no tagsLecture 022: The Nature of LightSteveSekula, 12 April 2011 (created 14 November 2010)Goals of this lectureExplain how four equations describing electricity and magnetism cametogether to explain the nature of lightWhat is light?What is light? This is a question that had troubled thinkers and scientists fora long time before the late 1800s. It is capable of carrying informationacross great distances - witness the light from our sun, which begins itsjourney 150 million kilometers away and arrives here on earth, deliveringenergy. It delights our eyes, which are optical systems sensitivity to arainbow (literally) of colors. But just what is light?A thing with a definite speedLight, whatever its nature, was already observed to travel at a great butfinite speed. Galileo Galilei, who lived in Italy in the 1500s and was the firstmodern scientist, wondered whether light, like sound, traveled at a finitespeed. He devised an experiment to measure this, in fact, but it failedbecause he did not appreciate just how fast light moves.You can measure the speed of sound quite easily, by comparison. Get someair horns, a stopwatch, and a few friends. Put one friend on the steps ofDallas Hall with an air horn, another friend 100m away (just south of the"Dedman College" sign on the Boulevard). Have a third friend stand on abench by the fountain between the Dedman College sign and Dallas Hall.Friend 3 will signal Friend 1 and 2 by waving their arms wildly. Friend 1 willfire their air horn and you'll start the stopwatch when that horn goes off.General Physics - E&M (PHY 1308) LectureNotesGeneral Physics - E&M (PHY 1308) LectureNotesGeneral Physics - E&M (PHY 1308) - Lecture Notes file:///home/sekula/Dropbox/Documents/Notebook...1 of 10 04/12/2011 09:06 AMWhen Friend 2 hears the first air horn, they will fire their horn. By doingthis, you make sound do a round trip from Dallas Hall, to a distance 100maway, and back again. You stop timing when you hear the second horn.Repeat the experiment, moving Friend 2 a distance 200m away from DallasHall. By doing this, you correct for reaction time (the time between hearingthe first horn and firing the second horn). Knowing the distance the soundmust travel, and the time it takes to make the trip, you can easily calculatethe speed of sound.Profs. Olness and Tunks run a "Physics of Musical Instruments" class with arequired lab, and in that lab you do this experiment. You may also have thepleasure of watching your TA swarmed by campus cops while conductingthe experiment, because apparently noise on a college campus is a seriouslaw enforcement problem these days.Sound travels at about 300m/s in air. To make the first round trip, itrequires 7/10 of a second. Human reaction time is about 2/10 of a second,so it's a big factor in this first trial. In the second trial, sound has to travel400m and that takes just over a second (1.3 seconds). Assuming thatreaction time is the same in both, and that the speed of sound is the same inboth, you can actually obtain a speed of sound that is accurate and has aprecision of about 5%. Not bad!Can we do this with light? Galileo tried. In fact, the above experiment withsound is a modern variation on the one he proposed for light. He put peopleon distant hills and have them lamps. The first person would open theirlamp, sending light to the second person. When the second person sees thelight from the first, they open their lamp. The first person stops timing theexperiment when the light from the second person arrives. Galileo himselfhas designed very good clocks, something in high demand in his day.However, human reaction time is 2 tenths of a second, while light actuallytravels at a speed so great that it crosses the distances in Galileo'sexperiment much too fast. But at the time, he didn't know that. He learnedthis by failing to succeed in his experiment.How fast does light travel, and why can't Galileo's experiment work asdesigned? Light, we now know, travels at a speed of about . Thefurthest you can see on the earth is about 60 miles, or 100km. Light makesa round trip of 200km in - far too fast for a human to react withsuch a simple experiment.Ole Roemer and Christian Huygens are two scientists credited withdetermining that light truly travels as a finite speed. A modern3:0 0 m=s  18Ø :7 0 s 0  1À7General Physics - E&M (PHY 1308) - Lecture Notes file:///home/sekula/Dropbox/Documents/Notebook...2 of 10 04/12/2011 09:06 AMinterpretation of their work suggests they came within 20% of the correctvalue. Roemer's work preceded Huygens, and corresponds to ameasurement of .The Nature of SoundSound is a wave. It occurs when air is compressed by a force, and thatcompression travels through air. When it strikes the eardrum in the humanear, a series of small bones that can respond to vibration, they cause thebones to shake and that becomes electrical impulses that our braininterprets as "sound". But, regardless of what we hear, sound is just acompression of a medium (air) that travels with a definite speed determinedby the mechanical properties of the medium. Sound cannot travel in theabsence of air, just as water waves cannot exist without water. All the wavesthat any scientist had ever encountered up to the late 1800s REQUIRED amedium to travel. The language of waves demanded a medium.Let's refresh a little on that language. A simple wave is just a variation inamplitude (e.g. air density) that repeats at regular intervals. Such a wavecan be described using terms like period - the time that passes betweensimilar parts of a wave traveling by you - and wavelength, - the physicaldistance between similar parts of a wave.Using a sine wave as an example, we can easily see the wavelength. Theperiod, , is just the time it takes for a wave to travel one wavelength - thatis, the time for similar parts of the wave to pass you. The frequency ( ) isjust , and is the rate at which similar parts of the wave pass you.The speed of a wave is given by distance traveled by the wave in a unit oftime. For instance, in one period, , the wave will travel one wavelength. .Thus the speed of the wave is given by:the product of the wavelength and the frequency.Sound is fast, but it's not fast enough. For instance, musicians in anorchestra pit have to use two important tools in order to remainsynchronized - that is, all be playing at the appropriate times. The first toolis the conductor and the second tool is called "leading the
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