Brain waves

1.4 ELECTROMAGNETIC RADIATION

17

Table 1.1 shows the various kinds cies of the receptors of your eyes. In of electomagnetic radiation that this region. each frequency (or have proved useful so far. Note the wavelength) corresponds to a differ­very small region of the spectrum ent color in the spectrum of colors around v = 1014 to 1015 cycles/sec· from red to violet. This tiny region or A = 10- 7 to 10-6 m that is visi ­ is. or course. incredibly important ble light-the frequencies are com­ to human life. The study of electro­parable to the resonance frequen- magnetic waves in this region is

called optics.· Much of what we will learn about

'cycles/sec = cycles per second (cps) = optics will be applicable to other hertz. When talking of radio parts of the spectrum. although the frequencies. one usually uses Mc technology is quite different-for(megacycle) = 106 cycles/sec = MHz = 106 bertz. as well as kc (kilocycle) = 103 cycles/sec = kHz = 103 hertz. Unfortunately. all these forms are used. ·Greek ops. eye.

TABLE 1.1 Electromagnetic radiation

Frequency Detected by in hertz Wavelength in meters Name

p 10- 15 (Size of nucleus) h P 1023

0 h t 0

0 t n 0 Gamma rays

g 1020

0 a u P p n h h 10- 10 = 1 A(size of atom) X-rays t 0

e t C r 0

s c e UltraViolet (UV) e m 1 u

Human 1 eye s s 10 - 6 = 1 ....m (diameter of Visible

i bacteria) Thermal 0

detectors n Infrared (IR)

c r

10-2 = 1 cm (size of a Microwave mouse)

T u n 100 = 1 m (size of a man) e d

c i Radio frequency (RF) r 103 = 1 km (size of a Village) c u i t s

10" ~distance from W' -hington. D.C. AudiO frequencyto hicago)

10 108 (distance to moon)

instance. devices to generate and detect radio waves are rather differ­ent from those for visible light or for x-rays. Thus. for example. not only can you take pictures using visible light. but you can also use other forms of electromagnetic radia­tion-gamma rays. x-rays. infrared. etc. All you need is a source of the radiation. some method of localiZ­ing the rays. and a detector (Fig. 1.18). The picture is a record of how much radiation was received at each point. The main difference be­tween different radiations is that the smaller the wavelength. the

Examples of use

Cancer treatment

Materials testing Medical x-rays

Atomic structure Germicidal "Black light. .. sun tan OPTICS IR photos. heat lamps "Heat rays." forest fire detection

Molecular structure. human body radiation

AtomiC clocks. Space research

Radar. microwave ovens (3 x 109 hertz) Radio astronomy TV. UHF: 470-890 MHz. VHF: 54-216 MHz.

FM: 88-108 MHz International Shortwave CB:27 MHz AM radio broadcast: 550-1600 kHz

Longwave broadcast

Long-range naVigation

AC power.

CHAPTER I: FUNDAMENTAL PROPERTIES OF LIGHT

18

(a) (b)

(e)

(e)

FIGURE 1.18

Pictures taken with electromagnetic radiation of different wavelengths. (a) A radar view of a squall line, 230 km across. White corresponds to regions of heaviest rain. (b) Pattern of heat distribution seen in the far infrared showing the heat emission from a hand (right) and the heat image where the hand was previously held against the wall (left). (c) Heliotropium curassavicum flowers are light against dark leaves in the visible (left), but reversed in the ultraviolet (right). Insects with vision in the UV (see Sec. 1.4D) see them differently than we do. (d) Action view in x-ray "light." Exposure time was 1 J.l.sec, and the motor turned at 116 revolutions per second. (e) Gamma-ray picture of human hand. Source of gamma rays is

(d) radioactive tracer inside patient.

a cavity with a small en­ in foundries, and of ceramic kilns.

1.4 ELECTROMAGNETIC RADIATION

19

smaller the structures with which they interact. For example, the an­tennas for radio waves (meters to kilometers wavelength) are long wires or high towers, whereas the resonators in your eyes that select light waves (a few hundred nano­meters in wavelength) are tiny or­ganiC molecules. Therefore, one must be careful in taking pictures with different wavelengths that the wavelength is small enough to de­tect the objects of interest. If the wavelength is comparable in size to the object, the wave will bend around the object (Chapter 12); if it is much larger, the wave won't be affected by the object. (This is why gynecologists, bats, and whoever else takes pictures with sound use very short wavelengths-high fre­quencies.)

Radiation of too short a wave­length (Le., too high a frequency) is also less useful in taking pictures. If the radiation oscillates at too high a frequency compared to the resonance frequenCies of the system of interest, the system will not be able to keep up with the oscillations (recall Fig. 1.12). At these high fre­quencies, then, there is very little interaction between the radiation and the system-the radiation just passes through the system. This is why many objects, such as your skin, that are opaque to visible light, are transparent to the higher­frequency x-rays.

B. How to make electromagnetic radiation

Sources of radiation differ as much as do detectors, particularly be­cause their size usually is compa­rable to a wavelength. Basically they all are devices to wiggle charges. For very high frequencies we try to get nuclei and atoms to do the wiggling for us, as these very small systems have very high resonant frequen­Cies. At low frequenCies, we use electronic circuits instead. One standard way of getting radiation at intermediate frequencies is to make some material very hot. As we heat it, the charges in it oscillate more­heating something means to get the

atoms in it moving more rapidly and randomly. These wiggling charges then radiate-the hotter the material, the faster they wiggle, and the higher the frequency they radiate. The radiation from a heated frying pan usually is not vis­ible, but you can feel it with your hand, which responds to the in­frared radiation. If you heat the pan suffiCiently, it begins to glow, and becomes "red-hot," hot enough to radiate in the visible. Your eyes are sensitive to radiation of this higher frequency, and you see it as red light.

In fact, a glowing body can give you radiation of any wavelength you like, provided it has the proper tem­perature. For instance, your radiant face emits radiation primarily with wavelength near 10,000 nm. (Al­though we cannot see this radia­tion. the poisonous pit viper can. This snake has deep hollows­pits-on the sides of its head that are sensitive to this frequency range. allowing it to locate its warm-blooded victims.) Heating and cooking goes on at about 1000 nm. and the sun's temperature cor­responds. very conveniently. to the visible region at about 500 nm, However. at low temperatures the intenSity of the emitted radiation is very low. and at high temperatures there is plenty of intenSity but the emitting body tends to burn. The radiation from hot objects is not given off at a single frequency. but as a broad band of frequencies (Fig. 1.19). since the random heat mo­tion has no particular single fre­quency. We see from Figure 1.19 that the hotter the object. the more light it radiates. and the shorter the wavelength of the predominant ra­diated light. Thus. the very hot sun radiates primarily in the visible. whereas most of the radiation from a 100-watt bulb is in the infrared. with very little in the visible (mak­ing it a rather ineffiCient light source).

The curves of Figure 1.19 are ac­tually for an ideal object called a black bot!-y. a body that absorbs all radiation that falls on it (Fig. 1.20). A good approximation to a black body is

Wavelength in nm

FIGURE 1.19

The spectrum of a glowing black body at temperatures of a light bulb, of a photoflood bulb, and of the sun. The actual spectra of these radiators are only a little different from this idealized black body approximation. (Remember, shorter wavelength means higher frequency.)

trance hole. Light that enters the cavity through this hole bounces around inside but. like a lobster in a lobster trap. rarely finds the hole again. so it does not get out. Your eye is a reasonably good black body because it contains a small opening with a big empty space behind it (Sec. 5.IA),

When a black body is heated it starts to glow. and. therefore. no longer looks black, But it continues to be black in the sense that it still absorbs all radiation that falls on it. A small window in a furnace is a good example of a glowing black body. If you try to illuminate this "body" (which is really the Window hole) with a flashlight. it will look no different in color or brightness-­it absorbs all the light you shine on it. Because the radiation stays in­side the furnace for a relatively long time before it manages to escape, it comes to equilibrium with the fur­nace. and the color emitted de­pends only on the temperature. (Temperatures of the molten metal

G ­

CHAPTER 1: FUNDAMENTAL PROPERTIES OF LIGHT

20

FIGURE 1.20

A good approximation to a black body radiator: a heated cavity with a small exit hole (furnace in a steel mill).

are often measured by examining the glowing color.) Most glowing bodies are not truly black bodies. For example, a log glowing in a fire­place Is nearly, but not quite, black, as you can check after it has cooled. You can verify its near blackness by shining a light at the glowing coals in your fireplace. (If the coals were really black bodies at uniform tem­perature, they would all appear equally bright. Inside a well-stoked furnace you see a uniform bright glow and cannot distinguish the in­dividual coals.) Similarly, the sun and light bulbs are not truly black bodies, though the essential fea­tures of the light they radiate are not very different from the black­body case.

Finally, we must mention that we cannot fully explain the curves of Figure 1. 19 from our understand­ing of light as a wave. In fact, these curves led to our knowledge that the wave picture is not the entire story (Sec. 15.2A).

c. Light sources

The fact that hot bodies glow, or in­candesce,· has played a major role in the history of artificial light sources. From the time Prometheus brought fire down from Olympus untU this century, all man-made light sources have been incandes­cent (except for those created by collecting fireflies). Until the advent of adequate generators of electricity in the nineteenth century, these lights were very little more than the fire Prometheus gave us; the only innovations being improvements in fuel from the campfires and torches that formed the earliest light sources.

The next known light source was the oil lamp, used by PaleolithiC cavedwellers to allow them to make those magnificent cave paintings. The oil lamp was a dish of stone, shell, or, later, pottery that con­tained oil and a reed wick. (In the nineteenth century, when kerosene replaced the oil and an air draft was introduced through the wick, the oil lamp began to evolve into the

-Latin tn-candescere, to become white.

lantern we now take on camping trips.)

Several millennia after the first oil lamp, in Egypt or PhoeniCia, a can­dle was made by Impregnating fi­brous material with wax (from in­sects or certain trees). The use of tallow, and much later spermaceti (from sperm whales), and improve­ments of the wick, provided the ma­jor changes in this light source.

There were various civic lighting projects. Main streets in towns had previously been lit only by lamps in shops, house entrances, shrines, temples, and tombs. In the larger towns this may have been signifi­cant. It is estimated that there was a lamp every one to two meters along the main streets of Pompeii. Around 450 A.D. the first street­lights (in the form of tarred torches) were Introduced in Antioch. Light­houses, primarily to mark the en­trances to ports, were another big project. Originally simple hilltop fires, these evolved into towers with bonfires of resinous wood, later coal, and, in the late eighteenth century, candles and whale 011 lamps. The first known attempt to concentrate the light from these fires was probably the great pharos of Alexandria (one of the seven won­ders of the ancient world, designed by Sostratus of Cnidos in about 280 B.C.), which may have used large mirrors of polished metal and whose light was said to be visible for 35 miles.

Except for a few oddities (the most bizarre being the burning of fatty animals, such as the candle­fish or the stormy petrel), the torch, the oil lamp, and the candle gave the world the bulk of its nighttime light untU the nineteenth century. Thus, when the sun went down, it was very dark-". . . the night cometh, when no man can work" (John 9:4). Well Into the nineteenth century battles stopped at sun­down, which was all to the good. but hospital care ceased also. Witches had to wait for a full moon for a nighttime ramble; the poor went to bed at sunset; only the rich had a nightlife. About a century ago, this began to change with new lighting innovations (a mixed

1.4 ELECTROMAGNETIC RADIATION

21

blessing-they brought the 12-hour workday).

The nineteenth century intro­duced gas lighting. While the Chinese had burned natural gas (piping it from salt mines through bamboo tubes), and coal gas was distilled from coal in 1664, gas was not used very much until it became economically attractive. around 1800. Introducing air. or oxygen. with the gas was found to improve the light. An even brighter light was produced by heating a block of lime to incandescence in an oxy­hydrogen flame. producing the limelight. which was used for "magic lanterns." and soon after mid-century for the theatrical appli­cations that preserve its name to­day. (The explosive nature of the gas. combined with the flammable scenery. made theatergoing some­what more of an adventure then.) Introduction in 1885 of the gas mantle. a mesh of inorganic salts heated to incandescence. increased the light by a factor of six over that obtained by just burning the gas. and kept the gas light industry alive into this century. (The improve­ment is a result of the fact that these salts are not ideal black bod­ies. Rather they tend to emit some­what more in the visible. thus mak­ing them more effiCient in pro­dUCing useful light. The purpose of the gas. then. is just to heat the mantle. so the gas can be less lu­minous and less smoky.)

The earliest electric light was the arc lamp in which a spark jumped across two electrodes attached to a large battery. Arc lamps of any prac­tical value had to await the devel­opment of big electrical generators in the mid-1800s. and shortly thereafter brilliant arc lights were in wide use. In these lamps. an elec­tric field is set up between two hot electrodes (here. carbon rods) that are separated by a narrow gap (Fig. 1.21). Electrons are emitted from one electrode. pulled across the gap by the electric field. smash into the air molecules in between. knock electrons off them. and create many charged atoms (ions), which in tum are also accelerated by the electriC field. All these charges smash into

FIGURE 1.21

An AC carbon arc. Only one of the carbon electrodes would glow if the arc were fed DC, as in the earliest arc lights. Most of the light comes from the very hot electrode tips.

each other and into the electrodes. give off 11ght. and further heat the carbon electrodes. In fact. over 90% of the light comes from the incan­descence of these very hot electrode tips. This produces a very concen­trated light. While it is much too bright a light for the home. the car­bon arc still is found in theatrical spotlights.

The incandescent filament lamp used today had to await the devel­opment of the mercury vacuum pump in order to produce the needed quality vacuum. The pump was produced in 1865 and by 1880 Edison had his patent for the in­candescent light (Fig. 1.22). En­closed within a glass bulb there is a little coil of thin wire. thejUam.ent, made of tungsten. because tung­sten can become very hot without melting. The filament is about half a meter long if unwound, and its ends are connected to the lamp-

cord. As the current runs through it. the filament becomes hot and ra­diates. Some radiation is in the vis­ible (Fig. 1.19) but most is in the infrared! You have undoubtedly felt that light bulbs get hot. In fact an incandescent bulb is only about 7% effiCient in converting electricity to visible light-the rest of the energy goes into heat. We could get propor-

Filament

Support wires

Base

FIGURE 1.22

Atom

@0­ 0-­

CHAPTER 1: FUNDAMENTAL PROPERTIES OF LIGHT

22

tionately more visible radiation if we heated the filament more, but the tungsten would then melt or bum. To prevent such burning some of the air is pumped out of the glass bulb. (That's why the bulb goes "pop" when it breaks, and why they needed the vacuum pump.) Ac-­tually, there is only a partial vac­uum in the bulb. It is filled with a mixture of gases (argon and nitro­gen) that do not react appreciably with tungsten. These gases tend to retard evaporation of the tungsten. The evaporated tungsten deposits on the glass (you can see this dark­ening in an old bulb) and makes the bulb dimmer, and the filament de­velops mechanically weak, hot spots. When the filament finally breaks, the bulb is "burnt out"; current can no longer flow.

In newer lamps, called "quartz­halogen" or "quartz-iodine" or "tungsten-halogen" lamps, the fila­ment is surrounded by a quartz en­closure containing a Uttle iodine gas (Fig. 1.23). The iodine picks up any tungsten that has been evapo­rated and redeposits it on the fila­ment. This allows the lamp to oper­ate at a higher temperature, which makes it more efficient since you get more visible Ught and propor­tionately less heat. Further, the evaporated filament doesn't blacken the bulb.

The relatively low efficiency of all incandescent sources led, this cen­tury, to the development ofjluores­cent lamps,· the first departure from the long historical precedent of producing light by heating some­thing. In jluorescence, certain substances (called phosphors) pro­duce visible light when they absorb ultraviolet ("black") light, and thus make light without using heat. Sur­prisingly, ultraviolet radiation can be more easily produced effiCiently. A glass tube is filled with some gas at low pressure, usually mercury va­por (Fig. 1.24). Electrodes at the

*Latinfluere. to flow. But not of current: fluorescence was first observed in the mineral fluorite (CaF2 1. which was used as a flowing agent to help metals fuse together when melted.

FIGURE 1.23

Tungsten-halogen lamp.

FIGURE 1.24

A fluorescent tube first makes UV light in an electric gas discharge and then converts most of the UV to visible light.

Electrode

Visible

end are connected to an alternatiIlj current (AC) source. which drive the charges first one way and thel the opposite way. (In the Unite. States. alternating currents g. through a complete cycle 60 times; second. so we have 60 hertz AC. The resulting electric field in th, tube pulls some electrons off th electrodes. These electrons collid with atoms. shaking them and th charges on them. The whole pro cess is called a discharge. The os cillation of charges on atoms occur, at the atoms' resonance frequency and this frequency for simple atom: Is mainly in the ultraviolet (wit] some in the visible).

To make a "black light." you coa the tube with material that absorb: the visible but transmits the ultra violet (UV). On the other hand, t. make visible light. the tube i: coated instead with material tha fluoresces. This way of making vis ible Ught is so efficient that a 40 watt fluorescent lamp provide: about 4 times as much visible Ugh as a 40-watt incandescent bulb The fluorescent lamp is mud cooler. hence wastes less energy ra diating infrared. Further. by choos ing different coating materials. ym can have fluorescent bulbs that giv, off different colors. Thus. specia lamps for growing plants indoor: use a phosphor chosen to give I

spectrum of light similar to sun Ught. or to match the resonance fre quencies of chlorophyll.

We could make a more efficielli Ught by using the Ught from tht discharge directly. without using c phosphor. The Ught from a dis­charge. however. has a frequenc) (and thus color) characteristic 01

the particular resonant system, here the atoms in the gas (see Secs. 15.3 and 15.4). To make a useful

Phosphor coating

light, we choose atoms that have resonances in the visible, for exam­ple, mercury or sodium. The strong coloration of the light emitted by these atoms is avoided in high-in­tensity discharge lamps, where high pressure or impurities broaden the range of frequencies emitted, making a light somewhat more like broadband white.

The production of light due to collisions of accelerated charged particles with atoms is not only a man-made phenomenon. The glow­ing aurora borealis is essential­ly the same phenomenon. Here

1.4 ELECTROMAGNETIC RADIATION

23

charged particles from the sun strike molecules in our atmosphere. The radiation produced depends on the energy to which the charges are accelerated by the earth's magnetic and electric fields, as well as on the molecules they hit.

D. Visible electromagnetic radiation

Well concentrate now, and for most of the rest of this book, on that tiny part of the electromagnetic spec­trum that can make the charges in

......1---- UV ----)10..,11-0..1--- VISIBLE ------------- ­

the receptors of our eyes respond: the visible. Figure 1.25 summarizes some of the important things that go on in and near this region of fre­quencies. At the top of this figure we indicate the visible region. Short wavelengths (400 nm) look Violet (though we often refer to the short­wavelength end of the spectrum as blue-see Sec. 10.4A). As we in-

FIGURE 1.25

Visible light and its interaction with life. The frequencies (and wavelengths) of light are marked along the top.

IR -------------i._

Frequency /I =

Wavelength A =

Color =

225 nm

1 I 1 I

7 X 1014 Hz 3 X 1014 Hz

400 500 600 700 nm

V BGYORI I 1

- .._----c-----Most of sun's radiation ---------------~Io 3200nm I I320 nm

----10-11.... I

Absorbed by 1----- ~ of sun's energy that ozone (03) in reaches earth is here upper atmosphere I

I I

I~ All that's left -------l I lat 25 m under I I

the sea :

1100 nm 2300 nm

10 1.. Diminished strongly by .1.. Absorbed by H20, ------'M--H20 in atmosphere --1-011---- CO2, ozone (03) in

atmosphere

1r--- All that's left at 100 m under the sea I

320 nm 1

"Hard UV" -------1 stopped by glass I

Insect vision ... :\ ~ ,., Skin response (sun burn)~':!V :

•. . il. I Effectiveness for -s-----, 04 \: killing a bacillus \. \ ".

I I I I 1

I 1 I 1 1 1

~ Human day vision [Photopic] " ' Human night vision [Scotopic) \.

300 400 500 600 700 nm 1400 nm 1900 nm I I I" Frequencies involved in "dark" chemistry ---_10­I I

....1----- Frequencies involved in (Iight·activated) ,. photochemistry

1 I 1 I I I I 1 '/\~~ Absorption spectrum of chlorophyll

_=-~'.::'"-'-_ Absorption spectrum of phytochrome__~=-=-"",__ 1

~ : I Frequencies that excite phototropic behavior in plants

1

crease the wavelength, the color changes to Blue, then Green, Yel­low. Orange. and finally Red when the wavelength gets to the long­wavelength end of the visible (700 run).

Most of the sun's radiation lies between 225 nm and 3200 nm (see also Fig. 1. 19), however. not all of this penetrates the atmosphere and reaches the earth's surface. -The short wavelengths (below 320 nm) are absorbed by the resonances of ozone in the atmosphere. the long wavelengths by water (above 1100 nm) and by carbon dioxide and ozone (above 2300 nm). The result is that about half of the sun's radia­tion reaching the earth lies in the visible.

In the center of Figure 1.25 we have plotted curves to indicate how various systems respond to light of different wavelengths. Thus. hu­man daytime vision is most effec­tive at about 555 run (yellow-green). Human night vision uses different receptors, which have their maxi­mum sensitivity toward the blue. Actually, under very intense sources, so intense that it feels warm, we can see in the infrared OR) up to as high as 1100 nm. Further. we could see in the ultraviolet (UV) except that the eye's lens absorbs UV. Peo­ple who have their lenses removed (for cataracts) are sensitive doWn to about 300' nm. Insects, however. are most sensitive to ultraviolet light. Since insects have little or no vision in the red and yellow. we can use yellow lights as "bug lights." The yellow light provides useful il­lumination for our eyes, but the in­sects don't see it and therefore aren't attracted to it. Conversely, to attract bugs and zap them with high voltage. we use blue or UV bulbs.

Since most vertebrates have vi­sion in the same range as humans, insects can have an interesting kind of protective coloring. In the visible, their coloring can be the same as that of a poisonous insect so that birds will leave them alone. but their UV coloring can differ from that of the poisonous insect so that no mistakes are made when they are looking for a mate.

CHAPTER 1: FUNDAMENTAL PROPERTIES OF LIGlIT

24

Notice that your skin is most sen­sitive to UV of about 300 run wave­length. but that glass absorbs the UV below 320 run-we don't sun­burn through a window. Notice also that hard UV. below 300 run, kills bacilli. but that the ozone in the upper atmosphere absorbs this short wavelength UV. thus saving both bacilli and our skin from seri ­ous damage.

In the range 250-1400 nm we find not only vision, but all the other light-dependent processes critical to life. because the frequen­cies of the resonances of chemical bonds occur in this range. Thus. at the bottom of Figure 1.25 we show the absorption spectrum of chloro­phyll (actually of several different kinds combined). Since only the green part of the spectrum is not absorbed. it is reflected or transmit­ted. so chlorophyll looks green. The chlorophyll responsible for the pho­totropiC· behavior of plants absorbs only in the blue. Therefore, if we grow plants in red light only, with­out blue light, the other chloro­phylls wlll absorb light and the plants will grow, but not toward the light. Also at the bottom of Figure 1.25 is the absorption spectrum of phytochrome-the enzyme that pro­vides the "clock" for plants, deter­mining when they germinate. grow. flower. and fruit. according to the length of the night. It measures the length of day by the amount of light it absorbs in the red. (See the FO­CUS ON Light, Life, and the Atmo­sphere after this chapter.)

Light from sources other than the sun may play a critical role in life. Many organisms, such as the firefly, are bioluminescent-emitttng their own light as part of their mating rites. (You can elicit a sexual re­sponse from a firefly with a flash­light, if you use the correct timing.) Humans, as you know. also find certain types of lighting to be ro­mantic. Probably the most extreme effect of light on human sex life was proposed by Shakespeare. Hamlet.

-Greek tropos, turn. Therefore phototropic means turning toward the light.

while feigning madness. suggests that it is possible to get pregnant from walking in the sun:

Hamlet:-Have you a daughter? Polonius: I have my lord. Hamlet: Let her not walk l' the sun:

conception is a blessing; but as your daughter may conceive,-frtend, look to't.

Light certainly seems to playa role in almost everything!

SUMMARY

To see the light, it must pass from a source, to an object (possibly). and then to a detector. Light trav­els at about 300.000 km/sec (in vac­uum) and carries energy and m0­

mentum. It is a type of wave (propagating disturbance), but is unusual in that it can propagate through a vacuum-it is an elec­tromagnetic wave. An oscillating charge creates a disturbance in the electric fteld (which descrihes the force on charged particles) as well as in the magnetic fteld. Electro­magnetic waves of different fre­quencies are emitted and absorbed by resonant systems (whose re­sponse is greatest at the resonance .frequency).

Periodic waves are characterized by frequency (v. number of oscilla­tions per second), wavelength (A,

separation between repeating parts). amplitude (size or amount of oscillation). pol.arl.zation (direc­tion of oscillation), and th,e direc­tion oj propagation (indicated by a ray). The attrtbutes of light corre­spond to our sensations of color (frequency, period, wavelength). brightness (amplitude), and the di­rection from which the light ap­pears to come.

Visible light corresponds to a very small range (wavelength 400 to 700 run) in the electromagnetic spectrum, which ranges from the very short wavelength gamma rays and x-rays, through the ultraviolet (UV). the viSible. the Uifrared (IR). to the very long wavelength radio waves.

PROBLEMS

25

Black bodies emit a characteris­tic black-body spectrum in which more energy is emitted from hot ob­jects than from cooler ones. Also, the peak emission occurs at higher

PROBLEMS

PI Briefly I ist some of the properties of light you have learned so far (e.g., how it travels, its speed, etc.).

P2 When you look at the daytime sky, away from the sun, it looks blue. Explain where this light comes from (Le., what is its source and how does it get to your eyes?).

P3 How do we know that light travels through a vacuum?

P4 Brand new windowpanes and mirrors often come with pieces of tape on them. Why?

P5 (a) Which of the following are self-luminous objects (that is, we see them by their own light, rather than light reflected from them)? The sun, the moon, a cat's eye, a television picture, a photograph. (b) In the case of the examples that are not self-luminous, what is the source of light that allows you to see them?

P6 Give an example of a resonance. In your example, who (or what) supplies the energy? (Example: A parent pushing a child on a swing. The parent supplies the energy.)

P7 At Cornell, there used to be a narrow suspension footbridge. If you walked across it on a windless day, it scarcely swayed at all. However, if you jogged across it at just the right speed, you could get it swaying wildly. (That's why it's not there any more!) Explain why there should be this difference.

P8 On November 7, 1940 at 10 A.M., a 47-mph wind set the Tacoma Narrows Bridge into (torsional­twisting) vibration. The length of the

(a)

(b)

frequencies for hot objects, lower frequencies for cooler objects. In­candescent electric lights consist of hot, gIowtngjilam.ents, whlleftu­orescent lights consist of gas glow­

bridge's main span was about 850 meters. The wavelength of the waves set up in the bridge was also 850 meters. Which of the two pictures in the figure represents more nearly the shape of the bridge that a snapshot taken at the time would show?

P9 Which of the following common everyday periodic phenomena are examples of resonance? (a) A cork bobbing up and down in waves in the water. (b) Grandparent rocking in his or her favorite rocking chair. (c) A singer hitting a high note and shattering a glass. (d) The people at a rock concert stomping their feet in rhythm with the music. (e) Floors of the auditorium vibrating and cracking as a result of the audience stomping at the rock concert. (f) A rattle in your car while idling, which stops as the motor increases speed.

PI0 Your car is stuck in the snow, and you can't push it hard enough to get it over a hump of ice. It sometimes hel ps to rock the car back and forth. Apply some of our discussion of vibrating systems to explain why this helps.

P11 The figure below shows a picture of a wave. Use a ruler and measure its wavelength in centimeters.

P12 Redraw the wave of problem P11, and label it "old wave." On top of it, draw a wave of half the wavelength and twice the amplitude, and label it "new wave."

P13 Redraw the wave of Problem P11, and label it "old wave." On top of it,

ing in the UV, and encased in a tube With a phosphorescent coat­ing, which converts the UV to visi­ble light.

draw a wave of half the frequency and the same amplitude, and label it Ii new wave."

P14 A light wave traveling in the vacuum comes to a plate of glass. On entering the glass, which, if any, of the following increase, decrease, remain unchanged: the frequency of the wave, its wavelength, its speed?

PIS What is the frequency of your heartbeat while you are resting? Give units with your answer, and tell how you measured it.

P16 light is an electromagnetic wave. Does that mean that there must be electrons present in the wave for it to propagate? Explain.

P17 Consider a radio wave and a visible light wave. Which has a higher frequency? Longer wavelength? Longer period? Higher speed in vacuum?

P18 (a) The color of light corresponds (in general) to which of the following (there may be more than one answer): frequency, speed, wavelength, intensity, polarization? (b) The brightness of light corresponds (in general) to which of the above list?

P19 (a) As a black body becomes hotter, does it emit more or less radiation? (b) Does it radiate predominantly at a higher or lower frequency?

P20 Identify the type (e.g., UV, visible, IR, etc.) of electromagnetic radiation of each of the following wavelengths in vacuum: 600 nm, 300 nm, 1400 nm, 21 cm, 0.1 nm, 3 km.

HARDER PROBLEMS

PHI How could you use a laser beam in a dark room to determine the amount of dust in the air?

PH2 What is the color of the sky on the moon, where there is no atmosphere? Why?

PH3 When soldiers march across a bridge, they are told to break ranks. That is, they are told not to walk in step with each other. Think about the Walls of Jericho and the Tacoma Narrows Bridge, and explain why the soldiers should break rank.

PH4 Cheap loudspeakers often have a resonance in the sound frequency region that we can hear (roughly SO to 20,000 hertz). You get a much larger output (sound) at the resonant frequency, for a given input, than you do at other frequencies. Better speakers don't have such resonances. Why is it bad to have such a resonance? (Think about what you would hear as someone played a muscial scale.)

PHS (a) What is an electric field line? (b) What do the arrows on an electric field line convey? (c) How can one physically determine whether an electric field is present at a given position?

PH6 The figure shows some wavefronts of a light wave. Redraw the figure and draw three different light rays on it.

ClfAPTER 1: FVNDAMBNTAL PROPERTIES OF LIGHT

26

PH7 Describe the physics of a standard incandescent light bulb. (a) What charges wiggle? What causes them to wiggle? (b) Why is there a partial vacuum-in the bulb? What gas is present inside? Why? (c) Why don't manufacturers simply make bulbs that last forever? (Sure, they have to stay in business, but what physical constraint mitigates against making a bulb that will last forever?)

PH8 Why can't we see x-rays directly? ("Because our eyes aren't sensitive to x-rays" is correct, but not a suitable answer. Why aren't our eyes sensitive to x-rays?)

PH9 Objects A and B are illuminated by a light source that produces only visible radiation. To the eye, A looks bright while B looks dark. Under the same illumination, a photograph is taken of the two objects, using film sensitive only to infrared radiation. In the picture, B shows up brighter than A. Explain how this could be so.

MATHEMATICAL PROBLEMS

PMI How long does it take light to travel from one of Galileo's hill tops to another, 1.5 km away?

PM2 When a laser beam is sent to the moon, reflected there, and returned to earth, it takes 2.5 seconds for the round trip. Calculate the distance to the moon.

PM3 A rocket probe is sent to pass close to the planet Jupiter. Suppose that at the time the rocket reaches Jupiter, Jupiter is 630,000,000 kilometers from Earth. How long will it then take a radio signal to travel from the rocket to Earth?

PM4 A radio signal takes about 2.5 x 10-3 seconds to travel from Boston to Washington, D.C. Calculate the distance between these two cities.

PMS (a) What is your height in meters? (b) Express the result of part (a) in millimeters and in nanometers. (c) Which of these three units is more reasonable to use for your height? Explain your choice.

PM6 (a) The note that orchestras tune to, middle A, has a frequency v = 440 Hz. The speed of sound in air is about v = 330 m/s. What is the wavelength of middle A? (b) What is the wavelength of the A one octave

lower than middle A? (As you go down an octave, you divide the frequency in half.) (c) Why do you think organs have big pipes and small pipes?

PM7 The figure shows (idealized) the way the Tacoma Narrows Bridge vibrated from 8 to 10 A.M. on November 7, 1940, shortly before it collapsed. The length of the bridge's main span was 850 m. Each up and down oscillation lasted 1f seconds. (a) This means that the frequency of the oscillations was v = 0.6 Hz. Show how one derives this result from the data given above. (b) What was the wavelength of the waves set up in the bridge? Give the reason for your answer. (c) What was the speed of the waves? (Show your calculation.)

PM8 In Washington, D.C., radio station WRC broadcasts on AM at 980 kHz. Station WET A broadcasts on FM at 90.9 MHz. What are the wavelengths (approximately) of the radio waves used in each case? (Give the units you use: e.g., meters, feet, cubits, versts, etc.)

PM9 The range of wavelengths, in vacuum, of visible light is about 400 nm to 700 nm. What range of frequencies does that correspond to?

PMIO What is the frequency of 575 nm (yellow) light?

PMII Consider a wave of wavelength 2 cm and frequency 1 Hz. Cou.ld this be an electromagnetic wave traveling in vacuum? Why?

PMl2 If a black body is heated to a temperature T (in degrees Kelvin, K = ·C + 273), the most intense radiation is at wavelength A (in meters), where

A x T = 2.9 X 10-3

(a) Find A for room temperature bodies (take T = 290 K). (b) What is the frequency of this radiation? (c) What kind of radiation is this (e.g., visible, IR, UV, x-ray, etc.)?

r---------­

___

FIGURE FO.t

Interaction of light and life.

Cellular respiration

, fOCUS ON . ..

Ught, life, and the atmosphere

That our atmosphere is so beneficent as to transmit visible radiation from the sun, but absorb killing ultraviolet, is a consequence of its history. We will outline its development so that we may see the interplay of light, life, and the atmosphere.

In the early days of the earth's development, the atmosphere did not contain many of the key ingredients of life. There was no oxygen (02 ) and consequently, no ozone (03), Nor was there carbon dioxide (C02), As a result, the ultraviolet (UV) radiation reached the surface of the earth quite easily, much more so than now (Fig. FO.1). This UV provided just th,eright frequencies (i.e., it excited resomlflces) for various organic molecules present in the seas to combine into the first living organisms. These primitive organisms had a better chance for survival than they would have now, since there were no other organisms to eat them, and no oxygen to oxidize them. Lacking oxygen, the organisms could only get the energy they needed to live by the process of fermentation.· If you've seen beer

'Latin fermentare, to boil. This process extracts energy by rearranging organic molecules. For example:

I I I I

~OG~s~ I I I I I I I IL

t­

i 1

ferment, you know that this process produces carbon dioxide (C02), These organisms did just that, pumping more CO2 into the atmosphere than currently is there. The presence of the CO2 then allowed new organisms to develop that could live by photosynthesis.· These new

sugar -+ CO2 + alcohol + energy

This process spends its "capital" (sugar) t9 '-produce energy, Once. the sugar is used up, the process stops, It is a very inefficient process. Only 5% of the chemical binding energy in the sugar is released, and half of that is lost as heat. (Fermentation tends to heat up the surroundings, as anyone who has made yeast bread will have noticed.) The half not lost is stored in the molecule ATP (adenosine triphosphate, the biological "energy currency"), which then, if there is raw material available, offers the energy for new cell production.

·Greek synthesis, putting together, hence putting together by I ight. Photosynthesis is the process:

CO2 + H20 + light -+ sugar + O 2

It thus is a new source of sugar from which organisms can derive energy, As such, this is a crucial step in the evolution of life because it allows organisms to take energy from the sun continuously. That is, at this point life developed a (very efficient) solar battery.

organisms removed some of the CO2 ,

fixing it in organic forms, and at the same time produced molecular oxygen (02), which entered the atmosphere, with two critical effects. One was that the sun's radiation converted some of this O2 into 0 3 (ozone). The ozone, as we've seen (Fig. 1.25), blocked the antibiotic UV from the earth's surface, thus permitting living organisms to leave the water for the land (about half a billion years ago). This would not have helped much unless there was a way the organisms could produce energy more efficiently. The process of fermentation produced barely enough energy for survival; none was left for motion. But the second effect of the O 2 in the atmosphere was to allow the much more efficient process of cellula, respi,ation.* This process uses the O 2 and replenishes the CO2 • Eventually these two balancing processes, photosynthesis and cellular respiration, came into equilibrium, keeping the atmosphere roughly in its present form for ages.

Currently, however, atmospheric CO2

is increasing, largely because of the destruction of the forests and the burning of fossil fuels, which have raised the CO2 content in the atmosphere by about 15% since 1850 (over 5% since 1958). This is thought to be responsible for the warming tr~nd in northern latitudes, from 1900 to 1940, by the greenhouse effed. The idea is that CO2 ,

like glass, lets the visible light through. The earth absorbs this, warms up, and radiates in the IR. But CO2 (again like glass) doesn't let the IR through, so the

"Latin respirare, to breathe. This is the way we get most of our energy. The process is:

sugar + O2 ..... CO2 + H20 + energy

This is the same process as burning sugar over a flame, but we can do it at body temperature in a more controlled fashion. It is far more efficient than fermentation, capturing over 85% of the chemical binding energy in the sugar. Further, the by-products are not harmful, unlike fermentation, which usually produces something poisonous (alcohol or some acid). With all this extra energy, organisms can now do more than exist, they can develop locomotion and eventually paint the Mona L.sa. Yeast, on the other hand, living by fermentation, do not lead very active lives.

28

energy stays inside the CO2 (or glass) barrier and the earth gets hotter.· But the story is more complicated. Although atmospheric CO2 continues to increase, a cooling trend seemed to appear in 1950. This may be due to other forms of pollution in the atmosphere that may reflect the incoming visible sunlight (like metal foil, instead of glass) so that less energy reaches the earth in the first place. That is, there are many other important molecules in our atmosphere besides CO2, such as nitrous oxide, methane, ammonia, sulfur dioxide, and even trace constituents. An important question is whether they reflect the sunlight (preventing the energy from reaching the earth's surface), or transmit the sunlight (allowing the energy through), or absorb the sunlight (thus heating up the atmosphere). The greenhouse effect shows the complication of transmission at one frequency but not at another.

Another 'critical constituent is the ozone, which protects us from the hard, killing UV. It is unclear how sensitive the ozone concentration is to various man­made effects such as supersonic transports, fluorocarbons (commonly used in aerosol spray cans), atmospheric nuclear testing, or even agriculture (with its effects on the nitrogen cycle). However, a modest change in the ozone content of the atmosphere can significantly change the amount of hard UV getting through, since most of it is currently blocked. Too much of this UV can cause mutants by altering the DNA of which our genes are made, produce skin cancer, and do other ecologically more complicated things. Alternatively, too little UV would prevent our bodies from properly metabolizing calcium.

The effects of human activity on atmospheric constituents, and their effects in turn on climate and ecology through the interplay of light with the atmosphere, constitute one of the more exciting fields of study today. The consequences are, literally, breathtaking.

'Actually, "greenhouse effect" is a bad name. The major effect of an actual greenhouse is to prevent the rising hot air from escaping.

Principles of Geometrical Optics

CHAPTER 2

does not bend around corners. We Those that are blocked don't reach 2.1 INTRODUCTION-How do we so easily decide where to place a beach umbrella to keep the sun out of our eyes, without worry­ing about the electric field, the wavefront, the wavelength, and the frequency of the light? The answer is that, for many simple problems it is suffiCient to concentrate on the light rays (Fig. 1. 17), the lines that describe in a simple geometric way the path of light propagation. Geo­metrical optics is the study of those phenomena that can be un­derstood by a conSideration of the light rays only. Geometrical optics is useful as long as the objects with which the light interacts are much larger than the wavelength of the light. As our beach umbrella is about a million times larger than the wavelength of visible light. geo­metrical optics is a very good ap­proximation for this and most other everyday objects. For smaller objects the beam will not propagate in only one direction, but rather spread out in all directions--much as sound waves, with wavelength of about a meter, spread out around obstacles in the street.

In geometrical optics, then, light

(a)

think of the light as traveling in straight lines as long as it is left alone (Fig. 1.4). This straight-line propagation enables us to locate the beach umbrella so its shadow falls on our eyes.

2.2 SHADOWS-To cast shadows you need light from a fairly concentrated source, such as the sun. The best shadows are cast by light that comes from just one pOint: a point source, which is an idealization, like a ray, that can only be apprOximated, for example, by a small light bulb or candle. (Even a source as large as the sun or a giant star can approx­imate a point source if it is far enough away.) You also need a screen, such as a flat, white sur­face, which redirects incident light into all directions, so that you can see the shadow (the light from the surrounding area must enter your eye).

If an obstacle blocks some of the light rays headed for the screen, the light rays that are not blocked still reach the screen and make that part of the screen bright.

the screen, so the places where they would have hit are dark-a shadow. We can figure out the shadow's location by drawing straight lines from the pOint source to the edge of the obstacle and con­tinuing them to the screen. These lines separate the regions where the rays reach the screen from the re­gion where they are blocked. The resulting shadow resembles the ob­stacle, but it is of course only a flat (two-dimensional) representation of the object's outline. Nonetheless, we can easily recognize simple shapes, such as a person's profile. Before photography, it was popular to trace people's shadows as silhouette portraits (Fig. 2.1a). Today's x-ray pictures are just shadows in x-ray

FIGURE 2.1

(a), (b) Various uses of shadows. (c) Silhouette of one of the authors. Etienne de Silhouette (1709-1767), France's finance minister for a year, was deposed because of his stinginess over court salaries. He used cheap black paper cutouts in place of conventional decorations in his home and invented a technique for making paper cutout shadow portraits to raise money. When he died, he was penniless and destitute, a shadow of his former self.