Electromagnetic Radiation
LIGHT AS WAVES
Astronomers have learned most of what we know about stars and galaxies by analyzing the electromagnetic radiation coming from them. Electromagnetic radiation, of which the light that our eyes respond to is one part, is a form of energy. Without any material aspects, it is energy that can move through the empty reaches of the universe.
Historically, this conceptual view began in 1862, when the Scottish physicist James Clerk Maxwell (1831-1879) showed that light is energy carried in the form of a traveling wave composed of electric and magnetic fields. The electric and magnetic fields vary in intensity, and they are at right angles to each other and to the direction in which the wave is propagating. The electric and magnetic fields continually interact, forming an electromagnetic wave. These fields maintain themselves and continue to propagate until the energy of the wave is converted to some other form of energy. At that point the electromagnetic wave ceases to exist. Maxwell's proposal that light is an electromagnetic wave, as we shall soon see, was not the last word in explaining the physical nature of light. But visualizing light as waves spreading out from a radiating source helps us to understand many aspects of it.
The speed of light measured in empty space is 299,792 kilometers per second (3 x 105 kilometers per second in round figures, or 186,300 miles per second). This appears to be the speed limit for all energy transported in the universe. As we discussed in the last chapter, the speed of light is a fundamental constant of nature and apparently has the same value throughout the universe.
Electromagnetic waves possess a range of wavelengths, the distance between successive crests or troughs, and a range of frequencies. The product of the wavelength and frequency gives the speed at which the electromagnetic wave travels. The amount of energy the wave transports is proportional to the square of the wave's amplitude.
ElECTROMAGNETIC SPECTRUM
Our eyes are sensitive to only a very limited portion of the entire range of wavelengths for electromagnetic radiation. If we order this range of wavelengths from the shortest on the left to the longest on the right, we produce an array of wavelengths called the electromagnetic spectrum. Toward the short-wavelength end we find that portion to which our eyes are sensitive, called the visible spectrum. The physiological response of the eye to the various wavelengths of the visible spectrum is color.
Short wavelengths in the visible spectrum are violet, with progressively longer wavelengths producing the response we identify as the range of hues from blue, green, yellow, and orange to red in the color spectrum. Visible light is electromagnetic radiation with wavelengths between approximately 35 x 10-6 and 70 x 10-6 centimeter. These wavelengths correspond to frequencies between 8.5 x 10'4 to 4.3 X 10'4 hertz. One hertz equals one cycle, or oscillation, of the wave per second. The lowest frequencies of visible light appear red to our eyes; the highest frequencies appear violet; and between these are the rest of the color spectrum.
All types of electromagnetic radiation show the properties of a wave; all propagate in the same way with the same speed in empty space; and all transport energy. For convenience, however, we divide the nonvisible portions of the electromagnetic spectrum into regions according to the radiation's wavelength, such as the ultraviolet or the infrared and so on. We label these different regions not because of any intrinsic difference in the radiation but because we have different ways of detecting radiation depending on its wavelength.
Gamma rays, X rays, and ultraviolet radiation are the wavelength regions shorter than visible light; most of this radiation that comes from outer space is absorbed high above the earth's surface by our atmosphere. Infrared radiation is the first wavelength region beyond visible light, and it is also partially absorbed by the earth's atmosphere. The next wavelength regions are the microwave and radio regions, for which there is a broad electromagnetic window (Figure 5.1) through the earth's atmosphere.
Because of the wide range of wavelengths, some units of measurement are more convenient than others for describing different regions of the electromagnetic spectrum. For the visible spectrum angstroms are convenient. An angstrom is a hundred-millionth of a centimeter (1 A = 10-8 cm). Visible radiation lies approximately between 3500 angstroms (the violet end of the spectrum) and 7000 angstroms (the red end). X rays are also measured in angstroms, but infrared wavelengths are generally expressed in microns (1 micron = 104 angstroms = 10-4 centimeter). Astronomers use the hertz as the unit for measuring frequency of all radiation.
WAVE PROPERTIES OF LIGHT
Light traveling through empty space moves in a straight line. In our everyday experience we encounter light not in empty space but passing through various media-light partially absorbed by the atmosphere, scattered by dust, transmitted through a
window or a telescope. In these circumstances the speed of light may be slowed and the direction of the light wave may be changed. These changes are best understood through the wave properties of light.
Several properties illustrate the wave characteristics of light. One is reflection, which occurs when light strikes the boundary between two media of different materials, such as glass and air. When a light ray moving in air reaches the boundary, part of it may be reflected. The reflected ray lies in the plane formed by the incident ray and the perpendicular to the boundary. The ordinary mirror, or looking glass, illustrates reflection.
Also, part of the incident ray may be transmitted through the glass rather than being reflected. The transmitted ray does not, however, continue along the same straight line; it is bent toward the perpendicular. This change in direction is called refraction. If the medium into which the ray moves is more dense than that from which it comes, the angle of refraction will be less than the angle of incidence. If its density is less, then the angle of refraction is greater. A good example of refraction is a spoon sticking out of a glass of water. The handle looks bent at the point where the spoon enters the water because part of the handle is in the same medium (air) as you, while for the part under water light must pass through the water-air boundary, where it is refracted.
Light shows another wave property, diffraction, which is the spreading out of light past the edges of an opaque body. Instead of being propagated in a straight line, light, like sound waves, bends around corners. The spread is greater for longer wavelengths. Because light's wavelength is very small, we do not normally observe diffraction in the everyday world. We can see diffraction, though, in the laboratory. Optical instruments, such as telescopes and microscopes, depend upon these wave properties of light for their operation.
Nearly all natural light sources, such as stars, emit electromagnetic waves composed of many wavelengths. How do waves of different wavelengths add to produce a composite wave? If waves of the same wavelength from two sources are superimposed so that their crests and troughs coincide, they are said to be in phase with each other, and their amplitudes add to produce a sum greater than the amplitudes of the individual waves; the light is said to "interfere constructively." If the crests of one set of waves fallon the troughs of the other, they are said to be out of phase with each other, and their amplitudes cancel each other; the light is said to "interfere destructively." nterference is common to all types of waves; in fact occurrence was strong evidence that light is a wave ohenomenon. Light waves of one or many different wavelengths may interfere constructively or destructively. Such waves are called composite waves, or white light, since that is the physiological response they evoke. If we can add waves together, then we must also be able to separate a composite wave into its constit'uent wavelengths.
BRIGHTNESS OF ELECTROMAGNETIC WAVES
The surface area covered by an expanding sphere of light (or a portion of it) increases as the square of the radius of the sphere, that is, as the square of the distance from the light source. Since the total amount of energy leaving the light source in all directions is the same at any distance, the amount of radiation passing through each unit of area of the expanding sphere must diminish with the square of the distance.
For example suppose at 1 meter from a light source that the apparent brightness of the radiation over 1 square meter of surface area is 1 unit. At twice the distance each square meter will receive one-fourth of a unit of illumination; at three times the distance,
INVERSE-SQUARE LAW OF LIGHT: The apparent brightness b varies inversely as the square of the distance d from the light source; that is, b x 1/d2•
DOPPLER EFFECT
If an observer is moving relative to a source of light or the source is moving relative to him, then the observer will see a change in the wavelength of the light:
DOPPLER PRINCIPLE: Electromagnetic radiation received by an observer will have a shorter wavelength if source and observer approach each other and a longer wavelength if they recede from each other; the amount of change in wavelength is directly proportional to the velocity along the line between source and observer.
To see why, suppose a stationary light source is radiating concentric waves of one wavelength in all directions. Then observers in any direction, if stationary, would see successive crests of the wave passing them at the same rate at which they were emitted by the source. If, on the other hand, the light source begins to move at uniform speed toward the right, the two observers 0 and P along the line of motion would see crests passing them at rates different from that with which they were emitted. Observers Q and R, located at right angles to the moving source, would detect no change in the rate for crests passing them. Observers elsewhere would notice some change, the amount depending on the angle between their radial direction to the source and the line of motion. This phenomenon is known as the Doppler effect, named for Christian Doppler (18031853), the Austrian physicist who first explained it.
Let us consider observers 0 and P in more detail. Wave 1 was produced when the light source was at position 1; wave 2, when it was at position 2i and so on. Because of the greater distance the wave travels in reaching observer 0, each successive wave crest passes him at a slower rate (lower frequency) than when the source was stationary. Because the waves travel a shorter distance to reach P, the successive crests pass at a faster rate (higher frequency). The wavelength is shifted toward longer wavelengths (red shifted) as the source recedes from 0 and toward shorter wavelengths (blue shifted) as the source approaches P.
An example of the Doppler effect familiar to all of us is the change in frequency of sound waves in the rising and falling pitch of a train whistle as the train approaches and then moves away. It is immaterial whether the light source is in motion, or the observer, or both: The size of the Doppler effect seen for light waves depends only on the net relative motion along the line of sight between the light source and the observer.
The amount of the wavelength shift due to the Doppler effect is directly proportional to the velocity of approach (blue shift) or recession (red shift) as long as the relative velocity is well below the velocity of light. (Later in this book we discuss the relationship when the relative velocity is a substantial fraction of the velocity of light.) The constant of proportionality is the rat,io of undisplaced wavelength to the velocity of light. This means that the wavelength shift is greater the longer the wavelength of the radiation.
As an example, if we are approaching two stationary radiation sources, with one emitting electromagnetic radiation twice the wavelength of the other, then we should expect twice the wavelength shift from that one. I n the nearby box we present the mathematical form of the Doppler effect. Because of the continual movement of all bodies in the cosmos, the Doppler effect is an important tool for detecting and measuring the amount of motion.
