An image of Jupiter andits moon Io (left) from the Cassiniprobe.c / The earth is moving towardJupiter and Io. Since thedistance is shrinking, it is takingless and less time for the light toget to us from Io, and Io appearsto circle Jupiter more quickly thannormal. Six months later, theearth will be on the opposite sideof the sun, and receding fromJupiter and Io, so Io will appearto revolve around Jupiter moreslowly.ments around the year 1675. Roemer observed Io, one of Jupiter’smoons, over a period of several years. Since Io presumably took thesame amount of time to complete each orbit of Jupiter, it could bethought of as a very distant, very accurate clock. A practical and accuratependulum clock had recently been invented, so Roemer couldcheck whether the ratio of the two clocks’ cycles, about 42.5 hoursto 1 orbit, stayed exactly constant or changed a little. If the processof seeing the distant moon was instantaneous, there would be noreason for the two to get out of step. Even if the speed of light wasfinite, you might expect that the result would be only to offset onecycle relative to the other. The earth does not, however, stay at aconstant distance from Jupiter and its moons. Since the distance ischanging gradually due to the two planets’ orbital motions, a finitespeed of light would make the “Io clock” appear to run faster as theplanets drew near each other, and more slowly as their separationincreased. Roemer did find a variation in the apparent speed of Io’sorbits, which caused Io’s eclipses by Jupiter (the moments when Iopassed in front of or behind Jupiter) to occur about 7 minutes earlywhen the earth was closest to Jupiter, and 7 minutes late when itwas farthest. Based on these measurements, Roemer estimated thespeed of light to be approximately 2 × 10 8 m/s, which is in the rightballpark compared to modern measurements of 3×10 8 m/s. (I’m notsure whether the fairly large experimental error was mainly due toimprecise knowledge of the radius of the earth’s orbit or limitationsin the reliability of pendulum clocks.)Light can travel through a vacuum.Many people are confused by the relationship between soundand light. Although we use different organs to sense them, there aresome similarities. For instance, both light and sound are typicallyemitted in all directions by their sources. Musicians even use visualmetaphors like “tone color,” or “a bright timbre” to describe sound.One way to see that they are clearly different phenomena is to notetheir very different velocities. Sure, both are pretty fast comparedto a flying arrow or a galloping horse, but as we’ve seen, the speed oflight is so great as to appear instantaneous in most situations. Thespeed of sound, however, can easily be observed just by watching agroup of schoolchildren a hundred feet away as they clap their handsto a song. There is an obvious delay between when you see theirpalms come together and when you hear the clap.The fundamental distinction between sound and light is thatsound is an oscillation in air pressure, so it requires air (or someother medium such as water) in which to travel. Today, we knowthat outer space is a vacuum, so the fact that we get light from thesun, moon and stars clearly shows that air is not necessary for thepropagation of light.136 Chapter 7 The Ray Model of Light
Interaction of light with matterAbsorption of lightThe reason why the sun feels warm on your skin is that thesunlight is being absorbed, and the light energy is being transformedinto heat energy. The same happens with artificial light, so the netresult of leaving a light turned on is to heat the room. It doesn’tmatter whether the source of the light is hot, like the sun, a flame,or an incandescent light bulb, or cool, like a fluorescent bulb. (Ifyour house has electric heat, then there is absolutely no point infastidiously turning off lights in the winter; the lights will help toheat the house at the same dollar rate as the electric heater.)This process of heating by absorption is entirely different fromheating by thermal conduction, as when an electric stove heatsspaghetti sauce through a pan. Heat can only be conducted throughmatter, but there is vacuum between us and the sun, or between usand the filament of an incandescent bulb. Also, heat conduction canonly transfer heat energy from a hotter object to a colder one, but acool fluorescent bulb is perfectly capable of heating something thathad already started out being warmer than the bulb itself.How we see nonluminous objectsNot all the light energy that hits an object is transformed intoheat. Some is reflected, and this leads us to the question of howwe see nonluminous objects. If you ask the average person how wesee a light bulb, the most likely answer is “The light bulb makeslight, which hits our eyes.” But if you ask how we see a book, theyare likely to say “The bulb lights up the room, and that lets mesee the book.” All mention of light actually entering our eyes hasmysteriously disappeared.Most people would disagree if you told them that light was reflectedfrom the book to the eye, because they think of reflection assomething that mirrors do, not something that a book does. Theyassociate reflection with the formation of a reflected image, whichdoes not seem to appear in a piece of paper.Imagine that you are looking at your reflection in a nice smoothpiece of aluminum foil, fresh off the roll. You perceive a face, not apiece of metal. Perhaps you also see the bright reflection of a lampover your shoulder behind you. Now imagine that the foil is justa little bit less smooth. The different parts of the image are nowa little bit out of alignment with each other. Your brain can stillrecognize a face and a lamp, but it’s a little scrambled, like a Picassopainting. Now suppose you use a piece of aluminum foil that hasbeen crumpled up and then flattened out again. The parts of theimage are so scrambled that you cannot recognize an image. Instead,your brain tells you you’re looking at a rough, silvery surface.d / Two self-portraits of theauthor, one taken in a mirror andone with a piece of aluminum foil.e / Specular and diffuse reflection.Section 7.1 Light Rays 137
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copyright 2006 Benjamin Crowellrev.
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ContentsMomentum compared to kineti
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Chapter 1Conservation of Mass andEn
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1.2 Conservation of MassWe intuitiv
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masses on the spring, and they both
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A common source of confusion is the
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Discussion questionA Each of the fo
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l / Galileo Galilei was the first p
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that this wasn’t really an argume
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the girl on the left goes up a cert
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1. kinetic energy2. gravitational e
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In fact, your body uses up even mor
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kinetic energy is twice as much. Bu
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ather than flying off straight. New
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of mass?Actually they’re not even
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ecause the square of the speed of l
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ProblemsKey√∫⋆A computerized
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13 How high above the surface of th
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Chapter 2Conservation ofMomentumFan
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win the Martian version of the Nobe
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a / How can we prove that this coll
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all.This is exactly like the rules
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Unequal masses example 4⊲ Suppose
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ForceDefinition of forceWhen moment
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ent relationship:(fingers on scale)
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pressed in modern units). If the ea
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p / A bowling ball is in the back o
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Kepler’s law of periodsLet T , ca
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2.5 WorkImagine a black box 8 , con
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ProblemsKey√∫⋆A computerized
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A tornado touches down in Spring Hi
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pensated for by an overall increase
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Kepler’s equal-area law example 4
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Torque distinguished from forceOf c
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ProblemsKey√∫⋆A computerized
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Chapter 4RelativityComplaining abou
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motion of the apparatus. For instan
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fore Einstein. In fact, George Fitz
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We are used to thinking of time as
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j / In the garage’s frame of refe
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is now sufficiently advanced to all
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twin paradox, 83units, conversion o