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In today's society, even non-scientists need a basic understanding of how science works. Physics and education professor Les Blatt develops physics courses designed to educate non-science majors to be scientifcally literate. |
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Discovering Physics
The following is a draft of the chapter 1 of Discovering Physics (in progress) by Mauri Gould, Harvey Gould, and S. Leslie Blatt. ©1991, 1993-2001 Mauri Gould, Harvey Gould, and S. Leslie Blatt.
CHAPTER 1: INTRODUCTION
1.A. What is scientific literacy?
Several years ago, the New York Times Magazine featured an article by Robert M. Hazen and James Trefil containing a quiz designed to "test your scientific literacy." That quiz was handed out along with the course introductory material. You should already have taken a few minutes to look over the questions, so you can now ask yourself whether knowing most of the answers would make you, personally, literate in science. Part of our reason for offering this course is to help more students achieve an active understanding of what science is about, and how we have learned and can continue to learn about the physical world around us. We do not agree with the viewpoint of the authors of the quiz, even though many scientists (and even more non-scientists) do think of scientific literacy as exactly the kind of "knowledge base" that the quiz implies. On the contrary, we believe that scientific literacy is not simply (or even primarily) an accumulation of facts, but rather a set of abilities, including being able to:
- recognize that scientific concepts such as speed or electrical charge are invented by acts of human imagination and are not tangible objects that could be accidentally discovered liked a fossil or a mineral;
- recognize that scientific concepts require careful operational definitions, rooted in shared experiences and in simpler concepts previously defined. A scientific concept involves an idea first and a name afterward;
- understand the distinction between observation and inference;
- distinguish between the occasional role of "accidents" in scientific discovery, our everyday use of the term "accident," and the scientist's deliberate strategy of forming and testing hypotheses, on the other;
- understand the meaning of theory in the scientific domain and develop some sense, through specific examples, of how theories are formed, validated or falsified, and accorded an appropriate degree of acceptance;
- recognize when questions such as "How do we know …?", "Why do we believe …?" and "What is the evidence for …?" have been addressed and when, on the other hand, something is being taken on faith;
- understand, through specific examples, the sense in which scientific concepts and theories are provisional rather than unalterable, as well as the sense in which many later alterations and improvements do not "destroy" the original theories;
o comprehend the limitations inherent in scientific inquiry and be aware of the kinds of questions that are neither asked or answered;
- develop sufficient basic knowledge in some areas of interest to allow intelligent reading and subsequent learning without additional formal instruction;
- be aware of some specific examples where scientific knowledge has had direct impact on intellectual history;
- be aware of a least a few specific examples of the interaction between science and other aspects of our civilization, including moral, ethical, and social questions; and
- be aware of the close analogies between certain modes of thought in natural science and in other disciplines, as well as the points where such analogies break down.
Although we doubt that all these aspects of scientific literacy can be achieved in a one-semester course, we will attempt to provide experiences that can help to get a substantial start in this direction.
NOTE: Hazen and Trefil, in later publications, have also considerably broadened their definition of "scientific literacy."
1.B. Outline of Course
We selected as the theme of this semester the subject of light both because it is a fascinating phenomenon in its own right and because studies of the characteristics and behavior of light lead naturally to investigations of other important physical phenomena, including particles, waves, energy, electricity, and magnetism. People have always been intrigued by light, and "sun worshipers," in one form or another, are common even today.
Humans are aware of the importance of light primarily because our sense of sight plays such an important role in our interaction with the world around us. Before we move into some of the more basic (but sometimes more abstract) aspects of light, therefore, we will spend a little time gaining some insights into the processes through which we see. As we go on to study other phenomena, we will return from time to time to see how our accumulating knowledge can help further our understanding of how our senses operate to keep us in contact with the rest of the world.
The most fundamental question about light is also probably the most difficult one: What is it? There are two quite different answers that have been developed and investigated over the centuries; one describes light as a wave, the other suggests that it is a stream of tiny particles. Since neither waves of light nor its particles can be seen directly, the only way to decide about these two models of the nature of light is by studying its actual behavior. We will therefore devote time early in the course to investigating the behavior of light in some detail. A substantial portion of the course will also be devoted to gaining a better understanding of the behavior of more readily observed kinds of waves, some of the characteristics of simple particles, and comparisons of these with the results of experiments we do with light itself. In trying to understand how some of the phenomena that we find characteristic of light might fit with a particle description, we will see whether the bouncing of steel balls follows the same pattern as the reflection of light from a mirror. To better understand why the idea of light as a wave was developed, we will study the behavior of waves that we can see and measure directly: waves in shallow pools of water, waves on springs and on ropes. These investigations will provide us with additional tools in our search for an understanding of the connections between wave phenomena and the behavior of light.
We note that both waves and particles have the ability to carry energy from one place to another. Ocean waves can do tremendous damage to structures along the shore; hailstones can make sizable dents in strong metal roofs. Light, likewise, carries energy; the production of electricity using solar cells and the winds created by the movement of heated masses of air are two examples of such energy, transmitted to earth in the form of light from the sun, 93 million miles away. We therefore will spend some time investigating some of the many forms of energy, how one form can be changed to another, and how energy can be carried from one place to another.
As we become more familiar with light, we will learn about some related phenomena: infrared and ultraviolet radiation, radio and TV transmissions, x-rays, and microwaves. This study will lead us to some experiments with electricity and magnetism, and to an appreciation of how these phenomena further add to our understanding of light.
Finally, we will return to the wave/particle question, making some measurements which will allow us to contemplate the depth and richness of the understanding we have achieved.
1.C. Experiments
The following experiments are designed to be done in "research teams" of four students each. Be sure to designate a research coordinator, a data and discussion recorder, and a publication and report coordinator for the activities of this chapter. These roles will be rotated among the members of your team as each new chapter is started, so that everyone gains the experience and responsibilities for all aspects of the team's research as the semester unfolds.
Experiment 1.1. Can the eye be fooled?
There are a great many "optical illusions" with which you are probably familiar. We reproduce a few of them here. For each, you should record your honest impression of the drawing as appears to you, as well as your guess as to the true facts in the situation depicted. Then describe and carry out a way to measure or otherwise determine as accurately as possible the properties being questioned in the drawing. Finally, indicate the team's guesses or hypotheses as to what may be the reasons for any observed discrepancies between appearances and measured result.
1.1a. Which horizontal line is longer in Fig. 1.1? After you have made a guess, use a metric ruler to measure both lines. Are you surprised at the result? What makes them appear to be so different? Propose different hypotheses and try to test them. How different in length would you have to make the lines so that they appear to be equal? Is the effect the same if the drawing is held vertically?
FIG. 1.1. Which horizontal line is longer, A or B? (Adapted from Paraquin, 1987)
1.1b. Another optical illusion that is very striking is shown in Fig. 1.2. Is the hat taller than the width of its brim? (Consider the height to be the distance from the top of the hat to the center of the slightly curved bottom line.) Measure the lines to see what the facts actually are. Make hypotheses and test them if possible.
FIG. 1.2. Compare the height of the hat with the width of its brim (Adapted from Paraquin, 1987)
1.1c. Now look at Fig. 1.3. Focus on the thin diagonal lines. Do they appear to be parallel, or would you expect that extending them beyond the drawing, in one direction or another, would soon have them meeting one another? Actual measurement may be a bit tricky, but you can gain a different perspective on this question by viewing the lines from the edges of the page, along the direction of the diagonals themselves. What do you find? Can you think of reasons you might have been fooled at first? Does knowing the actual situation make any significant difference in how you view the drawing?
FIG. 1.3. Are the thin diagonal lines parallel, or would they meet if extended beyond the figure? (Paraquin, 1987)
Experiment 1.2 Where do the colors come from?
EQUIPMENT
light box and power supply | slits ("beam formers") | plastic prisms
FIG 1.4. Schematic diagram of the light box, indicating connection to power supply.
PROCEDURE
When we look at a rainbow or the spectrum of colors produced when white light passes through a prism, we are conscious of only a few colors: red, orange, yellow, green, blue, and violet and the various in-between hues. In daily life, on the other hand, we see of thousands of different colors, many of which do not appear to be present at all in the rainbow. Where is "lilac," "olive," or "pink"?
FIG. 1.5. Setup for viewing white-light spectrum with prism.
Attach the wires from the power supply to the light box and plug the cord on the supply into the wall socket or distribution strip on your lab bench. Fig. 1.4 shows, schematically, how the box should be connected. Use a beam former with three or four slits at the end of the box closest to the focus knob, and adjust the knob's position so that the beams of light appear to be parallel. Now, substitute a single, narrow slit, so that only one beam emerges from the light box, and shine it through one of the prisms as shown in Fig. 1.5. You will be able to see the beam best if you put all of the equipment on top of a sheet of white paper.
What does the light do when it enters the prism? What happens when it exits? Find a position and orientation for the prism where the emergent beam shows the spectrum of colors noted above. Can you see all of the colors mentioned? Can you find the odd ones like lilac and olive? Think of other colors that are familiar to you - perhaps members of the class are wearing clothing in these colors - that do not appear to be in the white-light spectrum revealed through the use of the prism.
Are you convinced by what you have seen so far that the colors are really present in the white light, and that they are just treated differently enough by the prism (for example, bent by slightly different amounts) so that you can see them separated out? Consider, for a moment, the hypothesis that the colors are, instead, a property of the prism itself. This would be an alternate way to explain what you are seeing, and not any more far-fetched than the more familiar idea of separation of colors already present in the white light - if we had only the present experiment to go on! (Discuss this, and see whether and why you agree or disagree.) One way to probe the validity of these two different hypotheses about the origin of the colors would be to see if you can find a position for a second prism whereby the separated colors can be re-combined. What position might be most likely to do this? If the combination of colors again looks white, which of the hypotheses would be a better description of the way light really behaves? On the other hand, if the second prism always adds color, or the re-combination of colors remains substantially colored, which hypothesis would be better supported?
EXPERIMENT 1.3 Are three colors enough?
EQUIPMENT
Macintosh computer with "color" utility (or Windows computer with appropriate graphics software running) | small lens or magnifying glass (15X is a reasonable magnification for this purpose)
GENERAL SET-UP
In grade school, most of us learned that a great variety of colors -- perhaps every color imaginable -- can be created through the use of just three primary colors. This concept was taught to you in connection with paints or crayons, rather than colored beams of light. However, the idea of primary colors is also valid in connection with light. How many colors does a television screen actually produce? Color monitors connected to computers are very similar to TV screens, and we will investigate a number of color effects with the aid of such a monitor.
The color selection utility built into the Macintosh operating system provides a nice little laboratory to explore several properties of color vision, including the notion of primary colors. The computer should be set up with this utility displayed when you are ready to start the experiment, but if not, it can be found by using the mouse to select "control panels" from the apple menu, "color" from the additional selections this reveals, and then "other" from the "highlight color" list. The screen will show a circle on the right side and a set of variables on the left. If the color wheel is dark, or all black, use the mouse to slide the "intensity" lever to the top of the right-hand column. At this point, you should see a circle with bright, saturated colors around the rim, and progressively more washed-out colors as you look more toward the center. The numbers beside each variable are directly related to the colors you see on the wheel; you can change the numbers and see where the corresponding color is on the wheel, or you can select, with the mouse, any color on the wheel and see the corresponding numbers for each variable.
1.3a. Some things to try. The numbers in the lower-left corner of the display are the most important ones to understand. They correspond to the variables labeled "red," "green," and "blue." These three colors are the only ones that can be controlled on the computer. Take a good look at the screen, and note the large number of colors actually visible. Take a lens or magnifying glass and closely inspect a portion of the screen that appears white. What do you see? You can inspect other areas of the screen as well; in a moment we will show you a way to display a patch of whatever color you wish, so that you can inspect it in detail. Use the mouse to point to the area on the rim of the color wheel that shows the purest red you can see, and press the mouse button. Now look at the numbers beside the variables "red," "green," and "blue." What do you find? Similarly, select the purest green on the wheel, and note the values of the color variables. Without selecting blue, what do you think the values for the three variables will be for this third case? Test your hypothesis by clicking the mouse within the little boxes that contains the numbers for each of the three colors, deleting whatever number is in each box, and typing in your guesses. (Note that the range of numbers for each color on these computers is 0 to 65535, with 0 representing the complete absence of the indicated color and 65535 representing the brightest possible value of the color for the monitor you are using.) After typing in all three numbers, click the mouse in the top half of the color-sample box that appears in the upper left portion of the window. (Hitting the "enter" key, instead, selects this color and returns you to the computer's operating system.) The color equivalent of the three numbers you typed in should appear in the box, and also be selected by a little circle at the position of that color within the color wheel.
1.3.b. Combinations of primary colors. We have investigated the numerical equivalents for the three controllable colors.
Now, how about looking for combinations of the three? Try colors on the rim of the circle between any two of the three controllable colors. Look at the numerical values, and at the amounts of red, green, and blue light visible in a magnified view of the rectangular color patch.
Does it make sense to call the three controllable colors "primaries"? Experiment with different combinations of the three controllable colors.
Where, on the wheel, do mixtures of any two of these lie? (Set the third color to 0 to test this question.)
What happens to the location of the color when you add a bit of the third primary? What happens to its appearance? Take a look now at two of the variables in the upper left of the panel, "brightness" and "saturation." You can change the values for the primaries and see how these other two variables change. Alternatively, you can select different locations on the color wheel, or you can change these two new variables by hand (insert numbers in the corresponding on-screen boxes) and see how the other quantities are affected.
What are the most saturated colors?
What is the least saturated?
Knowing what you have observed with the prisms and the experiments so far with the color wheel, what combination of the three primaries would you expect to have to use in order to produce white? If you haven't tried this or seen it already, try it on the computer. Now, refer back to your earlier results. Select one of the primary colors, for example blue, and recall the values of the three primaries that correspond to that one color. Then look at the most saturated mixture of the other two primaries, in our example red and green, with the third one set to zero (full-scale green, full-scale red, zero blue). What is that color? Where does it appear on the color wheel, in relationship to the color you started with? These pairs of colors are called complementary colors. What do you get when you mix two colors that are complements of each other?
1.3.c. In the eye of the beholder. Physicists, physiologists, and psychologists have, together, discovered that there are three kinds of color receptors in the retina of the eye, each one sensitive to a different but overlapping set of spectral colors, peaking at red, green, and blue, respectively. This relationship is shown schematically in Fig. 1.6. In order to understand how just three primary colors can give you the sensations connected with the thousands of color variations on the color wheel, consider one example. Yellow spectral light, such as appears in the light spread out by a prism, is located on the chart of Fig. 1.6 at a position on the horizontal axis at about 570 nm. (This is a measure, in "nanometers," of the wavelength of yellow light, details of which we will investigate later.) Notice at this position that the sensitivities of the "red" receptors and the "green" receptors are about equal. If, instead of using 570 nm light, we were to combine two beams of light, one at 610 nm and one at 520 nm, we would again be exposing the red and the green receptors to about equal intensities. Your brain would interpret the second situation as being identical to the first, and you would in both cases have the sensation of yellow. (The "blue" receptors also have some response in both of these cases, but it is considerably lower than the red and the green, and just moves the perceived color slightly away from full saturation.) "Color-blind" persons do not have the same set of responses, in their color receptors or in the connections of the receptors to the brain, as persons with the more common (and therefore called "normal") color vision. In fact, there are many different kinds of deficiencies or enhancements of the various color receptors that have been found. If you have any kind of color blindness, some of the experiments we have done in this section may come out differently for you compared with your team partners. In particular, you may want to find the place on the rim of the color wheel that gives you the best match to a pure yellow; if your lab partners see that color as tending more toward the orange, your eyes may be more sensitive to green, and/or less to red, that theirs are. What would you conclude if they see your yellow as more a greenish yellow? Note: color-blindness is a "sex-linked" characteristic that shows up most frequently in males who inherit it in the x chromosome from their mother. Females do not exhibit color-blindness unless both of their x chromosomes, inherited from both parents, have this characteristic. Thus the incidence of color-blindness in women is much rarer than in men.
FIG. 1.6 Approximate relative responses of the three kinds of color sensors in the human eye. (Adapted from Falk et al., 1986.)
EXPERIMENT 1.4 What can we learn about our vision process just by staring?
EQUIPMENT
white paper } colored broad-tip pens
PROCEDURE
First, examine figure 1.7. There is a white cat on a black background on the left, and a small mouse on a white background on the right. Stare at the dot in the center of the cat for at least one minute, and then shift your eyes to stare at the dot in the middle of the white background on the right. What do you see?
FIG. 1.7. Follow the instructions below to see the mouse's fate. (Adapted from Falk, et al., 1986)
It may take a little while, but you should see something besides the white background in a few seconds. This effect is known as an afterimage. It is indicative of a certain fatigue (technically, a kind of "bleaching") of the visual receptors that sets in when a fixed pattern is viewed for more than a few seconds in normal room lighting conditions. The receptors that have more light on them (what part of the picture would they have been viewing?) become, for a period of time, less sensitive than usual. When you then look at an all-white area, the fatigued receptors cannot respond as fully as those that were not as stressed, and do not therefore send your brain signals that indicate as strong a white area as do the less-stressed ones.
In this experiment, how much fatigue would you expect the red-sensitive receptors to experience compared to the green or blue ones? You should be able to guess the answer to this question knowing what you now do about white light. Now, we will do a similar experiment but use colored objects rather than black-and-white ones. First, you will make a simple drawing, with a few large red areas and a few large black ones. You will then stare at your drawing for about a minute, and after that gaze at a blank piece of white paper. Before doing this, however, think about what you learned about color relationships in your color wheel experiments. If your red receptors become fatigued, how do you suppose your eye will respond to white light? That should give you some idea of the color to expect if there is any afterimage at all. Make the hypothesis first, and give a reason if you have any idea. Then do the experiment. What do you see? Do the results match your hypothesis? What is the relationship of the color of the afterimage to the original red? Can you refine the reasoning that helps you understand what is taking place in your eye?
Now try the experiment again using different colors. You will get best results if you do not use a lot of colors in any one picture, and if the colored areas are not very small. Can you begin to predict how the afterimages will look?
Artistic footnote
Artists often consciously utilize principles developed by scientists to produce the particular effects they desire. Conversely, scientists sometimes pick up important insights from the work of artists. In the late 1800's, French impressionist Georges Seurat adapted the newly-emerging knowledge about color perception, and the eye's ability to mix neighboring spots of color so as to produce the effect of a different color, into a new painting style he called pointillism. Instead of covering his canvasses with broad swaths of color, in broad or narrow brush strokes, he meticulously painted tiny dots of color, interspersing two or more different colors that could produce in the eye of a beholder standing at some distance from the painting a completely different perception than what might be seen if the individual dots were viewed close-up. More recently, Jasper Johns created a set of works based on afterimages; perhaps the best known of these is a painting that has the form of an American flag, but done entirely in the colors complementary to those of the actual flag. Why might he have done that?
1.D Questions and activities.
Bring the answers or results the next class. Some of the activities involve other students who are not taking Discovering Physics. We want them to participate in the scientific adventure, too!
1.1 What are the primary colors you learned as a child? Do they work well? Why do they seem to give different results for various mixtures than when light is mixed? Hint: how do paints and crayons differ from light beams?
1.2 Discuss your ideas on scientific literacy. Do you think that there should be a core set of facts about natural phenomena that all college graduates should know? Should all liberal arts students be required to take a one semester course in natural science? If so, is a one semester course sufficient?
1.3 Devise various hypotheses that could explain why most people do not guess the relative weight of the two objects seen in class. What was the main purpose of this demonstration?
1.4 Look at a TV screen with a magnifying lens. If possible, first adjust the "color" control to give a black-and-white image, and look close up to see how the screen creates the appearance of white. Then turn up the color control again and look at how various colors are produced. Turning to a channel displaying a test pattern might help. Can you determine just what is being changed when the "color" control is operated? What does the "tint" control do? On newer sets, the names of these controls may be different. See if you can figure out what changes each one makes, in any case.
1.5 Try some of the optical illusions in this chapter on your friends. See if they have any additional ideas as to what causes the effects.
NOTE: Figures 1.1, 1.2, and 1.3 are adapted from "The World's Best Optical Illusions," by Charles H. Paraquin, © 1987, Sterling (New York). Figures 1.6 and 1.7 are adapted from from "Seeing the Light," by David Falk, Dieter Brill, and David Stork, © 1986, Wiley (New York).
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