. How can you tell whether a pair of
sunglasses is polarizing or not? You may assume that the store has more than one pair of that
that type of sunglasses.
Explain Young’s two-slit experiment in your own words, being careful to show how he was
able to use a wave theory to explain the results. Was this experiment an example of diffraction,
interference or …? Explain your answer.
Explain the difference between interference and diffraction in your own words (and pictures if
necessary).