| Light as a Wave:
Wave Phenomena in General.
When we speak of waves, we generally think of those we see in the water, but there are in fact two different kinds. (We will be meeting this distinction again in the context of the transmission of seismic waves through the Earth's interior.) They are:
Longitudinal waves, which I demonstrated with a `slinky toy' in class. They consist of disturbances which pass through a medium by virtue of to-and-fro motions of and collisions between atoms. Sound is an example. I speak, and my vibrating vocal cords cause the atoms near me to `jiggle' in some way. As they move away from me and towards you, they bump into other atoms and rebound, but the other atoms carry the motion forward until they in turn collide with yet more atoms, and so on. The `jiggling' eventually reaches your ears (at the speed of sound, about 300 metres per second in the atmosphere) and set your eardrums to vibrating in a way that your brain can interpret as a sound which is comprehensible (I hope).
Transverse waves, which I demonstrated in class by wiggling up and down one end of a stretched rope. These waves consist of disturbances which are across (or transverse to) the direction in which the wave itself is going. For instance, if you were a bug on the rope, you would be moving up and down as the ripples pass by, but the disturbance itself passes along the length of the rope. The familiar wind-driven waves at the surface of a body of water are also transverse: a cork floating in the water bobs up and down where it is, while the disturbance passes through the water along the surface.
A common feature in both of these types of waves is that the medium itself does not suffer any net displacement: the atoms go back and forth or up and down, but if you look again a few minutes later you will see that they are still near where they were at the start. Likewise, a cork floating in the water merely bobs up and down `in place'. There is room for confusion here, because you are used to seeing waves breaking onto a beach. At the shore, individual atoms of water actually move quite a lot as the waves spill up onto the sand; but this phenomenon is caused by the complex interactions between the transverse wave and the lake bottom, which itself is sloped and irregular, causing friction and so on. In the open sea, the wave disturbance merely passes through the watery medium without carrying the constituent atoms along with it.
In what follows, we will consider the evidence for light being a transverse wave. (In preparation for that, you should read carefully the definitions of wavelength, frequency, and so on that you will find on pages 156-157 of the text.) When we speak of light as a wave phenomenon, we try to find ways in which its behaviour is not consistent with what you would expect from a bunch of little energy-carrying `bullets'. Are there such ways?
Diffraction: Waves Spreading Out from a Hole.Consider ocean waves arriving at a breakwater with a hole in it, as shown in the figure: The breakwater could consist of a cement wall, say, with an opening - the sort of thing you find near a yacht harbour. The boats enter through the gap in the wall, while the wall itself provides some protection against very strong waves crashing directly into the docks and the shore. Now, if you were standing at point X on the shore, directly opposite the gap in the wall, you would surely see waves breaking at your feet onto the beach. But what if you were standing at point Y, perhaps fifty meters north along the shore? Would the water there be as completely still as a millpond? No indeed! As you know from experience, the disturbances in the water would indeed spread out as shown in the figure, and people along a wide stretch of the shoreline would see the water slosh up and down, although less vigorously than would the person directly opposite the gap. This is quite distinct from the behaviour of lumps that move in straight lines - things like bullets, for instance. If you are ever being shot at, just step through a doorway in a cement wall and take cover to one side or the other. Unless the bullets ricochet off the back wall of the room you have entered, you will be safe -- there is no need, for example, to fear that the bullets will 'smear out' in all directions as they pass through the doorway. But now, on a much smaller scale, think of a source of light to the left of the figure and shining onto a little hole in an opaque card. If the light was like bullets, you would expect to see a tiny distinct spot of light directly opposite the hole, but no light at any other location. Instead, you will find that it spreads out into a fuzzy blob. (In fact, it does more than produce just a fuzzy blob. We would also see some interesting structure, including rings and so forth, which we will not concern ourselves with here, other than to note that this too is well understood in terms of the wave nature of light.) You may protest that you do not see this in day-to-day life! In general, an object held up in front of a source of light seems to cast a very sharp shadow. (Imagine making hand-shadows to entertain your kids at night, for instance.) That is true: most shadows do look quite sharp. The effects of diffraction are really only important if the hole is very small (comparable to the wavelength of light itself). In other words, light which passes through an extremely tiny pinhole gets smeared out into a relatviely large fuzzy patch; but if the hole is much larger, the effect is not readily seen.
Diffraction: Waves `Bending' Around Corners.We have considered a hole in a seawall (or, in the context of the bullets, a doorway in a cement wall), but in fact the phenomenon is more general than this. The effects of diffraction are seen wherever there is a sharp discontinuity. Waves, for example, can `bend,' or diffract, around corners. Indeed, this is how you can hear voices around corners, even if there are no walls or other buildings to provide echoes or reverberation. Sound waves diffract. Light can be shown to do the same thing. Once again this occurs on very small scales, since the wavelengths of visible light are so short. Consequently, one doesn't notice such phenomena in day-to-day life. As evidence, however, I showed you a picture in class, one in which we could see the sharp edge of a razor blade and a so-called `shadow diffraction pattern,' a series of dark lines parallel to the edges of the razor. (I do not want to go into the technical details of how these lines are formed. Suffice it to say that it is fundamentally due to this `bending around corners.') This is further evidence that light behaves like a wave. By the way, you might be tempted to think that the phenomenon of twilight is caused by something like this. Does the light from the sun diffract around the edge of the Earth so that we still see a bit of sunlight even after it has set? The answer is no - or, at least, that this effect is utterly negligible. Twilights are caused by the gas and dust in the Earth's atmosphere. If the Earth were completely airless, we would be plunged into pitch darkness the instant the sun set. Instead, we enjoy lingering twilights because of the scattering (bouncing) of light off molecules and atoms high in the Earth's atmosphere.
Interference: Waves Interacting with One Another.Just above, we considered ocean waves arriving at a breakwater with a single hole in it. A more interesting effect would be produced by a breakwater with two holes in it, as shown in the following figure: Upon the arrival of parallel waves from the open sea, each hole acts as an independent centre of new sets of waves propagating out towards the beach. In the figure, I have colour-coded the new waves, with the hole at the top producing a set of expanding black ripples (one of which has been coloured green, for reasons to become obvious in a moment) and the one at the bottom producing a set of expanding blue ripples (one of which has been coloured red). At the right of the picture, the dotted parts of a few of the waves show how they would have continued had they not run up against the beach, which is represented by the thin black line. Now ask yourself what you would see if you were standing on the beach in the various locations indicated. If you were exactly half-way between the two holes in the breakwater, at the point marked with a large red letter 'A', you would be seeing a peak (an upward surge of water, represented by the solid green line) in the wave coming from the top hole, and a peak in the wave coming from the bottom hole (the solid red line). At that location, therefore, the upward surge of the water would be redoubled as the independent waves arrive and their effects add. A moment later, you would see a trough (a downward displacement) in the waves arriving from the top hole, and another trough in the wave pattern arriving from the bottom hole, so the the total downward effect would also be doubled. These effects would repeat again and again at the frequency of the original waves. In other words, at point A you would see waves which are enhanced in effect because they are arriving in phase from the two holes in the breakwater. This is called constructive interference. In short, if you were at position A, you would see the water going up and down with great vigour! You can identify other positions where the behaviour would be qualitatively similar. At the points labelled 'B1' and 'B2,' for instance, we would expeience the coincident arrival of a wave from the top hole and another from the bottom hole. This situation differs from position A in that the arriving waves did not set off at the same time from the two holes. (At point B1, we are seeing the arrival of the black wave which is just ahead of the green one, whereas we see the arrival of the blue wave which is four waves in front of the red one.) But the effect is the same: we experience a vigourous up-and-down of the water as these disturbances arrive in phase. Now look at the position marked C1. Here we see an upward peak from the top hole (the green wave), but a downward trough from the bottom hole (we are exactly halfway between the successive crests represented by the blue waves). The net displacement of the water is zero, and that will always be the case. Whatever disturbance is arriving from the top hole, a disturbance of equal size but in the opposite direction will be arriving from the bottom hole. This, then, is a region of destructive interference, and the water should be as smooth as a millpond all the time at that particular location -- in principle! In real life, of course, things are not this simple. Water at the seaside is running up against the shore, which may be of irregular depth and roughness, and the wave disturbances rebound off the shore. Still, if you were sitting on the shore you would notice that there are regions where the water seems quite placid, and other regions where the water is sloshing up and down with great vigour. The remarkable thing is that light can be shown to produce the same kind of interference phenomena. There is a classical physics experiment known as the Young double-slit experiment. It duplicates, on a tiny scale, the two-holed ocean breakwater situation just described. Young cut two tiny slits into an opaque screen onto which he shone a light of a well-defined colour (which means, as we will see, that it contains light of just one wavelength). This did not produce two bright images, one of each slit, on the wall beyond the screen; neither did it produce two fuzzy blobs, as you might have expected from the discussion in the previous few paragraphs. Instead, Young saw a pattern of dark and light bands, as shown in the figure shown here (Moreover, if you were sitting near the front of the lecture hall, you will remember that I demonstrated the same behaviour by shining a laaser onto a card with various slits cut into it. This was probably not so easily seen from the back of the hall!). In the figure, the bright regions are locations where the `wavefronts of light' add constructively (so the light is very bright); the dark regions are locations where the separate wavefronts cancel out entirely by destructive interference. In other words, light is a wave!
Polarization: Yet More Evidence for Waves.In class, I demonstrated the effect of Polarizers. These are sheets of material which look like the stuff sunglasses are made out of (and, indeed, some sunglasses do use polarizers, for reasons I will touch on a few paragraphs later). You will remember that I had two polarizers, and laid each one down on the top of the overhead projector to show that they individually cut out a fair fraction of the light passing through (which is why they look dark). But when I first laid one on top of the other, there was only a little bit of extra dimming. The light did not seem to be very much diminished by the double layer. But then I rotated one of the polarizers so that it was lying at right angles to its previous orientation. The two polarizers together now cut out essentially all the light, and the double layer looked very dark indeed! Why? The effect depends on the fact that light is a wave, and is best understood with another analogy -- one which sounds ridiculously far-fetched, but one which I believe will help you to understand the essential physics. Suppose you like to travel around town on a pogo-stick. This means that you bounce along the road, going up and down four or five feet, say. If you now come to a very narrow alley, with high brick walls on either side, you have no problem. You can easily pass through the alley, still bouncing. But now suppose instead that you come to a wide but very low overpass, one which you could ordinarily just walk through with your head barely touching the roof. Your bouncing motion will be quickly suppressed as you bang your head repeatedly into the overhanging roof, and your progress will be stopped. Now visualize someone else leaping back and forth sideways in a great zig-zag as they travel down the road. You can see that they have the opposite problem. There is no way that they can keep up this odd motion through the narrow alleyway, but there is nothing to prevent them doing so as they pass under the low but wide overpass. Finally, imagine a crowd of people travelling down the road, with half of them on pogo sticks and the other half leaping from side to side in great zig-zag jumps. A narrow alley will stop about half of them (the `zig-zag jumpers') but allow the pogo-stick people to continue. A second narrow alley will have no further effect -- the pogo-stick people will get through again. But a low overpass will stop them, and no one will come out the other side! If you think about it, you will see that the order in which these obstacles are met doesn't matter. The final effect is the same: a narrow alley and a low underpass combine to prevent the passage of any of our eccentric travellers. This, in essence, is what the polarizers do. The light emitted by a lamp, or by the sun, consists of transverse electromagnetic waves which are oriented in random directions. In some, the disturbance passes through space with an up-and-down sense: these are pogo-stick riders. In other rays, the disturbance has a side-to-side motion as it passes; these are the zig-zag jumpers. On a microscopic scale, the crystal structure of the polaroid materials is such that the sheets of polarizer act like the alleyway and the overpass. Depending on how you orient the two sheets, you can prevent more of less of the light getting through. I will not discuss the physics of why the crystalline material has this effect, but it is clear that you would have a hard time to understand the phenomenon if the light was like little bullets, with no preferred direction. The effect clearly depends on the fact that light is a wave, each bit of which has a well-defined sense of vibration. Digression: in class, I mentioned one of the reasons for having polarized sunglasses. Imagine yourself in a boat on a sunny day, with sun glaring off the water; or skiing in a field of brightly lit snow; or in a car, with the sun glaring off the road and cars ahead. Well, for reasons I will not explain, it happens that sunlight which reflects at certain angles off such shiny surfaces winds up being very strongly polarised. In fact, the sun glaring off the water in front of the boat consists almost entirely of `sideways jumpers' with not very many `pogo sticks.' (If, however, you look towards the sun itself, before the light glances off the water at these critical angles, it is an even mix of both kinds.) Since the reflected glaring light is so strongly polarised under these circumstances, a polarised pair of sunglasses can cut out the vast majority of the light and make a big difference to your comfort. But if you take the sunglasses off and turn them through ninety degrees (holding the pair of glasses vertically, that is, with one lens above the other) you will find, on looking through them, that the glare isn't reduced very much. Try this sometime when you are driving -- or, more prudently, when you are a passenger in someone's car on a sunny day.
Waves in What?When we considered sound and water waves, we were speaking of mechanical disturbances in some medium. For instance, the sound of my voice is generated by vibrating vocal cords which set the air in motion; the waves in the ocean are set going by the effects of the wind pushing the water about; and so forth. Thereafter the disturbance propagates by simple physical laws. The atoms collide with other atoms and rebound, passing on their energy and momentum, etc. But light is different in that it can pass through a vacuum. (Sound, of course, cannot). There does not have to be a medium to carry the light. What is happening? A century or more ago, it was believed that there was a medium through which light propagated, a medium called the luminiferous (`light-bearing') ether. Since light passes between the stars and planets, it was obvious that the ether had to fill all space. Yet the Earth has clearly been orbiting the sun in a more-or-less-unchanging orbit for many millions of years, so it must experience a negligible amount of `wind resistance' from the ether. This consideration, and the extremely high speed with which light travels, implied some very unusual properties for the ether. A great goal of late 19th-century physics, then, was to find absolute proof of the existence of the ether, and to learn more about its properties. The death-knell came with a famous experiment, carried out by Michelson and Morley, which seemed to show that there was no ether. An almost direct consequence of this was Einstein's development of his special theory of relativity, in 1905, a theory which completely changed the way in which we think about space and time. I will not describe those developments now since they fit in more naturally nearer the end of the course. But the important point is that I want you to realize that light is not analogous to sound and other mechanical disturbances which pass through a substance or a medium. It can, and does, travel through the true vacuum of space.
Electromagnetic Waves.The modern physics interpretation is that light is a wave which consists of changing electric and magnetic fields which propagate through space (see the figure below). Before going further, let us remind ourselves of what we mean by an electric field. We say that an electric field exists in a location if a charged particle, like an electron, feels an electrical force there (perhaps because of the presence of other charged particles in its vicinity, for instance). That is what makes a spark leap from your fingertip to a doorknob when you build up what we call `static electricity' -- the electrical forces cause the negatively-charged electrons to leap across the gap. Light can be thought of as a transverse wave moving at high speed (300,000 kilometers per second) through intervening space, and consisting of rapidly changing electric and magnetic fields. Can you predict the effects such a wave might have as it passes by? Well, one answer is that a charged particle (like an electron) sitting by itself in empty space should 'bob up and down' as the wave goes by, just as a cork bobs up and down in the water when a wave passes by. (As you can see from the figure, there is also a changing magnetic field, which is at right angles to the electric field. You can imagine a small compass turning back and forth in quick response to this changing magnetic field as the wave passes by.) The reality of this interpretation can be tested. Take a strip of metal which is a good conductor (that is, one in which the electrons are fairly free to move) and send light of some wavelength (and associated frequency) towards it. Then design some simple electronics to detect whether or not the electrons are indeed bobbing up and down, an effect which would be tanatamount to producing small electric currents of varying size inside the conductor. This is exactly what happens in your radio antenna or TV antenna! . The signal which is broadcast from the radio or TV station is not visible light, of course, so our eyes are not sensitive to it, but it is light (electromagnetic radiation) none the less. It makes the electrons in the radio antenna ``bob up and down'', and the small electric currents so generated are detected, amplified, and used to determine how to make your speakers vibrate. This in turn creates the sound waves which you hear. Please note an important distinction. Radio waves are light, not sound. They are used by the circuitry in your radio to determine how to make the speakers vibrate, and that is where the sound comes from. Radio astronomers are collecting electromagnetic radiation from the stars and galaxies, not sound (which could never pass through the vacuum of space anyway). 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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(Monday, 17 May, 2021.)