1.4 ELECTROMAGNETIC RADIATION

17

Table 1.1 shows the various kinds cies of the receptors of your eyes. In instance. devices to generate and of electomagnetic radiation that this region. each frequency (or detect radio waves are rather differ­ have proved useful so far. Note the wavelength) corresponds to a differ­ ent from those for visible light or for very small region of the spectrum ent color in the spectrum of colors x-rays. Thus. for example. not only around v = 1014 to 1015 cycles/sec· from red to violet. This tiny region can you take pictures using visible or A = 10-7 to 10-6 m that is visi­ is. or course. incredibly important light. but you can also use other ble light-the frequencies are com­ to human life. The study of electro­ forms of electromagnetic radia­ parable to the resonance frequen- magnetic waves in this region is tion-gamma rays. x-rays. infrared. called optics.· etc. All you need is a source of the Much of what we will learn about radiation. some method of localiZ­ 'cycles/sec = cycles per second (cps) = optics will be applicable to other ing the rays. and a detector (Fig. hertz. When talking of radio parts of the spectrum. although the 1.18). The picture is a record of frequencies. one usually uses Mc technology is quite different-for how much radiation was received at (megacycle) = 106 cycles/sec = MHz = each point. The main difference be­ 106 bertz. as well as kc (kilocycle) = 103 cycles/sec = kHz = 103 hertz. tween different radiations is that Unfortunately. all these forms are used. ·Greek ops. eye. the smaller the wavelength. the

TABLE 1.1 Electromagnetic radiation

Frequency Detected by in hertz Wavelength in meters Name Examples of use p 10- 15 (Size of nucleus) h P 1023 0 h t 0 0 t n 0 Gamma rays g c r 1020 Cancer treatment 0 a u P p n h h 10- 10 = 1 A(size of atom) X-rays Materials testing t 0 Medical x-rays e t C r 0 s c e UltraViolet (UV) e m Atomic structure 1 u Germicidal Human 1 "Black light... sun tan eye s s 10 - 6 = 1 ....m (diameter of Visible OPTICS i bacteria) IR photos. heat lamps Thermal 0 "Heat rays." forest fire detection detectors n Infrared (IR) Molecular structure. human body radiation

10-2 = 1 cm (size of a Microwave AtomiC clocks. mouse) Space research T u Radar. microwave ovens (3 x 109 hertz) n 100 = 1 m (size of a man) Radio astronomy e TV. UHF: 470-890 MHz. VHF: 54-216 MHz. d FM: 88-108 MHz International Shortwave c CB:27 MHz i Radio frequency (RF) AM radio broadcast: 550-1600 kHz r 103 = 1 km (size of a Village) c Longwave broadcast u i Long-range naVigation t s 10" ~distance from W' -hington. D.C. AudiO frequency to hicago) 10 AC power. 108 (distance to moon) Brain waves CHAPTER I: FUNDAMENTAL PROPERTIES OF LIGHT

18

(a) (b)

(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 (e) per second. (e) Gamma-ray picture of human hand. Source of gamma rays is (d) radioactive tracer inside patient. 1.4 ELECTROMAGNETIC RADIATION

19 smaller the structures with which atoms in it moving more rapidly they interact. For example, the an­ and randomly. These wiggling tennas for radio waves (meters to charges then radiate-the hotter kilometers wavelength) are long the material, the faster they wiggle, wires or high towers, whereas the and the higher the frequency they resonators in your eyes that select radiate. The radiation from a light waves (a few hundred nano­ heated frying pan usually is not vis­ meters in wavelength) are tiny or­ ible, but you can feel it with your ganiC molecules. Therefore, one hand, which responds to the in­ must be careful in taking pictures frared radiation. If you heat the pan with different wavelengths that the suffiCiently, it begins to glow, and wavelength is small enough to de­ becomes "red-hot," hot enough to tect the objects of interest. If the radiate in the visible. Your eyes are wavelength is comparable in size to sensitive to radiation of this higher the object, the wave will bend frequency, and you see it as red around the object (Chapter 12); if it light. is much larger, the wave won't be In fact, a glowing body can give affected by the object. (This is why you radiation of any wavelength you Wavelength in nm gynecologists, bats, and whoever like, provided it has the proper tem­ else takes pictures with sound use perature. For instance, your radiant very short wavelengths-high fre­ face emits radiation primarily with quencies.) wavelength near 10,000 nm. (Al­ FIGURE 1.19 Radiation of too short a wave­ though we cannot see this radia­ The spectrum of a glowing black body at length (Le., too high a frequency) is tion. the poisonous pit viper can. temperatures of a light bulb, of a also less useful in taking pictures. This snake has deep hollows­ photoflood bulb, and of the sun. The If the radiation oscillates at too pits-on the sides of its head that actual spectra of these radiators are only a little different from this idealized black high a frequency compared to the are sensitive to this frequency body approximation. (Remember, resonance frequenCies of the system range. allowing it to locate its shorter wavelength means higher of interest, the system will not be warm-blooded victims.) Heating frequency.) able to keep up with the oscillations and cooking goes on at about 1000 (recall Fig. 1.12). At these high fre­ nm. and the sun's temperature cor­ quencies, then, there is very little responds. very conveniently. to the trance hole. Light that enters the interaction between the radiation visible region at about 500 nm, cavity through this hole bounces and the system-the radiation just However. at low temperatures the around inside but. like a lobster in passes through the system. This is intenSity of the emitted radiation is a lobster trap. rarely finds the hole why many objects, such as your very low. and at high temperatures again. so it does not get out. Your skin, that are opaque to visible there is plenty of intenSity but the eye is a reasonably good black body light, are transparent to the higher­ emitting body tends to burn. The because it contains a small opening frequency x-rays. radiation from hot objects is not with a big empty space behind it given off at a single frequency. but (Sec. 5.IA), as a broad band of frequencies (Fig. When a black body is heated it B. How to make 1.19). since the random heat mo­ starts to glow. and. therefore. no electromagnetic radiation tion has no particular single fre­ longer looks black, But it continues quency. We see from Figure 1.19 to be black in the sense that it still Sources of radiation differ as much that the hotter the object. the more absorbs all radiation that falls on it. as do detectors, particularly be­ light it radiates. and the shorter the A small window in a furnace is a cause their size usually is compa­ wavelength of the predominant ra­ good example of a glowing black rable to a wavelength. Basically they diated light. Thus. the very hot sun body. If you try to illuminate this all are devices to wiggle charges. For radiates primarily in the visible. "body" (which is really the Window very high frequencies we try to get whereas most of the radiation from hole) with a flashlight. it will look nuclei and atoms to do the wiggling a 100-watt bulb is in the infrared. no different in color or brightness-­ for us, as these very small systems with very little in the visible (mak­ it absorbs all the light you shine on have very high resonant frequen­ ing it a rather ineffiCient light it. Because the radiation stays in­ Cies. At low frequenCies, we use source). side the furnace for a relatively long electronic circuits instead. One The curves of Figure 1.19 are ac­ time before it manages to escape, it standard way of getting radiation at tually for an ideal object called a comes to equilibrium with the fur­ intermediate frequencies is to make black bot!-y. a body that absorbs all nace. and the color emitted de­ some material very hot. As we heat radiation that falls on it (Fig. 1.20). pends only on the temperature. it, the charges in it oscillate more­ A good approximation to a black (Temperatures of the molten metal heating something means to get the body is a cavity with a small en­ in foundries, and of ceramic kilns. CHAPTER 1: FUNDAMENTAL PROPERTIES OF LIGHT

20 lantern we now take on camping trips.) Several millennia after the first oil lamp, in Egypt or PhoeniCia, a can­ dle was made by Impregnating fi­ G ­ brous material with wax (from in­ sects or certain trees). The use of tallow, and much later spermaceti (from sperm whales), and improve­ ments of the wick, provided the ma­ jor 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 signifi­ cant. 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 street­ lights (in the form of tarred torches) were Introduced in Antioch. Light­ houses, primarily to mark the en­ trances to ports, were another big project. Originally simple hilltop fires, these evolved into towers with FIGURE 1.20 c. Light sources bonfires of resinous wood, later A good approximation to a black body coal, and, in the late eighteenth radiator: a heated cavity with a small exit The fact that hot bodies glow, or in­ century, candles and whale 011 hole (furnace in a steel mill). candesce,· has played a major role lamps. The first known attempt to in the history of artificial light concentrate the light from these sources. From the time Prometheus fires was probably the great pharos are often measured by examining brought fire down from Olympus of Alexandria (one of the seven won­ the glowing color.) Most glowing untU this century, all man-made ders of the ancient world, designed bodies are not truly black bodies. light sources have been incandes­ by Sostratus of Cnidos in about 280 For example, a log glowing in a fire­ cent (except for those created by B.C.), which may have used large place Is nearly, but not quite, black, collecting fireflies). Until the advent mirrors of polished metal and as you can check after it has cooled. of adequate generators of electricity whose light was said to be visible You can verify its near blackness by in the nineteenth century, these for 35 miles. shining a light at the glowing coals lights were very little more than the Except for a few oddities (the in your fireplace. (If the coals were fire Prometheus gave us; the only most bizarre being the burning of really black bodies at uniform tem­ innovations being improvements in fatty animals, such as the candle­ perature, they would all appear fuel from the campfires and torches fish or the stormy petrel), the torch, equally bright. Inside a well-stoked that formed the earliest light the oil lamp, and the candle gave furnace you see a uniform bright sources. the world the bulk of its nighttime glow and cannot distinguish the in­ The next known light source was light untU the nineteenth century. dividual coals.) Similarly, the sun the oil lamp, used by PaleolithiC Thus, when the sun went down, it and light bulbs are not truly black cavedwellers to allow them to make was very dark-". . . the night bodies, though the essential fea­ those magnificent cave paintings. cometh, when no man can work" tures of the light they radiate are The oil lamp was a dish of stone, (John 9:4). Well Into the nineteenth not very different from the black­ shell, or, later, pottery that con­ century battles stopped at sun­ body case. tained oil and a reed wick. (In the down, which was all to the good. Finally, we must mention that we nineteenth century, when kerosene but hospital care ceased also. cannot fully explain the curves of replaced the oil and an air draft was Witches had to wait for a full moon Figure 1. 19 from our understand­ introduced through the wick, the for a nighttime ramble; the poor ing of light as a wave. In fact, these oil lamp began to evolve into the went to bed at sunset; only the rich curves led to our knowledge that had a nightlife. About a century the wave picture is not the entire ago, this began to change with story (Sec. 15.2A). -Latin tn-candescere, to become white. new lighting innovations (a mixed 1.4 ELECTROMAGNETIC RADIATION

21 blessing-they brought the 12-hour workday). The nineteenth century intro­ duced 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 oxy­ hydrogen flame. producing the limelight. which was used for "magic lanterns." and soon after mid-century for the theatrical appli­ cations that preserve its name to­ day. (The explosive nature of the gas. combined with the flammable scenery. made theatergoing some­ what 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 FIGURE 1.21 cord. As the current runs through obtained by just burning the gas. An AC carbon arc. Only one of the it. the filament becomes hot and ra­ and kept the gas light industry alive carbon electrodes would glow if the arc diates. Some radiation is in the vis­ into this century. (The improve­ were fed DC, as in the earliest arc lights. ible (Fig. 1.19) but most is in the ment is a result of the fact that Most of the light comes from the very infrared! You have undoubtedly felt these salts are not ideal black bod­ hot electrode tips. that light bulbs get hot. In fact an ies. Rather they tend to emit some­ incandescent bulb is only about 7% what more in the visible. thus mak­ effiCient in converting electricity to ing them more effiCient in pro­ each other and into the electrodes. visible light-the rest of the energy dUCing useful light. The purpose of give off 11ght. and further heat the goes into heat. We could get propor- the gas. then. is just to heat the carbon electrodes. In fact. over 90% mantle. so the gas can be less lu­ of the light comes from the incan­ minous and less smoky.) descence of these very hot electrode Filament The earliest electric light was the tips. This produces a very concen­ arc lamp in which a spark jumped trated light. While it is much too Support wires across two electrodes attached to a bright a light for the home. the car­ large battery. Arc lamps of any prac­ bon arc still is found in theatrical tical value had to await the devel­ spotlights. opment of big electrical generators The incandescent filament lamp in the mid-1800s. and shortly used today had to await the devel­ thereafter brilliant arc lights were opment of the mercury vacuum in wide use. In these lamps. an elec­ pump in order to produce the tric field is set up between two hot needed quality vacuum. The pump electrodes (here. carbon rods) that was produced in 1865 and by 1880 are separated by a narrow gap (Fig. Edison had his patent for the in­ 1.21). Electrons are emitted from candescent light (Fig. 1.22). En­ one electrode. pulled across the gap closed within a glass bulb there is a by the electric field. smash into the little coil of thin wire. thejUam.ent, Base air molecules in between. knock made of tungsten. because tung­ electrons off them. and create many sten can become very hot without charged atoms (ions), which in tum melting. The filament is about half FIGURE 1.22 are also accelerated by the electriC a meter long if unwound, and its field. All these charges smash into ends are connected to the lamp- CHAPTER 1: FUNDAMENTAL PROPERTIES OF LIGHT

22 tionately more visible radiation if end are connected to an alternatiIlj we heated the filament more, but current (AC) source. which drive the tungsten would then melt or the charges first one way and thel bum. To prevent such burning the opposite way. (In the Unite. some of the air is pumped out ofthe States. alternating currents g. glass bulb. (That's why the bulb through a complete cycle 60 times; goes "pop" when it breaks, and why second. so we have 60 hertz AC. they needed the vacuum pump.) Ac-­ The resulting electric field in th, tually, there is only a partial vac­ tube pulls some electrons off th uum in the bulb. It is filled with a electrodes. These electrons collid mixture of gases (argon and nitro­ with atoms. shaking them and th gen) that do not react appreciably charges on them. The whole pro with tungsten. These gases tend to cess is called a discharge. The os retard evaporation of the tungsten. cillation of charges on atoms occur, The evaporated tungsten deposits at the atoms' resonance frequency on the glass (you can see this dark­ and this frequency for simple atom: ening in an old bulb) and makes the Is mainly in the ultraviolet (wit] bulb dimmer, and the filament de­ some in the visible). velops mechanically weak, hot To make a "black light." you coa spots. When the filament finally the tube with material that absorb: breaks, the bulb is "burnt out"; the visible but transmits the ultra current can no longer flow. violet (UV). On the other hand, t. In newer lamps, called "quartz­ make visible light. the tube i: halogen" or "quartz-iodine" or coated instead with material tha "tungsten-halogen" lamps, the fila­ fluoresces. This way of making vis ment is surrounded by a quartz en­ ible Ught is so efficient that a 40 closure containing a Uttle iodine watt fluorescent lamp provide: gas (Fig. 1.23). The iodine picks up about 4 times as much visible Ugh any tungsten that has been evapo­ as a 40-watt incandescent bulb rated and redeposits it on the fila­ The fluorescent lamp is mud ment. This allows the lamp to oper­ cooler. hence wastes less energy ra ate at a higher temperature, which diating infrared. Further. by choos makes it more efficient since you ing different coating materials. ym get more visible Ught and propor­ can have fluorescent bulbs that giv, tionately less heat. Further, the off different colors. Thus. specia evaporated filament doesn't blacken lamps for growing plants indoor: the bulb. use a phosphor chosen to give I The relatively low efficiency of all spectrum of light similar to sun incandescent sources led, this cen­ Ught. or to match the resonance fre tury, to the development ofjluores­ quencies of chlorophyll. cent lamps,· the first departure FIGURE 1.23 We could make a more efficielli from the long historical precedent Tungsten-halogen lamp. Ught by using the Ught from tht of producing light by heating some­ discharge directly. without using c thing. In jluorescence, certain phosphor. The Ught from a dis­ substances (called phosphors) pro­ charge. however. has a frequenc) duce visible light when they absorb FIGURE 1.24 (and thus color) characteristic 01 ultraviolet ("black") light, and thus A fluorescent tube first makes UV light in the particular resonant system, make light without using heat. Sur­ an electric gas discharge and then here the atoms in the gas (see Secs. prisingly, ultraviolet radiation can converts most of the UV to visible light. 15.3 and 15.4). To make a useful be more easily produced effiCiently. A glass tube is filled with some gas Electrode Atom at low pressure, usually mercury va­ por (Fig. 1.24). Electrodes at the

*Latinfluere. to flow. But not of @0­ 0-­ current: fluorescence was first observed in the mineral fluorite (CaF2 1. which Phosphor coating was used as a flowing agent to help metals fuse together when melted. Visible 1.4 ELECTROMAGNETIC RADIATION

23 light, we choose atoms that have charged particles from the sun the receptors of our eyes respond: resonances in the visible, for exam­ strike molecules in our atmosphere. the visible. Figure 1.25 summarizes ple, mercury or sodium. The strong The radiation produced depends on some of the important things that coloration of the light emitted by the energy to which the charges are go on in and near this region of fre­ these atoms is avoided in high-in­ accelerated by the earth's magnetic quencies. At the top of this figure tensity discharge lamps, where and electric fields, as well as on the we indicate the visible region. Short high pressure or impurities molecules they hit. wavelengths (400 nm) look Violet broaden the range of frequencies (though we often refer to the short­ emitted, making a light somewhat wavelength end of the spectrum as more like broadband white. D. Visible electromagnetic blue-see Sec. 10.4A). As we in- The production of light due to radiation collisions of accelerated charged particles with atoms is not only a Well concentrate now, and for most FIGURE 1.25 of the rest of this book, on that tiny man-made phenomenon. The glow­ Visible light and its interaction with life. ing aurora borealis is essential­ part of the electromagnetic spec­ The frequencies (and wavelengths) of ly the same phenomenon. Here trum that can make the charges in light are marked along the top.

...... 1---- UV ----)10..,11-0..1--- VISIBLE ------­ IR ------i._ 1 I 1 I Frequency /I = 7 X 1014 Hz 3 X 1014 Hz Wavelength A = 400 500 600 700 nm Color = V BGYORI I 1

225 nm - .._----c-----Most of sun's radiation ------~Io 3200nm I 320 nm I 1100 nm 2300 nm I Absorbed by ----10-11....1----- ~ of sun's energy that 1.. Diminished strongly by .1.. Absorbed by H20, ozone (03) in reaches earth is here ------'M--10 H20 in atmosphere --1-011---- CO2, ozone (03) in upper atmosphere I atmosphere I I I~ All that's left ------l I lat 25 m under I I the sea : 1 r--- All that's left at 100 m under the sea I 320 nm 1 I "Hard UV" ------1 1 stopped by glass I I 1 Insect vision 1 ... :\ ~ ,., 1 Skin response (sun burn)~':! V : ~ Human day vision [Photopic] •. . il. I " Effectiveness for -s-----, 04 \: ' Human night vision [Scotopic) killing a bacillus \. \ ". \.

I I I I 1 300 400 500 600 700 nm 1400 nm 1900 nm I I I" Frequencies involved in "dark" chemistry ---_10­ I 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 CHAPTER 1: FUNDAMENTAL PROPERTIES OF LIGlIT

24 crease the wavelength, the color Notice that your skin is most sen­ while feigning madness. suggests changes to Blue, then Green, Yel­ sitive to UV of about 300 run wave­ that it is possible to get pregnant low. Orange. and finally Red when length. but that glass absorbs the from walking in the sun: the wavelength gets to the long­ UV below 320 run-we don't sun­ Hamlet:-Have you a daughter? wavelength end of the visible (700 burn through a window. Notice also Polonius: I have my lord. run). that hard UV. below 300 run, kills Hamlet: Let her not walk l' the sun: Most of the sun's radiation lies bacilli. but that the ozone in the conception is a blessing; but as your daughter may conceive,-frtend, look between 225 nm and 3200 nm (see upper atmosphere absorbs this to't. also Fig. 1. 19), however. not all of short wavelength UV. thus saving this penetrates the atmosphere and both bacilli and our skin from seri­ Light certainly seems to playa role reaches the earth's surface. -The ous damage. in almost everything! short wavelengths (below 320 nm) In the range 250-1400 nm we are absorbed by the resonances of find not only vision, but all the ozone in the atmosphere. the long other light-dependent processes wavelengths by water (above 1100 critical to life. because the frequen­ nm) and by carbon dioxide and cies of the resonances of chemical SUMMARY ozone (above 2300 nm). The result bonds occur in this range. Thus. at is that about half of the sun's radia­ the bottom of Figure 1.25 we show tion reaching the earth lies in the the absorption spectrum of chloro­ To see the light, it must pass from visible. phyll (actually of several different a source, to an object (possibly). In the center of Figure 1.25 we kinds combined). Since only the and then to a detector. Light trav­ have plotted curves to indicate how green part of the spectrum is not els at about 300.000 km/sec (in vac­ various systems respond to light of absorbed. it is reflected or transmit­ uum) and carries energy and m0­ different wavelengths. Thus. hu­ ted. so chlorophyll looks green. The mentum. It is a type of wave man daytime vision is most effec­ chlorophyll responsible for the pho­ (propagating disturbance), but is tive at about 555 run (yellow-green). totropiC· behavior ofplants absorbs unusual in that it can propagate Human night vision uses different only in the blue. Therefore, if we through a vacuum-it is an elec­ receptors, which have their maxi­ grow plants in red light only, with­ tromagnetic wave. An oscillating mum sensitivity toward the blue. out blue light, the other chloro­ charge creates a disturbance in the Actually, undervery intense sources, phylls wlll absorb light and the electric fteld (which descrihes the so intense that it feels warm, we plants will grow, but not toward the force on charged particles) as well can see in the infrared OR) up to as light. Also at the bottom of Figure as in the magnetic fteld. Electro­ high as 1100 nm. Further. we could 1.25 is the absorption spectrum of magnetic waves of different fre­ see in the ultraviolet (UV) except phytochrome-the enzyme that pro­ quencies are emitted and absorbed that the eye's lens absorbs UV. Peo­ vides the "clock" for plants, deter­ by resonant systems (whose re­ ple who have their lenses removed mining when they germinate. grow. sponse is greatest at the resonance (for cataracts) are sensitive doWn to flower. and fruit. according to the .frequency). about 300' nm. Insects, however. length of the night. It measures the Periodic waves are characterized are most sensitive to ultraviolet length of day by the amount oflight byfrequency (v. number of oscilla­ light. Since insects have little or no it absorbs in the red. (See the FO­ tions per second), wavelength (A, vision in the red and yellow. we can CUS ON Light, Life, and the Atmo­ separation between repeating use yellow lights as "bug lights." sphere after this chapter.) parts). amplitude (size or amount The yellow light provides useful il­ Light from sources other than the of oscillation). pol.arl.zation (direc­ lumination for our eyes, but the in­ sun may play a critical role in life. tion of oscillation), and th,e direc­ sects don't see it and therefore Many organisms, such as the firefly, tion ojpropagation (indicated by a aren't attracted to it. Conversely, to are bioluminescent-emitttng their ray). The attrtbutes of light corre­ attract bugs and zap them with own light as part of their mating spond to our sensations of color high voltage. we use blue or UV rites. (You can elicit a sexual re­ (frequency, period, wavelength). bulbs. sponse from a firefly with a flash­ brightness (amplitude), and the di­ Since most vertebrates have vi­ light, if you use the correct timing.) rection from which the light ap­ sion in the same range as humans, Humans, as you know. also find pears to come. insects can have an interesting certain types of lighting to be ro­ Visible light corresponds to a kind of protective coloring. In the mantic. Probably the most extreme very small range (wavelength 400 to visible, their coloring can be the effect of light on human sex life was 700 run) in the electromagnetic same as that of a poisonous insect proposed by Shakespeare. Hamlet. spectrum, which ranges from the so that birds will leave them alone. very short wavelength gamma rays but their UV coloring can differ and x-rays, through the ultraviolet from that of the poisonous insect so -Greek tropos, turn. Therefore (UV). the viSible. the Uifrared (IR). that no mistakes are made when phototropic means turning toward the to the very long wavelength radio they are looking for a mate. light. waves. PROBLEMS

25 Black bodies emit a characteris­ frequencies for hot objects, lower ing in the UV, and encased in a tic black-body spectrum in which frequencies for cooler objects. In­tube With a phosphorescent coat­ more energy is emitted from hot ob­ candescent electric lights consist ing, which converts the UV to visi­ jects than from cooler ones. Also, of hot, gIowtngjilam.ents, whlleftu­ ble light. the peak emission occurs at higher orescent lights consist of gas glow­

PROBLEMS

PI Briefly I ist some of the properties of bridge's main span was about 850 draw a wave of half the frequency light you have learned so far (e.g., meters. The wavelength of the waves and the same amplitude, and label it how it travels, its speed, etc.). set up in the bridge was also 850 Ii new wave." P2 When you look at the daytime sky, meters. Which of the two pictures in P14 A light wave traveling in the vacuum away from the sun, it looks blue. the figure represents more nearly the comes to a plate of glass. On Explain where this light comes from shape of the bridge that a snapshot entering the glass, which, if any, of (Le., what is its source and how does taken at the time would show? the following increase, decrease, it get to your eyes?). P9 Which of the following common remain unchanged: the frequency of P3 How do we know that light travels everyday periodic phenomena are the wave, its wavelength, its speed? through a vacuum? examples of resonance? (a) A cork PIS What is the frequency of your P4 Brand new windowpanes and mirrors bobbing up and down in waves in heartbeat while you are resting? Give often come with pieces of tape on the water. (b) Grandparent rocking in units with your answer, and tell how them. Why? his or her favorite rocking chair. (c) A you measured it. P5 (a) Which of the following are self- singer hitting a high note and P16 light is an electromagnetic wave. luminous objects (that is, we see shattering a glass. (d) The people at a Does that mean that there must be them by their own light, rather than rock concert stomping their feet in electrons present in the wave for it to light reflected from them)? The sun, rhythm with the music. (e) Floors of propagate? Explain. the moon, a cat's eye, a television the auditorium vibrating and cracking P17 Consider a radio wave and a visible picture, a photograph. (b) In the case as a result of the audience stomping light wave. Which has a higher of the examples that are not self- at the rock concert. (f) A rattle in frequency? Longer wavelength? luminous, what is the source of light your car while idling, which stops as Longer period? Higher speed in that allows you to see them? the motor increases speed. vacuum? P6 Give an example of a resonance. In PI0 Your car is stuck in the snow, and P18 (a) The color of light corresponds (in your example, who (or what) you can't push it hard enough to get general) to which of the following supplies the energy? (Example: A it over a hump of ice. It sometimes (there may be more than one parent pushing a child on a swing. hel ps to rock the car back and forth. answer): frequency, speed, The parent supplies the energy.) Apply some of our discussion of wavelength, intensity, polarization? P7 At Cornell, there used to be a narrow vibrating systems to explain why this (b) The brightness of light suspension footbridge. If you walked helps. corresponds (in general) to which of across it on a windless day, it P11 The figure below shows a picture of the above list? scarcely swayed at all. However, if a wave. Use a ruler and measure its P19 (a) As a black body becomes hotter, you jogged across it at just the right wavelength in centimeters. does it emit more or less radiation? speed, you could get it swaying P12 Redraw the wave of problem P11, (b) Does it radiate predominantly at a wildly. (That's why it's not there any and label it "old wave." On top of it, higher or lower frequency? more!) Explain why there should be draw a wave of half the wavelength P20 Identify the type (e.g., UV, visible, this difference. and twice the amplitude, and label it IR, etc.) of electromagnetic radiation P8 On November 7, 1940 at 10 A.M., a "new wave." of each of the following wavelengths 47-mph wind set the Tacoma P13 Redraw the wave of Problem P11, in vacuum: 600 nm, 300 nm, 1400 Narrows Bridge into (torsional­ and label it "old wave." On top of it, nm, 21 cm, 0.1 nm, 3 km. twisting) vibration. The length of the

(a)

(b) ClfAPTER 1: FVNDAMBNTAL PROPERTIES OF LIGHT

26

HARDER PROBLEMS PH7 Describe the physics of a standard lower than middle A? (As you go incandescent light bulb. (a) What down an octave, you divide the PHI How could you use a laser beam in a charges wiggle? What causes them to frequency in half.) (c) Why do you dark room to determine the amount wiggle? (b) Why is there a partial think organs have big pipes and of dust in the air? vacuum-in the bulb? What gas is small pipes? PH2 What is the color of the sky on the present inside? Why? (c) Why don't PM7 The figure shows (idealized) the way moon, where there is no atmosphere? manufacturers simply make bulbs the Tacoma Narrows Bridge vibrated Why? that last forever? (Sure, they have to from 8 to 10 A.M. on November 7, PH3 When soldiers march across a bridge, stay in business, but what physical 1940, shortly before it collapsed. The they are told to break ranks. That is, constraint mitigates against making a length of the bridge's main span was they are told not to walk in step with bulb that will last forever?) 850 m. Each up and down oscillation each other. Think about the Walls of PH8 Why can't we see x-rays directly? lasted seconds. (a) This means that Jericho and the Tacoma Narrows 1f the frequency of the oscillations was Bridge, and explain why the soldiers ("Because our eyes aren't sensitive to x-rays" is correct, but not a suitable = 0.6 Hz. Show how one derives should break rank. v answer. Why aren't our eyes this result from the data given above. PH4 Cheap loudspeakers often have a sensitive to x-rays?) (b) What was the wavelength of the resonance in the sound frequency region that we can hear (roughly SO PH9 Objects A and B are illuminated by a waves set up in the bridge? Give the reason for your answer. (c) What to 20,000 hertz). You get a much light source that produces only larger output (sound) at the resonant visible radiation. To the eye, A looks was the speed of the waves? (Show your calculation.) frequency, for a given input, than bright while B looks dark. Under the you do at other frequencies. Better same illumination, a photograph is speakers don't have such resonances. taken of the two objects, using film Why is it bad to have such a sensitive only to infrared radiation. In resonance? (Think about what you the picture, B shows up brighter than would hear as someone played a A. Explain how this could be so. muscial scale.) PHS (a) What is an electric field line? MATHEMATICAL PROBLEMS (b) What do the arrows on an electric PMI How long does it take light to travel field line convey? (c) How can one from one of Galileo's hill tops to PM8 In Washington, D.C., radio station physically determine whether an another, 1.5 km away? WRC broadcasts on AM at 980 kHz. electric field is present at a given PM2 When a laser beam is sent to the Station WET A broadcasts on FM at position? moon, reflected there, and returned 90.9 MHz. What are the wavelengths PH6 The figure shows some wavefronts of to earth, it takes 2.5 seconds for the (approximately) of the radio waves a light wave. Redraw the figure and round trip. Calculate the distance to used in each case? (Give the units draw three different light rays on it. the moon. you use: e.g., meters, feet, cubits, PM3 A rocket probe is sent to pass close versts, etc.) to the planet Jupiter. Suppose that at PM9 The range of wavelengths, in the time the rocket reaches Jupiter, vacuum, of visible light is about 400 Jupiter is 630,000,000 kilometers nm to 700 nm. What range of from Earth. How long will it then frequencies does that correspond to? take a radio signal to travel from the PMIO What is the frequency of 575 nm rocket to Earth? (yellow) light? PM4 A radio signal takes about 2.5 x PMII Consider a wave of wavelength 2 cm 10-3 seconds to travel from Boston and frequency 1 Hz. Cou.ld this be to Washington, D.C. Calculate the an electromagnetic wave traveling in distance between these two cities. vacuum? Why? PMS (a) What is your height in meters? PMl2 If a black body is heated to a (b) Express the result of part (a) in temperature T (in degrees Kelvin, millimeters and in nanometers. K = ·C + 273), the most intense (c) Which of these three units is more radiation is at wavelength A (in reasonable to use for your height? meters), where Explain your choice. A x T = 2.9 X 10-3 PM6 (a) The note that orchestras tune to, middle A, has a frequency v = 440 (a) Find A for room temperature Hz. The speed of sound in air is bodies (take T = 290 K). (b) What is about v = 330 m/s. What is the the frequency of this radiation? wavelength of middle A? (b) What is (c) What kind of radiation is this the wavelength of the A one octave (e.g., visible, IR, UV, x-ray, etc.)? ,

fOCUS ON . ..

Ught, life, and the atmosphere

That our atmosphere is so beneficent as ferment, you know that this process to transmit visible radiation from the produces carbon dioxide (C02), These sun, but absorb killing ultraviolet, is a organisms did just that, pumping more consequence of its history. We will CO2 into the atmosphere than currently outline its development so that we may is there. The presence of the CO2 then see the interplay of light, life, and the allowed new organisms to develop that atmosphere. could live by photosynthesis.· These new In the early days of the earth's development, the atmosphere did not sugar -+ CO2 + alcohol + energy contain many of the key ingredients of life. There was no oxygen (02 ) and This process spends its "capital" (sugar) t9 '-produce energy, Once. the sugar is used up, consequently, no ozone (03), Nor was the process stops, It is a very inefficient there carbon dioxide (C02), As a result, process. Only 5% of the chemical binding the ultraviolet (UV) radiation reached the energy in the sugar is released, and half of surface of the earth quite easily, much that is lost as heat. (Fermentation tends to more so than now (Fig. FO.1). This UV heat up the surroundings, as anyone who provided just th,eright frequencies (i.e., has made yeast bread will have noticed.) it excited resomlflces) for various organic The half not lost is stored in the molecule molecules present in the seas to ATP (adenosine triphosphate, the biological combine into the first living organisms. "energy currency"), which then, if there is These primitive organisms had a better raw material available, offers the energy for chance for survival than they would have new cell production. now, since there were no other ·Greek synthesis, putting together, hence organisms to eat them, and no oxygen to putting together by I ight. Photosynthesis is oxidize them. Lacking oxygen, the the process: organisms could only get the energy they CO2 + H20 + light -+ sugar + O 2 needed to live by the process of fermentation.· If you've seen beer 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 'Latin fermentare, to boil. This process from the sun continuously. That is, at this extracts energy by rearranging organic point life developed a (very efficient) solar molecules. For example: battery.

FIGURE FO.t r------­ Interaction of light and life. I I I I ~OG~s~ I I I I I I I IL ___ Cellular respiration

t­ i 1 organisms removed some of the CO2 , energy stays inside the CO2 (or glass) fixing it in organic forms, and at the barrier and the earth gets hotter.· But same time produced molecular oxygen the story is more complicated. Although (02), which entered the atmosphere, atmospheric CO2 continues to increase, with two critical effects. One was that a cooling trend seemed to appear in the sun's radiation converted some of 1950. This may be due to other forms of this O 2 into 0 3 (ozone). The ozone, as pollution in the atmosphere that may we've seen (Fig. 1.25), blocked the reflect the incoming visible sunlight (like antibiotic UV from the earth's surface, metal foil, instead of glass) so that less thus permitting living organisms to leave energy reaches the earth in the first the water for the land (about half a place. That is, there are many other billion years ago). This would not have important molecules in our atmosphere helped much unless there was a way the besides CO2, such as nitrous oxide, organisms could produce energy more methane, ammonia, sulfur dioxide, and efficiently. The process of fermentation even trace constituents. An important produced barely enough energy for question is whether they reflect the survival; none was left for motion. But sunlight (preventing the energy from the second effect of the O 2 in the reaching the earth's surface), or transmit atmosphere was to allow the much more the sunlight (allowing the energy efficient process of cellula, respi,ation.* through), or absorb the sunlight (thus This process uses the O 2 and replenishes heating up the atmosphere). The the CO2 • Eventually these two balancing greenhouse effect shows the processes, photosynthesis and cellular complication of transmission at one respiration, came into equilibrium, frequency but not at another. keeping the atmosphere roughly in its Another 'critical constituent is the present form for ages. ozone, which protects us from the hard, Currently, however, atmospheric CO2 killing UV. It is unclear how sensitive the is increasing, largely because of the ozone concentration is to various man­ destruction of the forests and the made effects such as supersonic burning of fossil fuels, which have raised transports, fluorocarbons (commonly the CO2 content in the atmosphere by used in aerosol spray cans), atmospheric about 15% since 1850 (over 5% since nuclear testing, or even agriculture (with 1958). This is thought to be responsible its effects on the nitrogen cycle). for the warming tr~nd in northern However, a modest change in the ozone latitudes, from 1900 to 1940, by the content of the atmosphere can greenhouse effed. The idea is that CO2, significantly change the amount of hard like glass, lets the visible light through. UV getting through, since most of it is The earth absorbs this, warms up, and currently blocked. Too much of this UV radiates in the IR. But CO2 (again like can cause mutants by altering the DNA glass) doesn't let the IR through, so the of which our genes are made, produce skin cancer, and do other ecologically more complicated things. Alternatively, "Latin respirare, to breathe. This is the way too little UV would prevent our bodies we get most of our energy. The process is: from properly metabolizing calcium. The effects of human activity on sugar + O2 ..... CO2 + H20 + energy atmospheric constituents, and their This is the same process as burning sugar effects in turn on climate and ecology over a flame, but we can do it at body through the interplay of light with the temperature in a more controlled fashion. It atmosphere, constitute one of the more is far more efficient than fermentation, exciting fields of study today. The capturing over 85% of the chemical binding consequences are, literally, energy in the sugar. Further, the by-products are not harmful, unlike fermentation, which breathtaking. 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 'Actually, "greenhouse effect" is a bad eventually paint the Mona L.sa. Yeast, on name. The major effect of an actual the other hand, living by fermentation, do greenhouse is to prevent the rising hot air not lead very active lives. from escaping.

28 Principles of Geometrical Optics

CHAPTER 2

does not bend around corners. We Those that are blocked don't reach 2.1 think of the light as traveling in the screen, so the places where INTRODUCTION straight lines as long as it is left they would have hit are dark-a alone (Fig. 1.4). This straight-line shadow. We can figure out - propagation enables us to locate the the shadow's location by drawing How do we so easily decide where to beach umbrella so its shadow falls straight lines from the pOint source place a beach umbrella to keep the on our eyes. to the edge of the obstacle and con­ sun out of our eyes, without worry­ tinuing them to the screen. These ing about the electric field, the lines separate the regions where the wavefront, the wavelength, and the 2.2 rays reach the screen from the re­ frequency of the light? The answer SHADOWS gion where they are blocked. The is that, for many simple problems it resulting shadow resembles the ob­ is suffiCient to concentrate on the stacle, but it is of course only a flat -To cast shadows you need light light rays (Fig. 1. 17), the lines that (two-dimensional) representation of describe in a simple geometric way from a fairly concentrated source, the object's outline. Nonetheless, we the path of light propagation. Geo­ such as the sun. The best shadows can easily recognize simple shapes, metrical optics is the study of are cast by light that comes from such as a person's profile. Before those phenomena that can be un­ just one pOint: a point source, photography, it was popular to derstood by a conSideration of the which is an idealization, like a ray, trace people's shadows as silhouette light rays only. Geometrical optics that can only be apprOximated, for portraits (Fig. 2.1a). Today's x-ray is useful as long as the objects with example, by a small light bulb or pictures are just shadows in x-ray which the light interacts are much candle. (Even a source as large as larger than the wavelength of the the sun or a giant star can approx­ light. As our beach umbrella is imate a point source if it is far about a million times larger than enough away.) You also need a the wavelength of visible light. geo­ screen, such as a flat, white sur­ FIGURE 2.1 metrical optics is a very good ap­ face, which redirects incident light (a), (b) Various uses of shadows. proximation for this and most other into all directions, so that you can (c) Silhouette of one of the authors. everyday objects. For smaller objects see the shadow (the light from the Etienne de Silhouette (1709-1767), France's finance minister for a year, was the beam will not propagate in only surrounding area must enter your deposed because of his stinginess over one direction, but rather spread out eye). court salaries. He used cheap black in all directions--much as sound If an obstacle blocks some of paper cutouts in place of conventional waves, with wavelength of about a the light rays headed for the screen, decorations in his home and invented a meter, spread out around obstacles the light rays that are not blocked technique for making paper cutout shadow portraits to raise money. When in the street. still reach the screen and make he died, he was penniless and destitute, In geometrical optics, then, light that part of the screen bright. a shadow of his former self.

(a)