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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 singlecelled creatures we see under a microscope, to the most distant stars seen in a telescope, it is lightthat 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 fundamentalnatural phenomenon. The understanding physicists have today required the development ofelectromagnetic theory, relativity, and quantum mechanics. Even with the full array of techniques ofmodern 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 physicsand mathematics. We assume most of you do not have that preparation. And even if you did, thedevelopment necessary for a complete exposition would fill the semester. So a qualitative explanationis what we will aim for in the following, hoping to provide a hint of the subtlety and beauty of thisilluminating phenomenon. The amount of very abstract thinking required to obtain a qualitativeunderstanding 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 andtechnological environment in which we live.

Electromagnetic Radiation

Weve pointed out that light has wave-like properties. This was known by Huygens in theseventeenth century. But if light is a wave, what is waving? You know that a water wave is thepropagation of a disturbance through the medium of water. A sound wave is the 'propagation of adisplacement through the medium of a gas (or a liquid or solid as well). What is the medium throughwhich light waves propagate even in outer space? What is the nature of the disturbance that ispropagated? What provides the restoring force that causes the propagation? These questions wereanswered in 1864 by the most brilliant and profound thinker of nineteenth century physics, J ames Clerk

Maxwell, who, with Newton and Einstein, has had the greatest impact on our understanding of thephysical world and on the development of modern technology. (It is unfortunate that the magnitude ofMaxwell's achievements is not as widely-appreciated by the liberally educated as by the scientificcommunity.)

Maxwell arrived at his theory of light by his study of electricity and magnetism. Previouslyphysicists had unsuccessfully sought an explanation of light waves as some kind of mechanicalvibration of an ethereal medium, called ether, which was presumed to permeate the universe. That theexplanation was not mechanical but electromagnetic was probably as unexpected and astonishing asNewton's realization that the solar system is held together by the same forces that cause objects to fallto the ground. In both Newtons and Maxwells work it was the attempt to unify seemingly unrelatedphenomena 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. Twoelectrically charged objects repel or attract each other in proportion to the product of their charges. Ifthe objects considered are points or charged spheres, the force is inversely proportional to the squareof the separation. This force law Coulombs Law - is responsible for the flow of current in a wire aswell as the structure of atoms and molecules. It is universal in the sense that any charged object willhave 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 bybar 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 fundamentalprocess is responsible for the force, which has wider validity.

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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 currentflows through the wire, and probing the vicinity of the wire with a magnetic compass, Ampere foundthat the compass was deflected - as if by a magnetic force exerted on the compass needle by anothermagnet. This effect is present only when charges are moving. The deflection of the compass needlecan be mapped out to indicate the direction of the induced magnetic force, as in figure 7-1. For thestraight segment illustrated, the direction of the induced magnetic force is always perpendicular to thecurrent and tangent to an imaginary circle containing the wire at its center and the compass at a pointon the circumference. If the wire is coiled into a loop (fig. 7-2) these imaginary circles are bent towardseach other so that the force is enhanced through the center. The directional pattern of the magneticforce is similar to that of a bar magnet lined up along the axis of the loop. Finally, by taking many loopsof current carrying wire the magnetic force along the central axis will be very strongly enhanced (fig. 7-3) and the resulting directional pattern will be identical with a cylindrical bar magnet. This is thesimplest electromagnet.

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resulting magnetic force is then constant in time - that is, static. If the current increases in time, themagnetic force will also change. But the direction pattern of the force depends only on the configurationof the wire. What changes is the strength of the magnetic force. The strength of the magnetic force atany point in space is proportional to the current. Finally, if the current reverses direction of flow, themagnetic force will reverse direction, also. This is the essence of Amperes discovery of the inductionof 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 electronicdevices, from auto ignitions to house buzzers, telephone switches, stereo speakers, and computermemory 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 thecoil as shown in figure 7-3. With current flowing in the direction indicated, the magnetic force will bedirected toward the north pole of the magnet. The speaker coil will thereby experience attractive forcetoward the left in the diagram. This force pulls the speaker cone to the left. If the current is thenreversed the direction of the induced magnetic force will reverse, the speaker cone will be pulledtoward the right. Reversing the direction of the current anywhere from 30 to 30,000 times a second willproduce a displacement of the air molecules next to the speaker cone of frequency 15 to 15,000 Hzand will thus radiate audible sound waves. The loudspeaker is a device that converts electricalchanges 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 studyof electricity and magnetism led him to the discovery, around 1830, that electric forces could beinduced by moving magnets. His discovery can be demonstrated with a permanent magnet, some wireand 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 currentflow is in the direction indicated. The fact that current is flowing indicates that an electrical force ispresent-a force that causes the charge to move through the wire. The size of the current, and hencethe strength of the electrical force, is determined by the rate at which the magnet is pushed through theloop. The direction of the current and electrical force will reverse if the magnet's motion is reversed.

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Faraday's law, that a moving magnet induces electrical force, is complementary to Ampere'slaw. The applications of this law are as extensive as those of Ampere's law. Examples aremicrophones, 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 beused as microphones. We'll illustrate this with the loudspeaker of fig. 7-4. Suppose sound impinges onthe speaker cone. Part of that sound is transformed into mechanical motion of the speaker cone (justlike the motion of the eardrum). This motion causes the permanent magnet to move as well. Themotion of the magnet induces an electrical force that, in turn, causes current to flow in the wire. Thatcurrent then will be the input to an amplifier that can be used to drive another speaker or to record thesignal on tape or a CD.

Maxwell's unification: fields

In trying to understand the nature of electricity and magnetism, Maxwell was struck by thereciprocity 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 isinduced. The reciprocity applies to the forces themselves rather than the actual charged or magneticobjects. When a charge moves the electrical force it would exert on another charge, fixed somewherein space, will change. Maxwell considered force to be the fundamental entity from which to formulatethe laws of electricity and magnetism. He used Faraday's concept of a force field in order to facilitatehis explication.

Suppose an electric charge Q is located at a fixed position in space. If a second charge, q, is

placed at position a in fig. 7-6, it will experience a force, determined by Coulomb's law, which isrepresented by the arrow labeled Fa . The arrow points in the direction of the force and its length isro ortional to the stren th of the force. Such an arrow whose direction ives the direction of a

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some standard charge, then knowing what the force on q would be at some point in space would tellyou what the force on any point charge would be at that same point. By mapping out the force vectoron q for all points in space, as indicated in fig. 7-7, the force on any arbitrary charge can bedetermined. The collection of force vectors for all points in space is called the electric field (due to thecharge Q for this case). This can be done for any charge Q or any collection of charges. For anycollection of charges there is a corresponding electric field. Figure 7-8 illustrates the electric fields forsome more complicated examples.

The electric field is one example of an extremely useful concept used in all the physicalsciences, 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 velocityfield over the United States - namely the little flag indicators on a weather map. These indicators, onthe map in fig. 7-9, give the magnitude and direction of the wind at weather stations throughout theU.S. at some particular time. On the same map the temperature field is also given, as indicated by boldface numbers next to names of cities. Finally, the barometric pressure field is indicated by lines ofconstant pressure, or isobars, that are labeled by the pressure in inches of mercury. That is, anylocation on the isobar marked 29.88 (inches of mercury) has that barometric pressure. So you arealready familiar with three kinds of fields from meteorology. Note that the wind velocity field isrepresented by vectors - the magnitude and direction are specified by the flag symbols - but thetemperature field and the barometric pressure field are represented just by numbers. There is nodirection associated with the physical quantities temperature and pressure.

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Having defined an electric field, we next define a magnetic field, by analogy. Suppose we havea bar magnet, as in fig. 7-10. We take a small magnet, like a compass needle, and measure the forceon it at many points in the region of the bar magnet. At each point the magnetic force is plotted as avector. 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 themagnet on a piece of cardboard and shaking iron filings over the cardboard. The iron filings line up inthe same pattern as the field. This happens because each little chunk of iron becomes magnetized inthe presence of the bar magnet, and so lines up in the direction of the force. The filings do not getpulled onto the bar magnet because friction and the interposition of other filings balance the force oneach chunk.

It should be obvious now that the magnetic force lines drawn for the electric currents of figures7-1,2,3 are part of the magnetic field induced by the moving charges, and that the current flow of figure7-5 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

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be varying in time. But Ampere's law implies that a magnetic field will be induced. Maxwell's approachwas to associate the induced magnetic field with the changing electric field; in a region of space inwhich 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 ofspace (which is a segment of the surface of a sphere whose center is the charge) is shown with theelectric field due to the charge. The electric field through the area is shown at the instant that thecharge is in the position indicated. The magnitude of the field will be increasing as the charge is in theposition 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 inducedmagnetic field is perpendicular to the increasing electric field, and "circulates" around the electric fieldvectors. This is the same kind of result as obtained for the magnetic field induced in the region of thewires 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 parallelmetal plates connected to some source of charge, so that the plates can be charged to any desiredamount. 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 alwayspoints from the positive to the negative plate and has the same strength throughout the region. Fig. 7-12 depicts this uniform electric field. If the charges on the plates are fixed - not increasing ordecreasing - there is no magnetic field. But if the charges are increasing, the strength of the electricfield increases (although it still remains spatially uniform). And for this circumstance a magnetic field isinduced, as shown in the figure. The magnetic field is always perpendicular to the electric field andcirculates around the electric field.

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In both examples the magnetic fields have been drawn at an instant. What happens an instantlater? Maxwell's answer to this question is that if the electric field in a region of space is changing at auniform rate, the induced magnetic field will be constant in time. Alternatively, if the electric field ischanging at a non-uniform rate, the induced magnetic field will be varying in time. Hence, in fig.7-12, ifthe rate of increase of the charge is constant, the magnetic field will always have the same strength asindicated. If the rate of change of charge is not constant, the magnetic field strength will vary althoughthe 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, anelectric field will be induced. If the magnetic field is changing at a uniform rate, the induced electric fieldwill be constant in time; otherwise the induced electric field will vary in time.

Example - moving bar magnet.

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In fig. 7-13 a bar magnet is shown moving to the right at a velocity v. The magnetic field through anarea in space is shown. The strength of this magnetic field will be increasing as the magnetapproaches. Thus an electric field will be induced. The induced electric field will be perpendicular tothe magnetic field vectors and will circulate around those vectors. If you compare this example to themoving charge in Fig. 7-11 you will see that the fields are simply interchanged, with one importantdifference. The induced electric field vectors of fig.7-13 circulate counterclockwise. This distinction willbe of great significance.

Example - solenoid.

From a previous example (see fig. 7-3) you have seen how the magnetic field is induced bycurrent 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 beinduced, as shown for a region within the solenoid. The induced electric field circulates about theincreasing 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 isincreasing 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 electricfield is directed oppositely to the increasing current. But the current itself is due to a "driving" electricfield 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 theopposing induced electric field by making the driving field larger. This phenomenon is called the "backEMF" (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 tobe a paradox. Consider a region of space in which there is an electric field that suddenly startsincreasing at a non-uniform rate. Then from all we have said, you would expect that a magnetic fieldwould be induced, which will vary in time. In general, this variation will be non-uniform as well. Thenon-uniform variation of the magnetic field will, in turn, induce an electric field, which will also vary non-uniformly. 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 largerinduced electric field which in turn enhances the initial electric field, and so on? If this were the case,the theor would be meanin less. It would mean that an unbounded electric field would be roduced b

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been discarded long ago). We will consider the question more carefully. In fig. 7-15 (a) a spatiallyuniform electric field, which is increasing non-uniformly in time, is depicted. It induces the non-uniformlyincreasing magnetic field. In fig.7 -15(b) the magnetic field is redrawn along with the resulting inducedelectric field, which also increases non-uniformly. However, the induced electric field is in the directionopposite to the initial electric field. This is a result similar to the solenoid example, except that here thefields 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 hasprofound implications, as Maxwell realized.

Suppose there is a region of space in which there is a spatially uniform static electric field, as in fig. 7-l6(a). Next, suppose that for an instant the electric field is increased in a small region (fig.7-16(b). Amagnetic field will be induced in that region. That in turn induces an electric field, in fig. 7-16(c), whichopposes the initial change and tends to restore the electric field to its static value. The net electric fieldwill thus appear as in fig.7-16(d). The initial change will be reduced. But, the induced electric field willhave enhanced the electric field in the adjacent region. The disturbance will have propagated! Thesame sequence of inductions will maintain that propagation to the right. An electromagnetic wave willbe propagating.

In what sense is this process a wave propagation? The medium here is the initially staticelectric field. We might just as well have taken a static magnetic field. It would make no difference in

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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 aforce, because the medium itself is not a mechanical system - but a field. Perhaps this point will bemade clearer by recalling the meaning of waves on a string, in water, and sound waves. These aresummarized in Table 7-1.

Having realized that waves could be propagated in electric and magnetic fields, Maxwell nextcalculated the velocity of propagation of such waves through space. This calculation requires knowingthe electric and magnetic constants that enter the quantitative equations for the laws of induction - therestoring 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 108m/sec - the speed of light! We can only guess what went through his mind at that moment. He hadperformed a calculation involving the numerical constants of the laws of electricity and magnetism andarrived at the numerical value of the speed of light - a phenomenon previously believed to be totallyunrelated. By this Maxwell had finally answered the question --what is light? Light is electromagneticwaves. Centuries of speculation were over. Maxwell's attempt to unify electricity and magnetism lead toa 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 isthe 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 fieldcan exist in empty space. (Although this result is implicit in Maxwell's theory, it wasn't accepted untilearly in this century when experimental searches for an "ether" failed conclusively, and Einsteinshowed 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 ormagnetized objects. Non-uniformly moving charged or magnetized objects are sources for non-

uniformly changing electric and magnetic fields and these fields produce wave propagation. Atoms arecomposed of negatively charged electrons, positively charged protons and neutral neutrons. We will

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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 aconsequence of the directionality of the induction laws, the electric field, at any moment, isperpendicular to the magnetic field, and both are perpendicular to the direction of propagation. Thefields, at an instant, along a line of propagation, are illustrated in fig. 7-17 for a sinusoidal periodicwave. Since the fields are always perpendicular to the direction of propagation, electromagnetic wavesare transverse waves. In this sense they are like waves on a string. The particular sine wave in fig. 7-17 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 xdirection, or opposite to the x direction. This is a linearly polarized wave. It is the linear polarization wediscussed 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 wavepropagates along. This is illustrated in fig. 7-18. The magnetic field is not drawn for this figure, but willbe 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 7-17 (or for a circularly polarized sine wave as well), the usual quantities can be defined. The amplitude

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The wavelength of visible light ranges from 400m to 700m; the frequency from 4 x 1014 Hz to7 x 1014 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 radiateelectromagnetic periodic waves of the same frequency as the oscillation. So any frequency wave canbe produced, providing there exists some natural or artificial means by which charged objects can beset in oscillation.

All of the observed regions of the spectrum of electromagnetic radiation are summarized inTable 7.2. In the second column are some common names of the waves in these regions. Thesenames are merely associated with the varied sources and uses of the waves of these particularregions. The only physical differences among these regions are their frequencies and wavelengths.

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Source: climchange.cr.usgs.gov

Extended Electromagnetic Spectrum

Source: universe.nasa.gov/lifecycles/technology.htmlYou 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 eyehave their peak response determined by photochemical processes. Such processes are limited inprinciple, to the near infrared through the near ultraviolet region. There are some snakes that haveresponses to the near infrared, which allows them to track their prey in areas filled with vegetation. Thisability must not have had significant adaptive value for human hunters. Perhaps it is a principle ofeconomy 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 detectingfar ultraviolet would have to be based on some atomic system, the activation of which would have to beconverted into an electrical neural signal. The system would not be a simple modification of our existingapparatus, but an entirely different kind of system. The same can be said for the far infrared.