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table of contents introduction section 1 ­ optics chapter 1 reflection · plane mirrors lab reflection from a plane mirror mini project eye chart demonstrator · curved mirrors activity a comparison of plane convex and concave mirrors activity mirror ray diagrams lab reflection from a curved mirror · the mirror equation 1 3 5 5 7 21 25 26 32 37 42 54 56 57 61 67 70 74 77 80 83 89 97 101 105 107 109 109 113 115 119 120 122 125 130 131 133 141 149 161 163 168 170 178 180 182 183 chapter 2 refraction activity a first look at refraction lab optical refraction · snell s law activity optical refraction · atmospheric refraction effects · lenses activity the physics of lenses activity lens ray diagrams · the fresnel lens · the thin lens equation · total internal reflection activity total internal reflection · white light dispersion activity white light dispersion chapter 3 physics of the eye · the visual process · color · visual accommodation activity color section 2 ­ waves chapter 4 waves and sound labette introduction to waves · wave interference activity wave interference · sound waves activity orchestral sound · the doppler effect chapter 5 musical sound · resonance and standing waves · introduction to musical instruments · modes overtones and harmonics · the physics of musical scales · beats · musical intervals · the equal tempered musical scale

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frequencies of the 12-tone equal tempered scale · chordophones stringed instruments · aerophones wind instruments lab musical scales and instruments · idiophones percussion instruments lab a closer look at idiophones 189 190 196 205 207 211 217 219 226 229 236 241 245 247 250 252 255 263 263 265 267 268 270 273 274 276 277 285 291 295 297 299 303 chapter 6 wave phenomena lab two dimensional wave interference labette wave diffraction lab light diffraction and interference · thin film interference · polarized light section 3 ­ electricity chapter 7 static electricity · the forces charges exert on each other activity visualizing electric charge labette a survey of static electricity · the electric field and electric potential energy · visualizing the electric field · charge distribution on conductors · electric potential energy · voltage activity visualizing electric fields chapter 8 electric circuits · electrical resistance · ohm s law · power and energy in circuits lab electric circuits · thinking about series and parallel circuits lab lights in circuits labette combination circuits activity mystery circuits activity conceptualizing circuits appendix 309

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i have no special talents i am only passionately curious ­ albert einstein introduction all knowledge begins in wonder ­ aristotle i must have walked up and down the steps in the tamalpais high school science building 10,000 times during my first ten years at the school but it wasn t until the eleventh year that i noticed something unusual about those steps as you re going up the stairs the steps on the right side have significantly more wear on the slip-resistant surfaces than those steps on the left side i thought about it for a bit and then decided to think about how i climb and descend the stairs i went up and down over and over trying to mimic the way thousands of students have used the stairs over the last five decades as i went faster and faster it began to become clear to me i felt more of a potential to slip going down the stairs and so i tended to plant my feet squarely on the surface of the step going upstairs though i felt very stable and could easily skip steps i was more careless tending to plant my feet at a slight angle i scuffed a little and it s america i always moved up or down the stairs on the right side in order to accommodate traffic 1

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i suspect that in britain similar stairs are worn on the left side when people ask me what physics is and what physicists do i now start by telling them about the steps in the science building and about my curiosity over them and my answer to the question of why they are the way they are people ask me all the time what exactly is physics in one sense that s a difficult question to answer because the subject spans such a huge body of knowledge however the longer you study physics the more you begin to see it as a very basic pursuit it s a quest to know the nature of nature physics is the realm of the curious if you re curious that s the first step toward being a good physicist more than three centuries ago isaac newton wondered about the nature of gravity he mused correctly that the force holding the moon in its orbit was the same as that which caused an apple to fall from a tree his passionate curiosity keen insight and over-the-top intelligence led to his universal law of gravitation this combined with his other insights into motion in general with a good deal of help from galileo became the foundation of what is now known as mechanics they thought of the world as a giant mechanical machine their curiosity led to an understanding of how the machine worked it is so good a description of nature that even with primitive computers aerospace engineers were able to use this mechanics to land astronauts on the moon it all started with curiosity then there came big breakthroughs in the 18th and th 19 centuries which gave us an understanding of electricity magnetism and light maxwell s equations named for james clerk maxwell showed the intimate connection between these three phenomena formerly thought to be unrelated so by the end of the 19th century it appeared that physics had triumphed many physicists felt that through curiosity and hard work we had finally figured out how nature works this all changed though near the beginning of the 20th century in the early 1900 s albert einstein wondered about a certain consequence of maxwell s equations the equations require light to always travel at the same speed 3.0 x 108 m/s ­ in any frame of reference this meant that if someone shined a flashlight in one direction anyone would measure the beam of light moving at the same speed regardless of how fast he were moving if this doesn t seem odd think about it in terms of ups trucks if a ups truck is moving at 60 mph north and you are standing by the side of the road the truck passes you at a speed you measure to be 60 mph however if you are also moving north but at 40 mph the truck still passes you but now you only measure its speed to be 20 mph relative to you now imagine there is a rule that all ups trucks have to move at 60 mph in any reference frame then regardless of whether you were stationary or moving the passing truck would always have the same relative speed of 2 60 mph the idea seems crazy but that is exactly the case for the speed of light einstein eventually realized that the problem was that newton s idea of absolute time and space was wrong einstein s theory of special relativity showed that space and time were in fact relative depending on how the observer is moving another problem occurred as very small structures were investigated physicists wondered about the smallest possible structure was there a limit first there was the theory of the atom as the smallest indivisible particle but then the electron smaller than the atom was discovered at the end of the 19th century by the early 20th century the smallest known particles were the electron the proton and the neutron all matter could be constructed from just these three particles we now know that the proton and neutron are actually composite particles made up of even smaller particles known as quarks but there was a problem in using newton s mechanics to explain the observed behavior of these fundamental particles newton s mechanics didn t work for these smallest of particles quantum mechanics had to be used over the last many decades quantum mechanics has been tested to extraordinarily great precision and accuracy and has been found to agree perfectly with the way small particles behave so now in the early 21st century have we finally figured it out the mechanics of the universe ­ both large and small well let s just say that we ve come a long way curiosity has led to amazing discoveries about the nature of nature it has also opened up doors to mysteries that make what lies ahead at least as interesting as what physics has helped us to understand thus far for example nature seems to be so connected and simple in the parts that we do understand so there is a hope and belief that there is a connection between the realm of the very large that governed by gravity and that of the very small governed by quantum mechanics string theory or the theory of everything hopes to bring these two together a competing theory attempting to do the same thing is that of quantum gravity another area of interest is cosmology how did the universe start how will it all end and what s out there when tamalpais high school opened its doors for the first time the known universe was no larger than the milky way galaxy the milky way consists of 100 billion stars but we now know that ours is only one among 100 billion or so other galaxies and we ve since come to discover that over 90 of all matter in this vast universe appears to be some mysterious unknown dark matter it looks like 21st century physics will be at least as exciting and important as physics has ever been in the past the quest to understand the nature of nature is still drawing the curious welcome to physics!

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it suddenly struck me that that tiny pea pretty and blue was the earth i put up my thumb and shut one eye and my thumb blotted out the earth i didn t feel like a giant i felt very very small ­ neil armstrong section 1 optics d oes a person born blind miss the sense of sight or is it like a person with all five senses who tries to imagine a sixth sense what does a blind person think of color or brightness does it seem totally obscure to think of clashing colors and what does the person born blind think an optical illusion is i had a friend in fifth grade who was born on one side is darkness and the other side light the open eye darkness bringing blind and i used to watch allows the light to flow into the the body 70 of the with it information about the world outside human him as he slapped pieces of being s sensory input comes through the optic nerve rubber and plastic on a plaster wall and listen to the sounds they made i realized his sense of hearing was far more developed than mine he got so much more out of a sound than i could but he couldn t see you opened your eyes for the very first time and you were struck with a complicated world of visual images with your first gaze around your new environment the input became instantly dominated by the sense of sight the average person takes 70 of their sensory input through their sense of sight you looked for the first time and perhaps saw the face of your mother you saw other people too you saw the hard edges of the furniture in the room and the softness of the blanket you were wrapped in like a person blind his whole life and then given sight you saw so much that you couldn t make sense of ­ so much chaos and different and changing levels of 3 light but that s it that s all you saw and ever will see just light you didn t see the face of your mother that day you never have never will you simply saw the light reflected off her face you ve gotten used to the very unique way light reflects off her face and so whenever you see that pattern of light rays you think mom it s a little unsettling to think about sight that way at first we like to think that we see our mom and other objects that are important or dear but our eyes are not sensitive to things only light it s amazing to me when i think about it this way that the light reflecting off a can of coke on a hot day can make me feel thirsty the

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optiics pt cs light reflecting off the needle before i give blood can cause a bit of a panic and the light reflecting off my wife can make me feel affection all these emotions and just from different patterns of light that s why we ll start with light if all we see and all we ll ever see is light and it amounts to 70 of our sensory input it makes sense to me that we should know something about it when light strikes something it reflects off that something in a perfectly unique way consider the light reflecting off the face of your best friend if you look at that light your first thought is that you re not seeing light but you re really seeing the face of your best friend honestly i act this way myself unless i think carefully about what i m looking at now that light you re looking at brings you enough information about your friend that you recognize her instantly the light brings information about the size and structure of her body the softness of her hair the clench of her jaw if she s mad the playful smirk she wears when she s thinking something devious the light holds nothing back the unique arrangement of reflected rays can betray a new zit a poppy seed lodged between two teeth or an errant booger light any light is truly a warehouse of information there is one more sobering thing to consider ­ one more thing to let your non-physics friends ponder not only do you not see things but only the light reflected off those things but you don t even see images in real time what you see is not happening when you see it the reason for that is that light has a finite speed it s fast but still finite the speed of light in empty space is 300,000,000 m/s 3.0 10 8 m s that s really fast if you had a unfathomably large that astronomers use the term light year to describe the distances in terms of how many years light would have to travel in order to reach our eyes hence proxima centauri is 4.2 light years away from earth this closest star is over 267,000 times further away from us than the sun to get a feeling for the vastness of space if the sun and earth were separated by 60 feet the earth and proxima centauri would be separated by 3,000 miles other stars are hundreds thousands millions and even billions of light years away on the night of february 24 1987 the first nearby supernova in three centuries was observed in a nearby galaxy the large magellanic cloud its distance was 170,000 light years away there was massive excitement within the astronomical community it was the rage the event the inspiration for so many astronomers but the event observed in 1987 was very old history having occurred 40,000 years before the age of the earliest fossil of modern man what it means is that when you look at the night sky most of the light you see began its journey long before you were born and in most cases long before civilization existed the night sky is a vast canvas over which is painted a living history of the universe light is all history not only on an astronomical scale but even on the scale that you re working with now the light from the letters on this page takes a very short time to reach your eyes but it s not instantaneous so it truly is history that you re seeing in the light from the letters of this page and in the light coming from everything you will ever look at properties of light why is it that when you look into the curved surface of a shaving mirror you see a magnified image of your face how does a magnifying glass focus sunlight into a small intense point of bright hot light why do stars twinkle how does an optical fiber restrain light preventing it from escaping the fiber s totally transparent sides these are a few of the many many questions that people frequently ask about or at least think about light we could start by examining the various theories of what light is a particle a wave something else and then go about trying to prove or disprove them but i d rather start by trying to understand what light does and why and perhaps if we begin to understand the properties of light well enough maybe the essence of what light is will become clearer so that s where we ll start ­ trying to understand the properties of light flashlight with a beam that would bend with the earth s curvature and you shined it towards the horizon it would hit you in the back almost immediately if the beam had nothing to run into it would circle the earth seven times in one second it is almost impossible to imagine that kind of speed but if you have a bit of a grasp then you can begin to understand how vast the universe really is light takes just a bit over a second to reach us from the moon when you look at a sunrise though you re looking at light that left the sun over eight minutes earlier you re not seeing the sun as it really is but as it used to be it s a historical perspective it s more sobering when you consider light coming from outside the solar system light from the nearest star proxima centauri travels over four years before it reaches our eyes and that s the closest star the distances to stars and other galaxies are so 4

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optiics pt cs chapter 1 reflection plane mirrors w e love to look at plane mirrors we look at them as we enter and leave bathrooms at the gym we work out in front of them we can t help taking a quick look at the mirrored walls of elevators but let s be honest it s not the mirror we re looking at no we re really looking at ourselves well technically we re looking at images of ourselves the storefront windows of businesses act well enough as plane mirrors that we use them to check ourselves out while we pretend that we re looking through them at merchandise we love to look at ourselves and because of this it s hard to find places where there are no mirrors to make sure we can always get an image fix we carry them in our purses and backpacks i m sure that our prehistoric ancestors were probably just as fixated by the images they saw of themselves in flat pools of water we use plane mirrors more often than curved mirrors because plane mirrors produce images that are the best representation of ourselves the image produced by a plane mirror is identical in size and orientation to its object on the other hand curved mirrors concave and convex produce images that are sometimes larger sometimes smaller and sometimes upside down what is it about plane mirrors that causes them to produce so identical an image answering that is one of the goals for the following lab figure 1.1 any smooth and flat reflecting surface can act as a plane mirror our prehistoric ancestors probably used still water as a plane mirror reflector photo by kayvon beykpour class of 2006 figure 1.2 the image produced by a plane mirror gives the best representation of an object the image size and orientation are identical to the object can you tell which is the real building and which is its image photo by laura reed class of 2007 5

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optiics pt cs 6

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optiics pt cs lab reflection from a plane mirror introduction it s true that plane mirrors produce simpler images than curved mirrors but they certainly aren t trivial ask a group of people who have never studied optics where they think the image produced by a plane mirror is located and you ll get three responses some will say on the mirror surface of course others will say in front of the mirror s surface of course still others will say behind the mirror s surface of course people tend to be emphatic about what they know to be true but all three locations can t be right this lab will lead you to the discovery of this image position more important will be the discovery of two laws of reflection one of which is a universal rule that applies to all reflections not just those from flat surfaces in the space below write down where you think the image produced by a plane mirror is located include some explanation or evidence for your answer mirror reflected ray reflected angle incident angle incident ray normal the ray that initially strikes a mirror is the incident ray after it reflects it is then the reflected ray at the point of reflection a line drawn perpendicular to the surface of the mirror is the normal the incident angle is always measured between the incident ray and the normal and the reflected angle is always measured between the reflected ray and the normal figure 1.3 reflection terminology 7

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optiics pt cs purpose to become acquainted with the qualitative and quantitative relationships which exist between the object and its corresponding image in a plane mirror specifically you will discover the position of the image with respect to the object the relationship between the angle of incidence and the angle of reflection the relationship between the apparent path of light and the actual path of light procedure 1 2 3 4 5 place cardboard under the next page of the handbook place the reflective back edge on the line marked mirror on the next page place the florist pin on the point marked object place the straight pins on the points 1 and 1a note how when you get your eye level with the paper and look across the page so that the straight pins are lined up the image of the florist pin also lines up with them figure 1.4 look into the mirror from the right side and place the straight pins so they line up with the image of the florist pin as before figure 1.5 label these points 2 and 2a repeat this for a third angle for each of the three sets of points draw a dashed line representing the path that light appears to be traveling from the image of the florist pin to the eye i ve done this for the first set of pins use the intersection of these dotted lines to label the image position with the word image 6 7 8 figure 1.4 view into the mirror of the two stickpins lined up with the image of the florist pin 9 10 for each of the three sets of points draw a solid line from the florist pin to the mirror at the point the dashed line intersects the mirror to the straight pins this represents the path that light actually takes as it goes from the object florist pin to the eye 11 draw a perpendicular line normal to the mirror at the points where the solid lines touch the mirror 12 measure and record the three sets of incident and reflected angles figure 1.5 placing the pins to locate an additional apparent path of light from the image to the eye 8

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optiics pt cs lab drawing for part 1 mirror 1 1a object data record incident and reflected angles in the table below sighting 1 2 3 i r 9

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optiics pt cs part 1 questions centimeters 1 and calculations measure all distances in what is the relationship between the incident and the reflected angles 2 the image and object distances are measured from the object and image perpendicularly to the mirror what are these distances in cm and how do they compare to each other 3 measure the length from the image point to point 1a this is the apparent path of light now measure the length from the object point along the solid line that you drew to the mirror and then down to point 1a this is the actual path of light what are these distances in cm and how do they compare reflection from a plane mirror part 2 procedure 1 2 3 4 5 set up the two mirrors on the lines of the work sheet on the following page place one florist pin at the point marked object now place the other florist pin at point 1 using your knowledge of parallax figure 1.6 verify that this is the position of the image look carefully into the mirrors you should see two additional images one in the other mirror and one in the corner where the two mirrors meet use parallax to find these other two images and then label the image points with the word image figure 1.6 using parallax to locate the image position note the top of the locator pin is in line with the image 6 use a dashed line to draw the apparent path the light takes from each of the images to the computergenerated eye note when locating the images you don t have to put your eye in the position of this computer-generated eye it is only provided so that when drawings are made throughout the class they will all be similar now use your knowledge of the relationship between incident and reflected angles and your knowledge of the relationship between the apparent and actual path lengths to draw the actual path light takes in going from the object to the eye 10 7.

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optiics pt cs lab drawing for part 2 object 1 11

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optiics pt cs name 12

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optiics pt cs plane mirrors revisited w orking with plane mirrors is a great way to start thinking about physics it s easy to make some simple measurements that lead directly to some general rules one of these the law of reflection applies to all types of mirrors not just plane mirrors in fact whenever light strikes any surface and reflects it obeys the law of reflection the law of reflection whenever light reflects the angle of incidence as measured from the normal always equals the angle of reflection also measured from the normal background in physics is in erasing these incorrect preconceived notions new students don t come as blank slates that would be easier instead they come filled with misinformation and the misinformation is often held onto so tightly that even when the truth is evident they choose to continue believing the misconception that is certainly the case for many who do the plane mirror lab the proof is undeniable but it just doesn t seem right for there to be an image behind the mirror s surface it might help to apply the law of reflection to a simple situation involving a plane mirror and an object plane mirror i r another very good reason to begin with plane mirrors is because of the preconceived notion that most people have about the location of the image produced by a plane mirror it is very difficult for the typical person to believe that this image actually exists behind the mirror it s counterintuitive it doesn t make sense so we make up a reality that makes more sense to ourselves than the truth but this reality is not the truth it s just what we ve conjured up in our own private universe and it has nothing to do with how smart we are several years ago a movie was made that explored this idea of misconceptions and how they block learning in the beginning of a private universe simple questions are asked about the reason for the seasons or the phases of the moon the people who are asked the questions are at a harvard graduation they include recent graduates faculty and alumni twenty-one out of twenty-three answered the questions incorrectly to see how you would do log onto http www.learner.org/teacherslab/pup/surveys.html and take a five question survey many people hesitate taking a course in physics because they have heard that it is hard or because of their supposed limitations in math however they are unaware that some of the biggest if not the biggest limitations to their success in physics are their misconceptions about nature the biggest challenge i have working with someone who has no formal 13 figure 1.7a a dog stands in front of a plane mirror figure 1.7a shows a dog standing in front of a plane mirror now if the dog can see itself that means there must be light reflecting off the dog then striking the mirror and then finally reflecting from the surface of the mirror to produce an image of the dog although there are rays of light reflecting off the dog at every angle and from every point on the dog let s just look at two random rays reflecting from one point on the dog figure 1.7b two rays of light from the dog s nose strike the mirror.

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