Download PHYSICS 6 - The Nature of Light

PHYSICS 6 - The Nature of Light
Gary R. Goldstein (© 2005)
The perception of light is the principal means by which we know the world. From the single
celled creatures we see under a microscope, to the most distant stars seen in a telescope, it is light
that informs us. The incredible variety of forms and the structure of our universe are revealed by light.
Yet the nature of light eluded scientists and natural philosophers through most of recorded history.
Only since the mid-nineteenth century have physicists begun to understand this most fundamental
natural phenomenon. The understanding physicists have today required the development of
electromagnetic theory, relativity, and quantum mechanics. Even with the full array of techniques of
modern physics there remain unsolved problems having to do with the interaction of light with matter.
An accurate explanation of this phenomenon requires a considerable background in physics
and mathematics. We assume most of you do not have that preparation. And even if you did, the
development necessary for a complete exposition would fill the semester. So a qualitative explanation
is what we will aim for in the following, hoping to provide a hint of the subtlety and beauty of this
illuminating phenomenon. The amount of very abstract thinking required to obtain a qualitative
understanding is formidable. You will have to do a lot of cogitating to follow this development, but if you
do make that effort you will be rewarded with a significantly deeper appreciation of the natural and
technological environment in which we live.
Electromagnetic Radiation
We’ve pointed out that light has wave-like properties. This was known by Huygens in the
seventeenth century. But if light is a wave, what is waving? You know that a water wave is the
propagation of a disturbance through the medium of water. A sound wave is the 'propagation of a
displacement through the medium of a gas (or a liquid or solid as well). What is the medium through
which light waves propagate even in outer space? What is the nature of the disturbance that is
propagated? What provides the restoring force that causes the propagation? These questions were
answered in 1864 by the most brilliant and profound thinker of nineteenth century physics, James Clerk
Maxwell, who, with Newton and Einstein, has had the greatest impact on our understanding of the
physical world and on the development of modern technology. (It is unfortunate that the magnitude of
Maxwell's achievements is not as widely-appreciated by the liberally educated as by the scientific
community.)
Maxwell arrived at his theory of light by his study of electricity and magnetism. Previously
physicists had unsuccessfully sought an explanation of light waves as some kind of mechanical
vibration of an ethereal medium, called ether, which was presumed to permeate the universe. That the
explanation was not mechanical but electromagnetic was probably as unexpected and astonishing as
Newton's realization that the solar system is held together by the same forces that cause objects to fall
to the ground. In both Newton’s and Maxwell’s work it was the attempt to unify seemingly unrelated
phenomena that led to their great achievements. Some background material is necessary in order to
see what Maxwell unified.
Electric and Magnetic Forces
Sometime in your life you learned something about electric and magnetic forces. Two
electrically charged objects repel or attract each other in proportion to the product of their charges. If
the objects considered are points or charged spheres, the force is inversely proportional to the square
of the separation. This force law – Coulomb’s Law - is responsible for the flow of current in a wire as
well as the structure of atoms and molecules. It is universal in the sense that any charged object will
have its motion determined by adding up the forces exerted on it by all other charged objects in space.
The force law for magnetism was more specific in its applicability - it applied to the forces exerted by
bar magnets upon one another when the magnets were separated by distances much larger than their
sizes. Because it is more specific, the force law for bar magnets suggests that a more fundamental
process is responsible for the force, which has wider validity.
Ampere in 1820 discovered that magnetic forces could be generated or induced by the motion
of electric charges. Essentially by taking a wire connected across a battery, so that electrical current
flows through the wire, and probing the vicinity of the wire with a magnetic compass, Ampere found
that the compass was deflected - as if by a magnetic force exerted on the compass needle by another
magnet. This effect is present only when charges are moving. The deflection of the compass needle
can be mapped out to indicate the direction of the induced magnetic force, as in figure 7-1. For the
straight segment illustrated, the direction of the induced magnetic force is always perpendicular to the
current and tangent to an imaginary circle containing the wire at its center and the compass at a point
on the circumference. If the wire is coiled into a loop (fig. 7-2) these imaginary circles are bent towards
each other so that the force is enhanced through the center. The directional pattern of the magnetic
force is similar to that of a bar magnet lined up along the axis of the loop. Finally, by taking many loops
of current carrying wire the magnetic force along the central axis will be very strongly enhanced (fig. 73) and the resulting directional pattern will be identical with a cylindrical bar magnet. This is the
simplest electromagnet.
resulting magnetic force is then constant in time - that is, static. If the current increases in time, the
magnetic force will also change. But the direction pattern of the force depends only on the configuration
of the wire. What changes is the strength of the magnetic force. The strength of the magnetic force at
any point in space is proportional to the current. Finally, if the current reverses direction of flow, the
magnetic force will reverse direction, also. This is the essence of Ampere’s discovery of the induction
of magnetic forces by electrical current. In summary, moving electric charge induces magnetic force.
To Ampere, then, we owe the electromagnet, which is used in an endless number of electronic
devices, from auto ignitions to house buzzers, telephone switches, stereo speakers, and computer
memory cores.
Example
Loud Speaker - In essence, the loud speaker consists of coils of wire, as in the electromagnet,
connected to a flexible speaker cone, with a permanent magnet fixed through the center (fig. 7-4).
When current is produced by the amplifier and flows through the coil, magnetic force is induced in the
coil as shown in figure 7-3. With current flowing in the direction indicated, the magnetic force will be
directed toward the north pole of the magnet. The speaker coil will thereby experience attractive force
toward the left in the diagram. This force pulls the speaker cone to the left. If the current is then
reversed the direction of the induced magnetic force will reverse, the speaker cone will be pulled
toward the right. Reversing the direction of the current anywhere from 30 to 30,000 times a second will
produce a displacement of the air molecules next to the speaker cone of frequency 15 to 15,000 Hz
and will thus radiate audible sound waves. The loudspeaker is a device that converts electrical
changes into magnetic force variations, then into mechanical motion, and then into sound.
Laws of Induction-Faraday's Law
Michael Faraday was one of the most ingenious experimenters of his time. His extensive study
of electricity and magnetism led him to the discovery, around 1830, that electric forces could be
induced by moving magnets. His discovery can be demonstrated with a permanent magnet, some wire
and a device that measures electric current (called an ammeter). The arrangement is shown in fig. 7-5.
With the magnet sitting still, either inside or outside of the loop, no current flows through the wire.
When the magnet is moved, however, current flows. For motion to the right, as illustrated, the current
flow is in the direction indicated. The fact that current is flowing indicates that an electrical force is
present-a force that causes the charge to move through the wire. The size of the current, and hence
the strength of the electrical force, is determined by the rate at which the magnet is pushed through the
loop. The direction of the current and electrical force will reverse if the magnet's motion is reversed.
Faraday's law, that a moving magnet induces electrical force, is complementary to Ampere's
law. The applications of this law are as extensive as those of Ampere's law. Examples are
microphones, phonograph cartridges, electric guitar pick-ups, and tape recorder playbacks.
Example
Microphone--The microphone is like a loudspeaker in reverse. In fact, small speakers can be
used as microphones. We'll illustrate this with the loudspeaker of fig. 7-4. Suppose sound impinges on
the speaker cone. Part of that sound is transformed into mechanical motion of the speaker cone (just
like the motion of the eardrum). This motion causes the permanent magnet to move as well. The
motion of the magnet induces an electrical force that, in turn, causes current to flow in the wire. That
current then will be the input to an amplifier that can be used to drive another speaker or to record the
signal on tape or a CD.
Maxwell's unification: fields
In trying to understand the nature of electricity and magnetism, Maxwell was struck by the
reciprocity of the laws of induction. When the source of electric force (namely charge) is in motion,
magnetic force is induced. When the source of magnetic force (a magnet) is in motion, electric force is
induced. The reciprocity applies to the forces themselves rather than the actual charged or magnetic
objects. When a charge moves the electrical force it would exert on another charge, fixed somewhere
in space, will change. Maxwell considered force to be the fundamental entity from which to formulate
the laws of electricity and magnetism. He used Faraday's concept of a force field in order to facilitate
his explication.
Suppose an electric charge Q is located at a fixed position in space. If a second charge, q,
placed at position a in fig. 7-6, it will experience a force, determined by Coulomb's law, which
represented by the arrow labeled Fa . The arrow points in the direction of the force and its length
proportional to the strength of the force. Such an arrow, whose direction gives the direction of
is
is
is
a
some standard charge, then knowing what the force on q would be at some point in space would tell
you what the force on any point charge would be at that same point. By mapping out the force vector
on q for all points in space, as indicated in fig. 7-7, the force on any arbitrary charge can be
determined. The collection of force vectors for all points in space is called the electric field (due to the
charge Q for this case). This can be done for any charge Q or any collection of charges. For any
collection of charges there is a corresponding electric field. Figure 7-8 illustrates the electric fields for
some more complicated examples.
The electric field is one example of an extremely useful concept used in all the physical
sciences, the field. Generally speaking, a field of some physical quantity is the collection of values for
that physical quantity throughout a region of space. A familiar example of a field is the wind velocity
field over the United States - namely the little flag indicators on a weather map. These indicators, on
the map in fig. 7-9, give the magnitude and direction of the wind at weather stations throughout the
U.S. at some particular time. On the same map the temperature field is also given, as indicated by bold
face numbers next to names of cities. Finally, the barometric pressure field is indicated by lines of
constant pressure, or isobars, that are labeled by the pressure in inches of mercury. That is, any
location on the isobar marked 29.88 (inches of mercury) has that barometric pressure. So you are
already familiar with three kinds of fields from meteorology. Note that the wind velocity field is
represented by vectors - the magnitude and direction are specified by the flag symbols - but the
temperature field and the barometric pressure field are represented just by numbers. There is no
direction associated with the physical quantities temperature and pressure.
Having defined an electric field, we next define a magnetic field, by analogy. Suppose we have
a bar magnet, as in fig. 7-10. We take a small magnet, like a compass needle, and measure the force
on it at many points in the region of the bar magnet. At each point the magnetic force is plotted as a
vector. The resulting magnetic field is the collection of all vectors.
It is no accident that the field in fig. 7-10 looks like the pattern you would obtain by laying the
magnet on a piece of cardboard and shaking iron filings over the cardboard. The iron filings line up in
the same pattern as the field. This happens because each little chunk of iron becomes magnetized in
the presence of the bar magnet, and so lines up in the direction of the force. The filings do not get
pulled onto the bar magnet because friction and the interposition of other filings balance the force on
each chunk.
It should be obvious now that the magnetic force lines drawn for the electric currents of figures
7-1,2,3 are part of the magnetic field induced by the moving charges, and that the current flow of figure
7-5 is in the direction of the electric field induced by the moving magnet.
Having defined the electric and magnetic fields, then Maxwell could state the laws of induction
be varying in time. But Ampere's law implies that a magnetic field will be induced. Maxwell's approach
was to associate the induced magnetic field with the changing electric field; in a region of space in
which the electric field is changing a magnetic field would be induced.
Example - Moving Charge
An example is shown in fig. 7-11. A charge q is moving with a velocity v as shown. An area of
space (which is a segment of the surface of a sphere whose center is the charge) is shown with the
electric field due to the charge. The electric field through the area is shown at the instant that the
charge is in the position indicated. The magnitude of the field will be increasing as the charge is in the
position indicated. The magnitude of the field will be increasing as the charge approaches the area.
This increasing electric field induces a magnetic field throughout the area. Notice that the induced
magnetic field is perpendicular to the increasing electric field, and "circulates" around the electric field
vectors. This is the same kind of result as obtained for the magnetic field induced in the region of the
wires in fig. 7-1,2,3. (Why?)
Example - Parallel Plate Capacitor.
A second example involves what is called a parallel plate capacitor. This is basically two parallel
metal plates connected to some source of charge, so that the plates can be charged to any desired
amount. In the region between the plates (not near the edges) there is a spatially uniform electric field.
That is, for a fixed charge + q and -q on the two plates, the electric field between the plates always
points from the positive to the negative plate and has the same strength throughout the region. Fig. 712 depicts this uniform electric field. If the charges on the plates are fixed - not increasing or
decreasing - there is no magnetic field. But if the charges are increasing, the strength of the electric
field increases (although it still remains spatially uniform). And for this circumstance a magnetic field is
induced, as shown in the figure. The magnetic field is always perpendicular to the electric field and
circulates around the electric field.
In both examples the magnetic fields have been drawn at an instant. What happens an instant
later? Maxwell's answer to this question is that if the electric field in a region of space is changing at a
uniform rate, the induced magnetic field will be constant in time. Alternatively, if the electric field is
changing at a non-uniform rate, the induced magnetic field will be varying in time. Hence, in fig.7-12, if
the rate of increase of the charge is constant, the magnetic field will always have the same strength as
indicated. If the rate of change of charge is not constant, the magnetic field strength will vary although
the directional pattern will remain the same for this example.
Faraday's law can be formulated in a completely analogous way. The roles of the electric and
magnetic fields are simply reversed. In a region of space in which the magnetic field is changing, an
electric field will be induced. If the magnetic field is changing at a uniform rate, the induced electric field
will be constant in time; otherwise the induced electric field will vary in time.
Example - moving bar magnet.
In fig. 7-13 a bar magnet is shown moving to the right at a velocity v. The magnetic field through an
area in space is shown. The strength of this magnetic field will be increasing as the magnet
approaches. Thus an electric field will be induced. The induced electric field will be perpendicular to
the magnetic field vectors and will circulate around those vectors. If you compare this example to the
moving charge in Fig. 7-11 you will see that the fields are simply interchanged, with one important
difference. The induced electric field vectors of fig.7-13 circulate counterclockwise. This distinction will
be of great significance.
Example - solenoid.
From a previous example (see fig. 7-3) you have seen how the magnetic field is induced by
current flow through the coil of wire - a solenoid. If the current is constant the magnetic field will be
constant as well. (Try to see how this constancy is a result of Maxwell's formulation of Ampere's law.)
However, suppose the current is increasing. Then the induced magnetic field will also be increasing.
This situation is depicted in fig. 7-14. Because the magnetic field is increasing, an electric field must be
induced, as shown for a region within the solenoid. The induced electric field circulates about the
increasing magnetic field in a clockwise direction (when. viewed by looking into the magnetic field).
Suppose, for simplicity, that the current is increasing at a constant, rate. Then the magnetic is field is
increasing at a constant rate. This implies that the induced electric field is constant in time.
Now you may have noticed that there is something peculiar here. The induced constant electric
field is directed oppositely to the increasing current. But the current itself is due to a "driving" electric
field which points in the direction of the current. The driving electric field circulates counterclockwise.
Thus the induced electric field opposes the increasing driving electric field, which results in a
decreased current. To produce a desired amount of current, then, it is necessary to take account of the
opposing induced electric field by making the driving field larger. This phenomenon is called the "back
EMF" (electromotive force) of an induction coil, and is well known to electrical engineers.
Maxwell's waves
The beautiful symmetry of the laws of induction, when stated in terms of fields, suggests what seems to
be a paradox. Consider a region of space in which there is an electric field that suddenly starts
increasing at a non-uniform rate. Then from all we have said, you would expect that a magnetic field
would be induced, which will vary in time. In general, this variation will be non-uniform as well. The
non-uniform variation of the magnetic field will, in turn, induce an electric field, which will also vary nonuniformly.
What about "feedback"? Does the sudden change in the electric field lead to an
induced electric field that enhances the initial changing electrical field which in turn produces a larger
induced electric field which in turn enhances the initial electric field, and so on? If this were the case,
the theory would be meaningless. It would mean that an unbounded electric field would be produced by
been discarded long ago). We will consider the question more carefully. In fig. 7-15 (a) a spatially
uniform electric field, which is increasing non-uniformly in time, is depicted. It induces the non-uniformly
increasing magnetic field. In fig.7 -15(b) the magnetic field is redrawn along with the resulting induced
electric field, which also increases non-uniformly. However, the induced electric field is in the direction
opposite to the initial electric field. This is a result similar to the solenoid example, except that here the
fields are varying non-uniformly. The induced electric field opposes variation of the initial electric field.
We could say that the "feedback" is "negative feedback". This resolves the paradox, and also has
profound implications, as Maxwell realized.
Suppose there is a region of space in which there is a spatially uniform static electric field, as in fig. 7l6(a). Next, suppose that for an instant the electric field is increased in a small region (fig.7-16(b). A
magnetic field will be induced in that region. That in turn induces an electric field, in fig. 7-16(c), which
opposes the initial change and tends to restore the electric field to its static value. The net electric field
will thus appear as in fig.7-16(d). The initial change will be reduced. But, the induced electric field will
have enhanced the electric field in the adjacent region. The disturbance will have propagated! The
same sequence of inductions will maintain that propagation to the right. An electromagnetic wave will
be propagating.
In what sense is this process a wave propagation? The medium here is the initially static
electric field. We might just as well have taken a static magnetic field. It would make no difference in
We have used the term "analog" purposely. The laws of induction imply that there is a physical
mechanism for restoring the disturbed field or medium to its previous value. This mechanism is not a
force, because the medium itself is not a mechanical system - but a field. Perhaps this point will be
made clearer by recalling the meaning of waves on a string, in water, and sound waves. These are
summarized in Table 7-1.
Having realized that waves could be propagated in electric and magnetic fields, Maxwell next
calculated the velocity of propagation of such waves through space. This calculation requires knowing
the electric and magnetic constants that enter the quantitative equations for the laws of induction - the
restoring mechanism. Maxwell, of course, knew these equations and the relevant numerical constants.
He did the necessary algebra and obtained the result that the speed of propagation should be 3 x 108
m/sec - the speed of light! We can only guess what went through his mind at that moment. He had
performed a calculation involving the numerical constants of the laws of electricity and magnetism and
arrived at the numerical value of the speed of light - a phenomenon previously believed to be totally
unrelated. By this Maxwell had finally answered the question --what is light? Light is electromagnetic
waves. Centuries of speculation were over. Maxwell's attempt to unify electricity and magnetism lead to
a complete theory of light.
Properties and Sources of Electromagnetic Waves
We will now consider some of the implications of Maxwell's theory. If the propagation of light is
the propagation of electromagnetic waves, then no material medium is necessary for this propagation.
This follows from the fact that the medium of the wave is the field itself, and the electromagnetic field
can exist in empty space. (Although this result is implicit in Maxwell's theory, it wasn't accepted until
early in this century when experimental searches for an "ether" failed conclusively, and Einstein
showed that Maxwell's theory was consistent with relativity - without an ether.)
Because light is electromagnetic, it can be produced only by non-uniform motion of charged or
magnetized objects. Non-uniformly moving charged or magnetized objects are sources for nonuniformly changing electric and magnetic fields and these fields produce wave propagation. Atoms are
composed of negatively charged electrons, positively charged protons and neutral neutrons. We will
What is the structure of a periodic electromagnetic wave? To begin with, the electric and
magnetic fields must be varying periodically in time and along the direction of propagation. Then, as a
consequence of the directionality of the induction laws, the electric field, at any moment, is
perpendicular to the magnetic field, and both are perpendicular to the direction of propagation. The
fields, at an instant, along a line of propagation, are illustrated in fig. 7-17 for a sinusoidal periodic
wave. Since the fields are always perpendicular to the direction of propagation, electromagnetic waves
are transverse waves. In this sense they are like waves on a string. The particular sine wave in fig. 717 will travel to the right - the whole pattern moves to the right.
In the example, the electric field always points either along the same direction, labeled the x
direction, or opposite to the x direction. This is a linearly polarized wave. It is the linear polarization we
discussed and experimented with for both springs and light. The wave may also be circularly polarized,
wherein the direction of the electric field will rotate about the direction of propagation as the wave
propagates along. This is illustrated in fig. 7-18. The magnetic field is not drawn for this figure, but will
be perpendicular to the electric field at each point along the direction of propagation. Note that the field
vector rotates 360° as it propagates along one wavelength. For the periodic sine wave form of figure 717 (or for a circularly polarized sine wave as well), the usual quantities can be defined. The amplitude
The wavelength of visible light ranges from 400mµ to 700mµ; the frequency from 4 x 1014 Hz to
7 x 10 Hz. But there is no reason why electromagnetic waves should be limited to these values.
Given a charge in oscillatory motion (which of course, is non-uniform motion) it will radiate
electromagnetic periodic waves of the same frequency as the oscillation. So any frequency wave can
be produced, providing there exists some natural or artificial means by which charged objects can be
set in oscillation.
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All of the observed regions of the spectrum of electromagnetic radiation are summarized in
Table 7.2. In the second column are some common names of the waves in these regions. These
names are merely associated with the varied sources and uses of the waves of these particular
regions. The only physical differences among these regions are their frequencies and wavelengths.
Source: climchange.cr.usgs.gov
Extended Electromagnetic Spectrum
Source: universe.nasa.gov/lifecycles/technology.html
You may wonder why our vision is limited to such a narrow band of frequencies. This is one of
those questions that involves physics, chemistry, and biology. In the natural environment most of the
electromagnetic radiation lies between the infrared and the ultraviolet. The light receptors in the eye
have their peak response determined by photochemical processes. Such processes are limited in
principle, to the near infrared through the near ultraviolet region. There are some snakes that have
responses to the near infrared, which allows them to track their prey in areas filled with vegetation. This
ability must not have had significant adaptive value for human hunters. Perhaps it is a principle of
economy that determined the least complicated visual system by which Homo sapiens could survive.
Aside from the biological argument, however, there are physical limitations. An apparatus for detecting
far ultraviolet would have to be based on some atomic system, the activation of which would have to be
converted into an electrical neural signal. The system would not be a simple modification of our existing
apparatus, but an entirely different kind of system. The same can be said for the far infrared.