| Full Spectrum of Light:
An Introduction to the Electromagnetic Spectrum.
It was Isaac Newton himself who first demonstrated that the light of the sun could be spread out into its component colours with a prism, and then recombined with a second "upside-down" prism to make white sunlight again. The first of these processes, the spreading of sunlight out into its component colours, is what happens in the formation of a rainbow: the droplets of water suspended in the air act as little prisms which disperse the different colours of light.
What this means in essence is that the light from the sun is made up of a host of different waves, some of which would look red (if we could see them in isolation), others of which would look blue (if we could see them in isolation). When we look at objects lit by the sun - a car, a shirt, an apple - the colours we see depend on which wavelengths are preferentially reflected and/or absorbed by the pigments in the object. An object which reflects light of all visible wavelengths, so that the eye sees the same balance of colours as is present in sunlight, is `white'; an object which reflects no light at all at any wavelength is black.
( A digression: It is interesting to note that if we went to a planet orbiting a red star, the sunlight there would contain a higher proportion of red light, and an object which looks white here on Earth would, to our eyes, have a distinctly reddish and unnatural look under that sun's illumination. But to the people living there, it would be a `white' - i.e. purely reflecting - object, with a neutral colour.)
What is it, though, that distinguishes blue light (say) from red light? The answer is that it is the wavelength of light. Blue light is of shorter wavelength than red light. We will see later, when we discuss light as particles, that there is a more natural way of thinking of this: the little `lumps,' or photons, of blue light each carry more energy than the little lumps of red light. But let us think in terms of waves for a little longer.
Imagine water waves passing through the sea. You can visualise these being of very long wavelength (say, thirty metres from crest to crest, as in a very heavy storm at sea); and you can equally well imagine waves of short wavelength (little waves with peaks only a few centimeters apart, like ripples on a pond). You may also imagine these waves as being of different heights, but that is not my point: I want you instead to focus on the fact that the crests, or peaks, of the waves can be far apart or rather close together, just as a comb can have teeth which are widely spaced or closely packed.
Now visualise a cork floating in the water. If a pattern of widely-spaced waves of the `storm at sea' variety passes by, the up-and-down motion of the cork will be fairly slow, as the cork is raised up the side of one long wave and down into the following trough. (Imagine floating out there yourself in a life jacket. How would it feel?) But if waves of the `ripple' sort pass by at the same speed, the cork will bob up and down quite frequently.
Of course, the rate of the up-and-down motion would also depend on how fast the pattern of waves passes by. If the wave pattern were moving only very slowly, then the up-and-down motion would be of low frequency even if the wave crests are close together. But for light the critical point is that all wavelengths (colours) travel at the same speed in the vacuum of space - and, as it happens, at very nearly the same speed in air. This means that the frequency - the `up and down' motion associated with the wave - is higher for the short wavelengths than for the long wavelengths as the light passes by.
In summary, then, we can think of blue light as being of shorter wavelength or equivalently of higher frequency than red light. The latter means that, in principle at least, a electron would `bob up and down' faster when blue light reaches it than it does when red light reaches it. By the way, if you find these notions a little confusing, you may find clarification when I introduce the notion of the energy carried by a photon (a `particle of light'); that may help your visualisation.
How Does a Prism Work? Refraction.Even if you don't know it, you are all familiar with the effects of refraction. You would not be able to focus light onto the retina of your eye if not for the refraction induced by the cornea and lens of your eye (and the lens of your glasses, if you wear them). The word comes from the fact that light can change direction, or refract, when it passes from one medium to another. This is why the stem of a plant standing in a stream may look bent or broken just where it enters the water: the light abruptly changes direction when it passes from water to air, and gives a mistaken impression of the compromised integrity of the stem. Why does light do this? You may not be surprised to learn that the details of the physics are actually quite subtle. Fundamentally it has to do with the fact that the light, an electromagnetic wave, is moving from a medium of one kind, which consists of atoms arranged in some way, into a new medium in which the atoms are disposed differently. Since all atoms contain charged particles (their electrons and protons), the way in which electromagnetic radiation passes through the new material -- and in particular the speed at which it does so -- may be different because of the way in which the wave interacts with and influences those particles. Let us not worry about the details, but focus on the essential fact that refraction is caused because of the change in speed of the wave as it enters the new medium. In class, I offered you an analogy which is common in introductory physics textbooks and which captures the fundamental idea moderately well. Imagine a body of soldiers in formation marching at an angle from a paved parade ground into a muddy field. Since the soldiers are slowed down entering the mud, the line which represents the 'front of the pack' gets turned in direction, even if the individual soldiers continue doggedly moving in the same direction that they were marching originally. In effect, the whole formation gets a distorted shape, and a person looking only at the orientation of the front line would be misled about the direction from which the soldiers are arriving. In this example, of course, you could look carefully at the direction each individual soldier is travelling, and work out what must have happened -- namely that the ones to the left of the sketch have been slowed down more in their progress than the ones on the right. In the case of light, this is not possible (the analogy breaks down here). When we see a `wavefront' coming from some direction, we cannot work out, from an inspection of its `inner parts,' whether it has recently changed direction in the way shown. What really matters for light is what the wavefront itself is doing, and thus the net effect is that light really does change direction when it enters a new medium. The reason again is simply that light travels more slowly in materials than it does in air or vacuum. (For example, it travels about thirty percent more slowly in water than in air.) A final important point: if the group of soldiers hits the mud head-on (so that all the soldiers in the front line meet it at the same time), they all get slowed up together, and there is no change in direction. By the same reasoning, a beam of light will not refract (change direction) if it shines perpendicularly onto the surface of some new material; but if it hits at some other angle, it will.
How Does a Prism Work? Dispersion.Reconsider our soldiers. Suppose you had two formations: one a troop of regular soldiers, who get badly slowed down in the mud, and the second a troop who are equipped with special boots so that the mud is not a serious problem. Clearly, the front line (the `wavefront') of the second group will scarcely change in orientation, while the first group will be affected as described above. Light is just like that! In a beam of sunlight, the red and the blue (and the yellow and the green....) waves travel together through space, all at exactly the same speed. But when they pass into some new medium, such as glass, they slow down to various extents, in a way which depends on the wavelength - or equivalently the colour - of the light. What this means, of course, is that the light gets dispersed: red light is slowed somewhat and (unless it lands perpendicularly) changes direction a little; blue light is slowed quite a bit more, and changes direction more appreciably; and so on. That is why a prism forms a spectrum, with the light spread out from blue to red. A rainbow is caused by nothing more than this. The light from the sun enters a drop of water, with the blue and red being refracted to different extents and thereafter following quite different paths. Some of the light is reflected by the shiny back face of the raindrop, and turns back in our direction. As it passes from the drop back out into the air, there is a further change in direction which again depends on the colour. The geometry of the whole situation -- droplets floating in the air ahead of us, the sun behind us -- explains the arc-like shape of the rainbow we see.
An Important Technical Point.Physicists usually pass light through a narrow slit before it hits the prism. Why do we do this? Why not just allow a broad beam of light from a lamp to fall onto the prism? The main reason is that it allows us to examine one particular wavelength in detail, without light of other wavelengths mixed in with it. We talk about the spectral purity of the spectrum we produce in this way. In class, I explained this by analogy to a competition in which you want to sort out good swimmers from poor swimmers, perhaps as the first part of the Kingston triathlon. There are various ways of doing so. The usual approach would be to have all the swimmers enter the water at the same time, and see who takes the least time to swim the full distance across a placid bay. But an equally effective approach would be to have the people swim across a fast-flowing stream, so that the poor swimmers are carried a long way downstream while the strong ones go almost straight across. Then if you find a competitor a long way downstream, you may conclude that he or she is a weak swimmer. This approach would not work very well if the swimmers were allowed to enter the river from just anywhere on the bank. If you are standing on the far bank and see a swimmer clamber out of the water, you don't know if that person is a strong swimmer who entered the river directly opposite you and crossed with a few easy strokes, or a poor swimmer who entered the river far upstream and has only just struggled across. Instead, you can see that you get good and bad swimmers intermixed. The solution is straightforward. Just use a narrow gate to restrict the swimmers to a single takeoff point. Then we can judge, merely on the basis of where they come out of the water on the far side , which ones are strong swimmers and which ones are weak. This is what the slit does for the physicist: it defines a narrow location from which light can enter the prism, and then the red light and the blue light are dispersed by the action of the prism to different spots. There will be no blue light mixed in with the red light, and vice versa, and we can study one particular wavelength in detail if we like. By the way, Isaac Newton used a fairly wide hole to admit sunlight into his prism, so he had rather poor spectral purity. To his eye, then, the spectrum was completely continuous: he failed to detect the 'missing' bits of light which define the absorption lines about which we will learn so much more later. It is a real pity that a scientist of his powers missed out on this fundamental discovery -- what might he have made of it?
Reflected versus Emitted Light.When you look around you, you see a few things which are clearly emitting electromagnetic radiation (light): the sun, the stars, light bulbs, fires, and so on. The majority of everyday things you see, however, are visible to you merely because they reflect sunlight or room light. This is true of the moon and planets, for instance: they would not be visible to our eyes if the sun were not shining on them. What causes the colours of everyday objects that we see by reflected light? Why, for instance, is your shirt green? Why are your jeans blue? The answer is that sunlight (white light) is made up of light of all colours, but when the sunlight falls onto an object, certain of the wavelengths are absorbed by the pigments in the cloth or the material of which it is made, while the other wavelengths are simply reflected. It is the reflected light, of course, which reaches our eyes and determines what colour we perceive. Light of various wavelengths carries varied amounts of energy, as we will learn. (`Photons' of blue light are more energetic than photons of red light, for instance.) The energy of the incoming light determines what pigments (chemical enzymes) in the retinas of our eyes get chemically altered, and this changing chemistry sends a signal to the brain which is interpreted as a pretty colour of one sort or another.
Why Do Only Some Objects Emit Light?What distinguishes the objects which are clearly luminous? (things like the sun or a light bulb). The obvious answer, of course, is that they are hot. But if you think about it, you will realize that every body has a certain amount of heat, or internal energy: its temperature is just a measure of how vigorously the atoms within it are jiggling about. As a lump of burning coal emits energy and gradually cools down, it is seen to fade away; but it does not become absolutely stone cold, and one might speculate that its residual lower temperature implies that it could still be emitting energy - but perhaps at a wavelength our eyes cannot detect. Indeed, this is correct. All objects emit electromagnetic radiation - not just the ones that are exceptionally hot. The only objects which would fail to radiate electromagnetic energy are those completely without any temperature, at absolute zero, the temperature at which all atomic jiggling might be expected to cease. (Such a temperature is, by definition, zero on the Kelvin scale, and corresponds to -273 degrees centigrade.) In a later lecture, we will study the very fundamental relationship between the internal energy of a body (the jiggling of its atoms) and the nature of the light it emits.
The Entire Spectrum.It was once thought that visible light is "all there is" - after all, we don't see any other colours. But this is because our eyes are simply not sensitive to other frequencies, and we now recognize that there is an entire electromagnetic spectrum ranging from very short wavelengths (and high frequencies) to very long wavelengths (and low frequencies). This is shown diagrammatically in the text on page 157. A helpful analogy is to an infinitely long piano keyboard, with keys at the top end producing notes far too high in pitch for us to hear, and keys at the bottom end producing very low-pitched sounds also below our threshold. Visible light, which covers a range of about a factor of two in frequency, is just a single octave in the whole "piano." Let us explore this a little further. I pointed out that striking the `A' below middle C on a piano sets the associated piano string to vibrating 440 times a second. Striking the A an octave higher sets that string vibrating 880 times a second; the one an octave lower vibrates at 220 times a second. Now imagine a piano keyboard stretching for miles in either direction, rather than its familiar span of 88 keys. Striking a key far to the right might make a hypothetical string vibrate trillions of times a second, producing a sound far too high in pitch for us to detect; one far to the left might make a string vibrate once a century, producing low-pitched sounds far below the human threshold. A standard piano spans a little over seven full octaves, the notes of all of which can be heard by most people (and if the keyboard were extended a little more, we would hear some additional notes). The electromagnetic spectrum has, in principle, no upper and lower limits (although it is not very meaningful to talk about an electromagnetic wave with a wavelength longer than the size of the entire visible universe!), but our eyes are sensitive to only one octave out of the enormous range of frequencies or colours known to exist: red light is about twice as long in wavelength, and vibrates at about half the frequency, of blue light. How do we know that these other electromagnetic waves exist? The answer is that we can detect them with other devices. For instance, infrared radiation is nothing more than heat! Hold your hands out to a fire and feel the glow with your skin. (How do you know your skin is not responding to the visible light itself? You can do this for coals which have cooled enough not to be giving off any visible light, so that they are not red-hot, but which still produce lots of infrared radiation). Similarly, the circuitry in your radios is designed to pick up the electromagnetic waves sent out by your local stations, and so on. By the way, it was the astronomer William Herschel -- the man who discovered Uranus by accident -- who was the first to detect infrared radiation. He set up a thermometer so that its bulb lay just beyond the red part of the spectrum of sunlight created by a prism. The thermometer warmed up, indicating that some radiant energy, invisible to the eye, was falling on the bulb.
What Can We See?Now that we have considered the entire spectrum, it might be interesting to look out into space to see what electromagnetic waves are being produced by various astronomical objects. Or would it? You might think that there is no particular value in studying, say, the infrared radiation given off by a star since we can already see it in the visible, but there is a very important point to note. We carry out astronomical studies at a variety of different wavelengths not just to study familiar objects in alternative ways but also because there are certain objects which can be detected only at these other wavelengths. We will return to this general topic later, but here are a couple of examples: Stars form in dense clouds of gas which are too cool to give off visible light. We learn about star formation by studying the infrared and radio radiation these clouds emit. Massive black holes and dense neutron stars can produce X-rays, for reasons we will explore later in the course. A study of such emissions may be the best way to find and develop an understanding of black holes. For these reasons, astronomers now observe the skies at every wavelength they can - all the way from gamma rays to radio radiation. The history of this diversification is short: World War II led to the development of radar and the technology needed for radio astronomy, and the other techniques date from even more recently than that. In general, what we might see in the sky depends on two things: Are there indeed any objects out there giving off light of the frequency (or wavelength) we are interested in? Will the light even reach our detectors? To take a specific example, we can predict that very hot clouds of gas (at temperatures greater than a million degrees) will give off X-rays, by something like the same physical process used on a small scale in the machine in your dentist's office. The X-rays travel through space all right, but do not reach the ground because they are absorbed high in the Earth's atmosphere. There are reasons to be grateful for this, because an excess of X-rays is not good for your health; but it means that astronomers have to use satellites outside the Earth's atmosphere to make such observations, a requirement that makes this particular branch of astronomy difficult and expensive. The figure on page 157 of your text shows the interesting ranges. Electromagnetic radiation of the lowest frequency and longest wavelength is called "radio radiation"; then comes infrared; then visible light; then ultraviolet; then X-rays; and finally gamma rays, which have the highest frequency and shortest wavelength. The atmosphere of the Earth is opaque to essentially all of these except for the visible and for some "windows" in the radio and infrared. To be specific: Much of the radio radiation is reflected by the ionosphere of the Earth (a layer of charged particles high in the atmosphere). The ionosphere is also responsible for reflecting "ham" radio signals sent out from our Earth-based transmitters back down to the ground so that they don't go out into space, which is is how Canadian 'hams' can send a radio signal all the way to Australia, for instance. The signal bounces off the ionosphere, back down and off the ground, then back up, and so on, making multiple reflections until it finally reaches Australia. While this is helpful for radio communications, it is bad for radio astronomy because any incoming radiation at those wavelengths (light from remote galaxies, say) will just reflect back off into space. Most of the infrared radiation is absorbed by water vapour (not just the visible lumps of cloud, but the invisible quantities of water uniformly distributed in the air). This is in fact one of the main reasons for building observatories high on mountains: up there you are above much of the water vapour, and the air is very dry - and thin, to the astronomer's discomfort! To get above it all, though, one has to use something like the Infrared Astronomical Satellite (IRAS) which was launched into Earth orbit to get right outside the atmosphere and to study sources of infrared radiation in the sky. Most of the ultraviolet radiation is blocked by the ozone layer high in the atmosphere. Ultraviolet radiation is what gives you a tan. Too much of it can be damaging: it can produce skin cancers, for instance. That is one reason why there is grave concern over the depletion of the ozone layer (the so-called "ozone hole") which is thought to be caused by our wide-spread use of fluorocarbon chemicals. Again, successfully studying the ultraviolet (which is the kind of radiation given off by very hot stars) can be accomplished through the use of the International Ultraviolet Explorer satellite and other space platforms. X-rays and gamma rays are absorbed in the atmosphere. They can cause showers of energetic charged particles which are created when the X-rays and gamma rays collide with atoms high up, but observing them directly requires satellite like the Einstein X-ray satellite, and the COS-B gamma-ray satellite. (By the way, please do not bother committing the names of these satellites to memory!)
Light Carries Energy and Momentum.Before going any farther, let us stop to consider the clear-cut evidence that light carries energy and momentum through space, in much the same way that any moving object does. (If, for example, I throw a snowball at someone, the ball has kinetic energy and linear momentum. The conservation of the linear momentum in particular means that an accurate throw can knock the person's hat from their head, with the hat now moving in the direction that the snowball was originally.) Is the same sort of consideration valid for light? Can you transport energy from one location to another in the form of light? And does it have an associated momentum? The answer is to these questions is `Yes.' By way of example, I noted the following points in class (in a very incomplete list - there are many more examples, and technical experiments which you can do to quantify the following remarks in a more precise way) : The sunlight which falls on our faces warms us; the sunlight landing on the Earth melts snow and warms up the lakes; and so on. Since the temperature of a lake is a measure of the rapidity with which the atoms and molecules within it are jiggling about, it is clear that the warming effect must be attributed to the conversion of radiant energy (the energy carried by the light) to kinetic energy (the motion of the particles) or, more generally, to the heat content. Arriving sunlight drives the process of photosynthesis, providing the energy needed by plants for the chemical conversion of molecules of water and atmospheric carbon dioxide to sugars, cellulose, and so on. Radiation can make the vanes of a `radiometer' turn. This is an example which warrants elaboration, for reasons which will become apparent, so let's spend a little time on it. First of all, what is a radiometer? Many of you will have seen one as a novelty item. It consists of a clear glass ball within which is a special sort of horizontally-mounted windmill, consisting of vanes which are shiny on one side and dark on the other. (These are sometimes sold as desktop toys for busy executives.) Now think about how these devices work: Start by considering a very narrow beam of light, one which we can aim quite precisely. If the light is trained upon the black face of one of the radiometer vanes, it will be absorbed (which is why the surface looks black, of course - no light bounces off towards your eyes). If, before arrival, the light had some associated linear momentum, something else now has to be moving in the direction the light was travelling because the light itself has come to a halt. In other words, the vane will start to move. This follows logically from one of the great conservation laws: to be specific, the total linear momentum has to remain the same (`be conserved') in the system. In other words, the blackened vane will feel a `radiation pressure' which tends to push it in the direction the light was originally travelling. Please note that this argument is generally applicable. When light falls on the front of your black coat, you experience a backwards push as a result, just as if someone was peppering you with tiny snowballs - a push which is so utterly feeble that you don't notice it, however. What happens if the narrow beam of light hits the shiny side of a vane? The shininess, of course, is an indication that the light is reflecting from (bouncing off) the surface, which means that it has completely changed direction and is now travelling the other way. If the light had some momentum in the original ('forward') direction, but is now travelling in the `backwards' direction, it must have changed its momentum quite a lot. The only way this can happen, consistent with the conservation law, is that the vane itself must be moving in the `forward' direction - and moving fairly rapidly , so that the total momentum is conserved. A comparison of these two cases reveals that you can make the radiometer vane move more briskly by training the light on the shiny side than when you train it on the dark side. But what happens if a very broad beam of light falls on the radiometer, illuminating both the dark and the shiny sides of the various vanes? From the preceding considerations, you would expect the pressure on the shiny side to dominate, so that the `windmill' will turn with the black side in the lead . This is quite correct, as can be demonstrated with well-constructed radiometers. Unfortunately, this evocative piece of physics usually works the wrong way around in cheap radiometers because it depends on having a good vacuum in the glass sphere. If there is much air inside, complicated heating effects confuse the issue. The dark surfaces absorb more energy and get warmer than the shiny surfaces, thereby inducing air currents which swamp the expected effects. Nevertheless, careful experiments of this and other sorts can show that light indeed carries linear momentum and exerts a pressure. I have a considerable time discussing the radiometer principally because I wanted everyone to be aware of the reality of radiation pressure - and then to consider its potential use. It is theoretically possible, and will surely be practical some day, to unfurl a gigantic `sail', perhaps kilometers across and made of the finest shiny metal foil, from a spaceship stationed between the planets. This ship could literally sail through the solar system, using the sun's radiation as the wind. It would be possible to `tack' towards the sun, or sail out to the farthest planets, with no expenditure of fuel at all. Of course, progress would be slow, but there are many applications in which this would not matter at all. Previous chapter:Next chapter
0: Physics 015: The Course Notes, Fall 2004 1: Opening Remarks: Setting the Scene. 2: The Science of Astronomy: 3: The Importance of Scale: A First Conservation Law. 4: The Dominance of Gravity. 5: Looking Up: 6: The Seasons: 7: The Spin of the Earth: Another Conservation Law. 8: The Earth: Shape, Size, and State of Rotation. 9: The Moon: Shape, Size, Nature. 10: The Relative Distances and Sizes of the Sun and Moon: 11: Further Considerations: Planets and Stars. 12: The Moving Earth: 13: Stellar Parallax: The Astronomical Chicken 14: Greek Cosmology: 15: Stonehenge: 16: The Pyramids: 17: Copernicus Suggests a Heliocentric Cosmology: 18: Tycho Brahe, the Master Observer: 19: Kepler the Mystic. 20: Galileo Provides the Proof: 21: Light: Introductory Remarks. 22: Light as a Wave: 23: Light as Particles. 24: Full Spectrum of Light: 25: Interpreting the Emitted Light: 26: Kirchhoff's Laws and Stellar Spectra. 27: Understanding Kirchhoff's Laws. 28: The Doppler Effect: 29: Astronomical Telescopes: 30: The Great Observatories: 31: Making the Most of Optical Astronomy: 32: Adaptive Optics: Beating the Sky. 33: Radio Astronomy: 34: Observing at Other Wavelengths: 35: Isaac Newton's Physics: 36: Newtonian Gravity Explains It All: 37: Weight: 38: The Success of Newtonian Gravity: 39: The Ultimate Failure of Newtonian Gravity: 40: Tsunamis and Tides: 41: The Organization of the Solar System: 42: Solar System Formation: 43: The Age of the Solar System: 44: Planetary Structure: The Earth. 45: Solar System Leftovers: 46: The Vulnerability of the Earth: 47: Venus: 48: Mars: 49: The Search for Martian Life: 50: Physics 015 - Parallel Readings.
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(Wednesday, 21 April, 2021.)