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1 A Walk Through the Electromagnetic Spectrum K. Morgan, Student Member, IEEE Paper for ENGR302 Professor Paulo Ribeiro May 15, 2002 Abstract – This paper explores the fundamental mathematical principles behind electromagnetic waves and also the various natures of light. This theory is presented to give a background for a discussion of the different sections of the electromagnetic spectrum, including its applications, properties, and sources. interact. These equations are fundamental for an understanding of electromagnetic waves, so they will be expanded on below. I. INTRODUCTION Light today plays an important role in a vast array of technologies. But light is not limited to what we can see with the eye. In fact, the light that we see is a very small portion of the wide range of light in nature. All light has one thing in common: it is all electromagnetic waves. When charges move, their movement is communicated to the rest of the universe via an electromagnetic wave. So all light, from radio, to visible, to x rays, to gamma rays, are all variants of the same thing. This paper aims to explore a little of the fundamental theory behind the electromagnetic waves that make up the spectrum. Then it will take a walk through the spectrum starting with the low-frequency radio waves and ending up at the very high-frequency gamma rays. At each stop along the walk, this paper will explore the various ways mankind has found applications for that part of the spectrum and also how that section has manifested itself in nature. It is important to realize that the divisions of the electromagnetic spectrum are artificial and are only for organizational purpose. In reality, the spectrum that has also been called “Maxwell’s rainbow” is continuous and has properties that span over 25 orders of magnitude. II. THE ELECTROMAGNETIC WAVE The effects of electricity and magnetism were observed as far back as the ancient Greeks. They knew that if amber was rubbed with fur, it would attract bits of straw. They also saw that pieces of a magnetic mineral called lodestones repelled and attracted one another. It was not until 1820, however, that the Danish physicist Hans Christian Oersted realized that electricity and magnetism were related when he found that an electric current in a wire could deflect a compass needle. Until then, the two sciences had been developing separately. Around the 1870s, they became completely intertwined when James Clerk (pronounced “clark”) Maxwell (Fig. 1) presented a mathematical electromagnetic theory. Maxwell’s genius shines through the elegance of his four equations, and they have held through every test to which they’ve been subjected. They completely describe the way electricity and magnetism Fig. 1 – James Clerk Maxwell A. Gauss’ Law for Electricity Maxwell’s equations can be written either in integral or differential form. Both forms are equivalent and provide useful insights. Boldface symbols represent vectors that have components in all three directions. D dS dv S v (1) and in differential form, D (2) In (1) and (2), D is electric flux, S is a vector normal to the surface S, v is some volume, and represents spacecharge density. In words, the equation states that the only source that produces a nonzero flux through a closed surface is free electric charge. The form of (1) makes it clear that the amount of electric flux passing through a closed surface S is equal to the total charge in the volume enclosed by S. The form of (2) says that the divergence of the electric flux at a point is equal to the charge density there. 2 B. Gauss’ Law for Magnetism B dS 0 S (3) and in differential form, B 0 (4) In (3) and (4), B is magnetic flux, and S is a vector normal to the surface S. In words, the equation states that no analog of free electric charges exists for a magnetic field (there are no magnetic monopoles). The form of (3) makes it clear that the net magnetic flux through any closed surface is zero. The form of (4) says that magnetic flux does not diverge from any single point. C. Faraday’s Law B dS S t E dl C (5) and in differential form, E B t (6) In (5) and (6), E is the electric field, l is a vector on the contour C, B is the magnetic flux, and S is a vector normal to the surface S. In words, the equation states that a timevarying magnetic field is a source of an (evidently timevarying) electric field. The form of (5) makes it clear that a changing flux through a surface S gives rise to an electric field on the contour of that surface. The form of (6) makes it clear that a changing magnetic field at a point produces a nonzero curl of E (an E that could produce a current in a small loop). Faraday’s law is of profound importance since electric generators are based on the principle of electromagnetic induction. D. Ampere’s Law C currents and a time-varying electric field. The form of (7) makes it clear that current and displacement-current (timevarying electric flux) passing through a surface S give rise to a magnetic field on the contour of that surface. The form of (8) says that current and displacement-current at a point produce magnetic field loops at that point. Ampere’s law is also of profound importance since electric motors rely on the magnetic fields produced by currents in a wire. E. The Uniform Plane Wave The essence of any electromagnetic radiation (light) is the traveling electromagnetic wave. In this section, the equations describing a light wave are derived from Maxwell’s four equations. In a uniform plane wave, all electric and magnetic field lines are uniform throughout any plane where z is constant. A strict uniform plane wave doesn’t actually exist since all waves exhibit some curvature. However, at points far from a source of light (observing a star from earth), the wave is nearly uniform. First, two assumptions are made about wave motion in free space. One, there are no charges in the region of the traveling wave, and two, since there are no charges, there is no current density (there is displacement current, however). With these assumptions, Maxwell’s equations can be written as, D 0 (9) B 0 (10) B t D H t E (11) (12) Notice that and J are both zero since there is no charge. Now, let us assume that an electric field is changing sinusoidally and has only an x component. E E x E ( x, y, z ) cos(t ) (13) Using Euler’s identity and the standard phasor notion of electrical analysis, we can write (13) as, D H dl J dS S t (7) and in differential form, H J D t E s E xs a x (14) Using the notation of (14), we can rewrite (9), (10), (11), and (12) as, (8) In (7) and (8), H is the magnetic field, l is a vector on the contour C, D is the electric flux, J is the current density, and S is a vector normal to the surface S. In words, the equation states that the sources of a magnetic field are electric Es 0 (15) Hs 0 (16) E s j 0 H s (17) H s j 0 E s (18) 3 The wave equation can be produced with just a little vector analysis, E s ( E s ) 2 E s j 0 H s 2 0 0 E s 2 E s c 1 00 and the wavelength of the electromagnetic wave is 2 c k0 f Therefore, 2 E s k 02 E s (19) where k0 is the free space wavenumber, defined as With a solution for Ex, a formulation of the magnetic field can be found from (17). H y ( z, t ) E x 0 k 0 μ0 ε 0 A solution of (19) is given by E x ( z, t ) E x 0 cos(t k 0 z ) (20) 3 10 8 m/s 0 cos(t k 0 z ) 0 (21) Fig. 3 is a visual representation of (21). It can be seen from (21) that the oscillations of the magnetic field are in phase with the electric field oscillations but are rotated 90 in space. Fig. 2 is a visual representation of (20). The traveling wave nature of light can be deduced from this equation. Since is the radian time frequency, it can be seen that at a particular point in space, the wave repeats itself over time. That is, if one were to watch a particular point on the wave, the electric and magnetic components would oscillate at the frequency 2f . It can also be seen from (20) that the wave repeats itself in space. That is, if one were to take a “snapshot” of the wave at a particular instant, the electric and magnetic components would oscillate through space at a frequency k0. Fig. 3 Obviously, energy is transferred with a traveling electromagnetic wave. Similar to the definition of power in electrical analysis is the power of an electromagnetic wave, known as the Poynting vector, P Fig. 2 Other important information can also be gleaned from (20). First, it can be seen that the velocity of light in free space is 1 EB 0 (22) Note that the Poynting vector points in the direction of power transfer as well as the direction of the traveling wave. In (22), B can be put in terms of E and the power can be averaged to provide a formula for the intensity of an electromagnetic wave, I 1 2 E rms c 0 4 F. A More Qualitative Approach While the rigorous mathematical derivation of the wave equation contains useful insights and shows the validity of Maxwell’s equations, it doesn’t give a very intuitive idea of electromagnetic wave propagation. It is instructive for visualizing a traveling wave to look at a more qualitative approach at how Maxwell’s equations imply wave propagation. First, we will assume that a wave already exists as shown in Fig. 4. slightly larger than B on the left so that the induced electric field opposes the change in E. Fig. 6 Fig. 4 Next, let us focus at the point on the wave in the gray shaded circle (Fig. 4). At the instant in time and the particular point in space shown, the magnetic field B is decreasing (if the wave were to move slightly in the x direction, B would be slightly smaller). Now let us draw a very small rectangle around this point as shown in Fig. 5. Fig. 5 Due to Faraday’s law of induction [(5)], a nonzero curl will be induced. That is, at the point where B is decreasing, a small electric field loop is induced. Moreover, the electric field on the right side of the small rectangle is slightly bigger than the field on the left side. This is because the induced electric field is in the direction so as to produce a magnetic field (out of the page) that opposes the changing B. The same argument can be made with the roles of the electric and magnetic fields reversed. Suppose E is decreasing at a point as shown in Fig. 6. According to Ampere’s law [(7)], the changing E field induces a magnetic field. B on the right side of the small rectangle is Thus, it can be seen that the traveling electromagnetic wave “rides” on itself. A changing electric field induces a changing magnetic field. That induced magnetic field then induces a changing electric field. That induced electric field then induces another magnetic field, and so on. It sustains itself and can, in theory, travel forever. An electromagnetic wave is different from all other kinds of waves in that it doesn’t require a medium to travel through. We are able to see stars because electromagnetic waves travel many light years through the vacuum of space. It is important to note that the wave as seen in Fig. 4 does not exist like that as a single “ray” of light. According to Maxwell’s equations, such a ray by itself is impossible because at each point on the ray, electric and magnetic field lines have a nonzero divergence (they are coming out of the line). This is contrary to both (9) and (10), which state that the divergence of E and B is zero. Thus, one should not think of pictures of an electromagnetic wave as in Fig. 4 as a single ray of light. Rather the picture in Fig. 4 is meant to represent the way E and B vary on a single line in an entire field of varying electric and magnetic field lines. A picture of this could be seen by taking the wave in Fig. 4 and rotating it through every point in space. The key concept to realize is that the electric and magnetic field lines are part of closed loops of force that extend throughout space. G. The Nature of Light Maxwell’s equations describe mathematically what is actually a very complex process that is difficult to understand. In fact, physicists today don’t have a completely clear picture of the nature of light. Experiments have shown that light behaves according to three separate paradigms. The first is that light is an electromagnetic wave, the second is that light is a stream of photons, and the third is that light is a probability wave. Only one paradigm doesn’t explain all the observed phenomena associated with light. Thus, physicists say that light is all three paradigms simultaneously. The above derivations using Maxwell’s equations show how light can be though of as an electromagnetic wave. It was Thomas Young, however, who first proved that light is a wave with his famous double-slit experiment in 1801. As 5 shown in Fig. 7, incident light that can be considered a uniform plane wave strikes the first plate with a single slit. The single slit can then be thought of as a point source of light. The light from this source travels through the two slits on the other plate producing two more waves that interfere with each other. The result is an interference pattern (variations of intensity) on the screen. This result can be explained only if the light travels as a wave. The wave theory of light seems to best describe lower frequency light. Finally, light can be described as a probability wave. This aspect of light is probably the strangest and the farthest away from everyday experience. If a photon detector were to be placed on the screen in Fig. 7, it would be seen that photons strike the detector at random intervals. Thus, the intensity of the light at a specific point can be though of as a probability that a photon will strike that point. An even stranger effect of light is that if instead of a wave striking the double-slit plate in Fig. 7, a single photon were fired from the point source, an interference pattern like that shown in Fig. 9 would still build up on the screen. Although the single photon can only travel through a single slit, it still seems to be aware of the presence of the other slit, so it interferes with itself. Fig. 7 Fig. 9 As the frequency of light increases to that of ultraviolet and x rays, the photon theory of light seems to make more sense than the wave theory does. At these frequencies, light seems not like a wave, but like tiny packets of energy called photons. In the photoelectric experiment as shown in Fig. 8, it can be seen that light of a certain minimum frequency is not able to knock electrons out of the target T no matter how intense the incident light is. This is due to the fact that the electrons need a certain minimum energy to be knocked out of their orbitals. The energy of a photon doesn’t depend at all on the intensity of the light it travels in; its energy is given by E hf where h is Planck’s constant and f is the frequency. Increasing the intensity of light only increases the number of photons present. III. THE ELECTROMAGNETIC SPECTRUM Fig. 8 The previous section of this paper explored the concept of the electromagnetic wave. Maxwell’s equations allow for waves with extremely long and extremely short wavelengths (and all lengths in between). Collectively, this continuous range of wavelengths is known as the electromagnetic spectrum. Our modern-day electromagnetic spectrum as seen in Appendix A is a result of centuries of discoveries. In 1665, Francesco Grimaldi claimed that light was a wave. Gradually, forms of radiation near visible light (infrared and ultraviolet) were discovered. After the introduction of Maxwell’s electromagnetic theory, physicists realized the possibility of much longer and much shorter waves. Heinrich Hertz soon discovered longer waves in the 1880s, and then Wilhelm Roentgen and others discovered shorter waves in the 1890s. This section aims to explore a very small portion of the information scientists know about our current electromagnetic spectrum. A. Radio Fueled by Maxwell’s electromagnetic theory, Heinrich Hertz (Fig. 10) discovered and transmitted radio waves in 1887. It was M. G. Marconi, however, who came up with the idea of using radio waves for communication. Thus, the ever-popular radio was born. Radio continues today to have a wide array of applications. In fact, the radio section of the electromagnetic spectrum extends farther than any other section, and it is the most regulated. Because of its use in communication, the radio spectrum has been tightly 6 regulated as shown in Appendix B. Fig. 12 Fig. 10 – Heinrich Hertz The frequency of radio waves ranges from about 10 3 to 10 Hz, and the wavelength from about 104 to 10-3 m. Fig. 11 shows that these waves range from about the size of a mountain to the size of a period on a page. The energy of radio photons ranges from about 10-30 to 10-23 J. Thus, radio waves are very low-energy electromagnetic waves. 10 . A period Mountains Radar, which stands for radio detection and ranging, is one of the most important applications of the radio spectrum. It was developed by the British around the 1930s for use in World War II. When the resonant-cavity magnetron was invented, radar with very short wavelengths (microwave) became possible. Instead of radar, it was called LIDAR for light detection and ranging. In a radar system, a transmitter produces a radio wave. When the wave strikes distant objects, part of it is reflected back to where it was transmitted where it can be detected. Because the radio waves have a finite velocity, the time it takes for the wave to return can be measured and used to determine how far away the object is. Humans are not the only source of radio waves. Many objects in the universe emit electromagnetic radiation in the radio spectrum. In fact, an organization called SETI (Search for ExtraTerrestrial Intelligence) constantly monitors the radio waves coming from space hoping they can “listen in” on radio transmissions from other forms of life in the universe. Radio astronomers use very large telescope arrays to observe radio from space. Fig. 13 is an image of the Crab Nebula; it is caused by the radio emission from neutral hydrogen atoms. These arrays can be groundbased because there is a very large atmospheric window for radio waves as shown in Appendix C. Fig. 11 All manmade radio waves can be generated with variants of the system pictured in Fig. 12. As shown, an energy source excites an LC oscillator, which induces an AC signal that travels the transmission line to the antenna. At the antenna, charge oscillates back and forth giving rise to changing electric and magnetic fields. These changing fields travel outward from the antenna as an electromagnetic wave. The frequency of the wave is 1 / LC . Antennas need to be approximately the same dimensions as the wave they are intended to produce, so some antennas are many kilometers long and some are small enough to fit in an integrated circuit. One reason radio is used so heavily in communications is that radio waves reflect off the ionosphere, the part of the earth’s atmosphere composed of charged particles. Because of the reflective properties of this layer, radio signals can be broadcast to points far away from the source. Fig. 13 B. Microwave The usefulness of microwaves was discovered by accident in 1945 by the American engineer Percy Le Baron Spencer at Raytheon. While working with radar (which can also be in the microwave range), he found that food in his 7 pocket would heat up when he was struck with radar radiation. The concept was quickly applied commercially, and the microwave oven was born. The optimal frequency for heating food turns out to be around 2.45 GHz, which is a wavelength of about 12.2 cm. The inside dimensions of a microwave oven are even multiples of 12.2 cm so that the waves constructively interfere to deliver more power to the food being heated. Microwaves heat food because they are the right frequency to be able to break bonds between water molecules. Molecules in water are effectively tiny dipoles. As a result, they tend to “stick” to one another. When these bonds are broken, energy is released and contributes to the temperature of the water. Microwaves cause the tiny dipoles to rotate (Fig. 14), thus breaking bonds with other water molecules. The temperature of the water increases and heats the food. Microwave ovens are able to heat food faster than a convection oven because microwaves can penetrate into the food. C. Infrared In 1800, William Herschel (Fig. 16) wanted to measure the temperature of the different colors of the visible spectrum. He found that the hottest part of the spectrum was actually where there was no color at all. The region he was measuring was what is now known as infrared. It is called infrared because it is “below” red visible light on the spectrum. Fig. 16 – William Herschel The frequency of infrared waves ranges from about 1010 to 1014 Hz, and the wavelength from about 10-3 to 10-6 m. Fig. 17 shows that these waves are about the size of cells, which is one reason why skin is able to detect infrared radiation as the sensation of heat. The energy of infrared photons ranges from about 10-23 to 10-19 J. Fig. 14 Microwave radiation is also observed coming from space. In 1965, scientists working on a radio telescope at Bell Laboratories noticed a strange microwave signal causing background noise in their telescope. It was later determined that this signal was radiation remnants of the Big Bang, and it was termed CMB for Cosmic Microwave Background. A picture of this background radiation is shown in Fig. 15. Fig. 15 Cells Fig. 17 Infrared radiation is produced by thermally excited atoms and molecules. Thus, anything that is above absolute zero will emit some infrared energy. Infrared has found applications in remote controlling and wireless data communication. Some light emitting diodes will produce light in the infrared region. This is useful because an infrared signal can be sent just as a signal would using visible light, but the infrared signal is invisible to humans. Infrared has also been used to image the clouds in the earth’s atmosphere. Meteorologists are able to get better cloud information using infrared and visible rather than just visible light. Infrared light is also used in determining types of chemical bonds. Parts of the universe are above absolute zero, so space is of course a source of infrared waves. Fig. 18 is an infrared image of the Crab Nebula. These images must be taken from a satellite because most of the infrared radiation from 8 space is absorbed by the earth’s atmosphere (see Appendix C). Fig. 18 Fig. 19 D. Visible The frequency of visible light is of the order of 10 14 Hz, and the wavelength about 10-6 m. Thus, visible electromagnetic waves are near the sizes of cells as shown in Fig. 17. While visible waves make up a very small portion of the entire spectrum, they are the most important to humans because of the amazing detection instrument called the eye. The energy of visible photons is about 10 -19 J. The concept of light reception and perception in the eye is not completely understood, but scientists do have some idea of how it works. Visible waves coming into the eye are focused onto the retina (Fig. 19), which contains different kinds of cells capable of converting the incoming light to a chemical signal to be sent along the optic nerve. The outer segment of the receptors in the eye contain photopigment molecules. When a photon strikes one of these molecules, the molecule undergoes a shape change called isomerization. There are four types of receptors: 1. Rods, which don’t detect color, but are used to detect lowintensity light. 2. L-receptors (for long wavelengths) are most sensitive to red light. 3. M-receptors (for middle wavelengths) are most sensitive to green light. 4. Sreceptors (for short wavelengths) are most sensitive to blue light. The color receptors are also known as cones. The atmospheric windows chart in Appendix C shows why evolution decided that the eye should see visible light. As can be seen, there is a small window that allows the sun’s visible radiation to reach all the way to the earth’s surface. An interesting question to ask is “why is the sun yellow”? The primary law governing blackbody radiation is the Plank Radiation Law [(23)] where is the wavelength, T is the absolute temperature, h is Planck’s constant, c is the speed of light, and k is Boltzmann’s constant. E ( , T ) 2hc 2 1 5 hc / kT e 1 (23) Since the surface temperature of the sun is about 5800 K, it emits radiation at the intensities and wavelengths shown in Fig. 20 according to (23). Notice that the sun produces electromagnetic waves of many different wavelengths, but the radiation is most intense at about 5000 Angstroms, which is the wavelength of yellow light. Fig. 20 By way of comparison, the Crab Nebula pictured in Fig. 13 and Fig. 18 is shown in visible light in Fig. 21. 9 Fig. 21 E. Ultraviolet The discovery of ultraviolet light came about in a story similar to that of infrared. In 1801, Johann Ritter (Fig. 22) was trying to find out which color of light caused the quickest chemical reaction of silver chloride. To his surprise, he found that light past the visible violet light caused the most vigorous reactions. Thus, ultraviolet light was discovered. It is called ultraviolet because it is “beyond” the visible violet light in the electromagnetic spectrum. so there are not many manmade sources. There are, however, many commercial products designed to block ultraviolet (often called UV). Suntan lotion is designed to block UV rays from the sun. Although most of the sun’s UV radiation is blocked by the earth’s atmosphere, even the small amount that reaches the surface can be detrimental to human health. It is known that long-term exposure to UV rays can cause cancer. While there are not many manmade UV sources, scientists still study it, and they generate very high intensity ultraviolet radiation at facilities like the ALS (Advanced Light Source) in San Francisco. Astronomers also study the ultraviolet radiation coming from space. Stars and other objects in the universe that are much hotter than the sun are good sources of ultraviolet. Satellite telescopes like the Hubble Space Telescope must be used to observe ultraviolet because almost all ultraviolet radiation is absorbed by the earth’s atmosphere as shown in Appendix C. Fig. 24 is an ultraviolet image taken by the Hubble. Fig. 24 Fig. 22 – Johann Ritter The frequency of ultraviolet waves ranges from about 1014 to 1016 Hz, and the wavelength from about 10-6 to 10-8 m. Fig. 23 shows that these waves are on the order of virus and protein sizes. The energy of ultraviolet photons ranges from about 10-19 to 10-17 J. Viruses F. X-Ray X-rays, like many other parts of the electromagnetic spectrum, were discovered by accident in 1895 by Wilhelm Roentgen (Fig. 25). He was a German physicist working on cathode ray tubes when he noticed a glow coming from a chemical called barium platinocyanide. He found that the rays coming from the tube could pass through many objects including flesh. They had a much higher frequency than visible light and were called “X-rays” because of their unknown nature. Proteins Fig. 23 There are not many applications that use ultraviolet light, Fig. 25 – Wilhelm Roentgen 10 The frequency of x rays ranges from about 10 16 to 1019 Hz, and the wavelength from about 10-8 to 10-10 m. Fig. 26 shows that x rays are molecular and atomic scale electromagnetic waves. The energy of x-ray photons ranges from about 10-17 to 10-14 J. Molecules shown in Fig. 28 emit x-rays because they are at extremely high temperatures. Atoms Fig. 26 Fig. 28 Scientists at the ALS in San Francisco produce extremely intense x rays for experimental purposes. Perhaps the most common application, however, is the x-ray machines used in doctors’ offices. Fig. 27 is a simplified schematic of how x rays are produced in these machines. A voltage is applied to a filament F, which heats up to the point that electrons boil off its surface. A high voltage V sets up an electric field that accelerates these electrons toward the target T (this is similar to the electron beam in a cathode ray tube). The target (which is often made of Tungsten) emits photons in the x-ray region when struck by electrons. These photons then pass only through the window W, which is usually made of quartz. X rays have such small wavelengths that they pass through flesh, but are absorbed by bones, which are denser than flesh. This is how images are formed on xray film. The film starts out white, and the areas exposed to x rays darken. X rays are very high energy and can tear through molecules like DNA. This is why it is recommended that people limit their exposure to x rays. G. Gamma-Ray In 1898, Ernest Rutherford (Fig. 29) discovered gamma rays while performing experiments with nuclear emissions. He named them gamma rays to follow the theme of alpha and beta rays, whose existence he had discovered earlier. Fig. 29 – Ernest Rutherford The frequency of the most energetic waves called gamma-rays ranges from about 1019 to 1024 Hz, and the wavelength from about 10-10 to 10-14 m. Fig. 30 shows that these waves are near the size of the fundamental particles in physics. The energy of gamma-ray photons ranges from about 10-14 to 10-10 J, which represents an extremely high energy for a single photon. Gamma rays are the most electron energetic of the electromagnetic spectrum. neutron Fig. 27 One of the main areas of astronomy is x-ray astronomy. Satellite telescopes such as Harvard’s Chandra X-ray Observatory can take striking pictures of the x-ray emissions of cosmic objects. Objects like the Crab Nebula proton Atomic Nuclei Fig. 30 11 Manmade gamma rays are produced only in complex physics experiments involving atomic nuclei and in some medical equipment. Doctors use these high-energy waves to kill cancerous cells. Gamma-ray radiation from spent nuclear fuel must be tightly controlled since this highenergy radiation can be very hazardous to human health, even at very low doses. A very interesting natural source of gamma-ray photons is the proton-proton cycle as shown in Fig. 31. This process is the energy source of the stars and is also known as thermonuclear fusion. Two protons combine to form deuteron, a process that also produces a positron and a neutrino. This proton-proton event is actually extremely rare (otherwise the sun would explode almost instantly), but because of the huge number of protons in the sun, deuterium is actually produced at the rate of 10 12 kg/s. Two gamma rays are first produced when the positron annihilates a free electron. Deuterium again combines with a proton to form helium and a gamma-ray photon. Thus, in one cycle, six gamma-ray photons are created. Fig. 32 IV. CONCLUDING REMARKS The intricacies of light continue to remain a mystery to physicists. The exact nature of light cannot be explained. Light seems to be a strange mixture of electromagnetic waves, photons, and probability. The fact that we do not fully understand light has not kept humans from taking full advantage of the electromagnetic spectrum. New uses for light are always being discovered and are pushing technology forward. Knowledge of the electromagnetic spectrum has also helped us learn more about the universe. The four different images of the Crab Nebula in this paper show that we can’t limit ourselves to things that can only be seen by the eye. V. REFERENCES Fig. 31 [1] [2] [3] Space is a source of a wide range of electromagnetic waves, and gamma rays are no exception. Probably the most interesting phenomenon in gamma-ray astronomy was discovered in the late 1960s. Detectors on the Vela satellite recorded bursts of gamma rays (Fig. 32) coming from deep space. Today, astronomers record these events about once every day. During these bursts, the whole sky lights up with gamma-ray radiation. While the source of these bursts is unknown, it is suspected that they may be glimpses of cataclysmic events during the early stages of the universe. [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] Halliday, D., R. Resnick, J. Walker, Fundamentals of Physics, 5th ed., John Wiley & Sons, 1997. Bickerstaff, P., “Electricity and Magnetism,” http://www.phys. uidaho.edu/~pbickers/Courses/310/Notes/book/node193.html. Katsiavriades, K., “KryssTal: The Electromagnetic Spectrum,” http:// www.krysstal.com/spectrum.html. Popovic, Z., Popovic, B. D., Introductory Electromagnetics, Prentice Hall, 2000. Hayt, W. H., Buck, J. A., Engineering Electromagnetics, 6th ed., McGraw-Hill, 1958. NASA, “The Electromagnetic Spectrum,” http://imagers.gsfc.nasa. gov/ems/. “Physics Time-Line,” http://www.weburbia.com/pg/hist1.htm. US Department of Commerce, “United States Frequency Allocations: The Radio Spectrum,” 1996. California Institute of Technology, “Caltech Archives: PhotoNet,” http://archives.caltech.edu//photoNet.html. University of California, “Electromagnetic Spectrum,” http://www. lbl.gov/MicroWorlds/ALSTool/EMSpec/EMSpec2.html. University of Chicago, “Protein Structure,” http://sosnick.uchicago. edu/precpquastru.html. Frontier Public Schools, “Viruses,” http://pc65.frontier.osrhe.edu/hs/ science/bvirus.htm. Bloomfield, L. A., “How Things Work: Microwave Ovens,” http:// rabi.phys.virginia.edu/HTW//microwave_ovens.html. “Ritter,” http://www.geocities.com/bioelectrochemistry/ritter.htm. Weisstein, E. W., “Eric Weisstein’s World of Biography,” http:// scienceworld.wolfram.com/biography/. 12 [16] Calligeros, E., Hehir, D., Jacobs, R., “Military Communications,” http://murray.newcastle.edu.au/users/staff/eemf/ELEC351/SProjects/ Calligeros/invent_radar.htm#Invention%20radar. [17] Read, M., “What is the Ultimate Fate of the Universe?” http://cmb. physics.wisc.edu/tutorial/cmb.html. [18] SETI Institute, http://www.seti.org/. [19] NASA, “Remote Sensing Tutorial,” http://rst.gsfc.nasa.gov/Intro/ Part2_3.html. [20] University of Tennessee, “Astronomy 162,” http://csep10.phys.utk. edu/astr162/lect/. [21] NASA, “Astronomy Picture of the Day,” http://antwrp.gsfc.nasa.gov/ apod/ap011121.html. [22] Adelson, E., “Optics and the Eye,” http://www.ai.mit.edu/~vkumar/ perception/optics1/index.htm. [23] Kaiser, P., “The Joy of Visual Perception,” http://www.yorku.ca/eye/. [24] Harvard, “Chandra 101,” http://chandra.harvard.edu/edu/ chandra1012.html. [25] Virginia Tech, “The Chemistry Hypermedia Project,” http://www. chem.vt.edu/chem-ed/scidex.html. 13 Appendix A. Electromagnetic Spectrum Chart 14 Appendix B. Radio Chart 15 Appendix C. Atmospheric Windows