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Light and Everything Lab Manual I-142 – Fall 2001 Mount Holyoke College Lab 1. Newton’s Opticks.........................................................1-1 Lab 2. Additive Color Mixing ...................................................2-1 Lab 3. Color Mixing on the Computer Screen ............................3-1 Lab 4. Subtractive Color Mixing...............................................4-1 Lab 5. Color naming ..............................................................5-1 Lab 6. Color Printing ..............................................................6-1 Lab 7. Reflections in a Spectrum .............................................7-1 Lab 8. Color Vision and the Retina...........................................8-1 Lab 9. Color Vision, Part II .....................................................9-1 Lab 10. There’s More to this than Meets the Eye ...................... 10-1 Lab 11. Making Waves........................................................... 11-1 Lab 12. Sound Interference.................................................... 12-1 Lab 13. The Wavelength of Light ............................................ 13-1 Lab 14. Electricity.................................................................. 14-1 Lab 15. Electrical Resistance................................................... 15-1 Lab 16. Photoelectric Effect .................................................... 16-1 Light and Everything Lab Manual 1-1 Lab 1. Newton’s Opticks (Light is a ray!) prerequisites: none lab credits: 2 Newton’s task in presenting his results on colors was to persuade his readers that white light is a composite of “heterogeneous” rays (“different kinds of” rays, in modern English), i.e., that “[white] light consists of rays differently refrangible.” Furthermore, “There is no one sort of ray which alone can accomplish [whiteness]. It is ever compounded, and to its composition are requisite all the aforesaid primary colors, mixed in due proportion.” Because he met so much opposition to his theory, Newton continually refined his demonstrations; the method of Proposition XI of the Opticks (see page 48, Selected Readings) is the culmination of decades of trying to persuade his readers. On the bench in the laboratory is an apparatus designed to project a spectrum onto a screen. An important difference between our apparatus and Newton’s is that we need to use an artificial light source instead of the sun. Because the sun is 93 million miles away, its light rays are traveling nearly parallel; those from a light bulb are highly divergent over the short distance we use on the lab bench. We use a special “line light”, and focus the beam with lenses. We use this apparatus to observe the spectrum of visible light, the bending angles of different colors of light, the action of colored filters on the spectrum, the appearance of the spectrum projected on white, gray, or black surfaces, and the reconstitution of the refracted light into a single point. In Lab 7, we use a bigger spectrum, produced in a dark room, to observe the appearance of variously colored objects in different regions in the spectrum. Work with a small group (3-5) of your colleagues, examining each of these phenomena, in order to fully comprehend Newton’s color theory. Discuss your observations with the others in your group, explain yourself and ask questions of them until you are sure you understand. Take careful notes in the space provided; no matter how good your memory, when you sit down to study, you will be glad to have your written account of what you did and what you saw. 1-2 Newton’s Opticks WHAT COLORS ARE IN THE SPECTRUM? Carefully adjust your apparatus so that you project a good, bright spectrum on the little screen. Get up close to your spectrum to see that it has no white in the middle (white in the middle is a sign of poor focus). You can follow the spectrum from the prism to the screen by inserting another screen into the beam right at the prism, then moving it slowly away. Newton used the color terms: violet1, indigo2, blue, green, yellow, orange, and red to describe the spectrum. How many colors do you see in the spectrum? What are some colors not in the spectrum? Is there a nearsighted person in your group who wears glasses? Take off your glasses and look at the spectrum from a distance. Do you still see the colors? Many of you with 20/20 vision can still get this effect simply by backing up from the spectrum. More on this effect later. WHAT PATH DOES THE LIGHT TAKE? Make a qualitative sketch of the path the light takes from the projector through the prism and to the screen. Indicate the location and order of the colors, making sure your diagram shows which end of the spectrum deviates furthest from the original straight path of the light. (Hint: don’t bother trying to render three-dimensional effects. Stand above the board, look down, and represent what you see as a map.) In Newton’s words, which are the “most refrangible” rays? Which are the least? 1 This is the proper term for the color you see at this end of the spectrum. “Purple” represents a different, non-spectral color, more akin to magenta. 2 It was important at the time for mystical reasons that there be seven colors, to match the days of the week, the notes of the musical scale, and the number of known planets in the solar system (Neptune and Pluto had not yet been observed). Most people have trouble identifying indigo in the spectrum or elsewhere, and it has become standard practice to leave it out. Light and Everything Lab Manual 1-3 WHAT DOES A FILTER DO? Insert a red, green, or blue filter in the path of the light. What does it do to the white light leaving the projector? What happens to the spectrum projected on the screen? (Think about the width of the spectrum as well as the colors in it.) filter color observed spectrum blue green red WHAT HAPPENS WHEN THE LIGHT IS RECONSTITUTED? Reconstitute the spectrum. This takes some rather fine adjustments, but you can place the lens between the prism and the screen so that you get a single line of light on the screen. What do you see in the very center of this spot? What happens to this spot of light when you make a shadow in the spectrum with the post (as above)? Try moving the post across the path of the light while observing the little focused spot. 1-4 Newton’s Opticks WHAT ARE WHITE, GRAY, AND BLACK? It was the whiteness of the whale that above all things appalled me. … [I]s it, that as in essence whiteness is not so much a color as the visible absence of color; and at the same time the concrete of all colors; is it for these reasons that there is such a dumb blankness, full of meaning, in a wide landscape of snows- a colorless, all-color of atheism from which we shrink? And when we consider that other theory of the natural philosophers, that all other earthly hues—every stately or lovely emblazoning—the sweet tinges of sunset skies and woods; yea, and the gilded velvets of butterflies, and the butterfly cheeks of young girls; all these are but subtile deceits, not actually inherent in substances, but only laid on from without; so that all deified Nature absolutely paints like the harlot, whose allurements cover nothing but the charnel-house within; and when we proceed further, and consider that the mystical cosmetic which produces every one of her hues, the great principle of light, for ever remains white or colorless in itself, and if operating without medium upon matter, would touch all objects, even tulips and roses, with its own blank tinge—pondering all this, the palsied universe lies before us a leper; and like wilful travellers in Lapland, who refuse to wear colored and coloring glasses upon their eyes, so the wretched infidel gazes himself blind at the monumental white shroud that wraps all the prospect around him. And of all these things the Albino whale was the symbol. Wonder ye then at the fiery hunt? Herman Melville, 1851. Chapter 42, “The whiteness of the whale”, Moby Dick You have already observed the spectrum on a white surface. What is white? Try projecting the spectrum on a black and a gray surface. What do you see? What is the difference between white, gray, and black? What do they have in common? Light and Everything Lab Manual 2-1 Lab 2. Additive Color Mixing prerequisites: none lab credits: 1 Vision is arguably our most compelling sense. (“Seeing is believing.”) Although we can easily interpret colorless images (black-and-white photographs, paths through the woods on a moonlit night, etc.), we tend to find images in color far more interesting and informative. In one important way, however, our color vision is impoverished relative to other senses. When we taste a solution of sugar and salt, we experience both sensations (sweet and salty), and not some “average.” But when we observe mixtures of paints of different colors, we experience a color different from the constituent colors. This happens for lights, as well. Often, more than one combination of pigments or lights can yield a single color sensation. We will begin to explore this phenomenon in lab this week. During the semester we will return repeatedly to the concepts investigated here, and explore them further. Some useful concepts Hue: Main color (e.g., red, orange, yellow, etc.). Brightness: The overall intensity of the light from dark to dazzling. Saturation: The purity of a color. The absence of other colors of the spectrum that would combine to make white (or gray), therefore the degree of difference of a hue from gray (or white) of the same brightness. Red is saturated, pink is unsaturated. Notice that this is unrelated to brightness. Additive color mixing: Mixing lights of different colors so you see them in a single spot simultaneously. The lights are added together. Subtractive color mixing: Combining the filters through which one light shines (or the pigments off which one light reflects). Each filter subtracts part of the light. Resolving power: The minimum distance between two objects necessary for a lens to distinguish (resolve) them as distinct objects. [This is a useful idea when you consider color printing and TV screens.] The resolving power of the human retina is about 1 60 of a degree. Saturation refers to how bold or washed-out a color is. The more gray or whiteness that has been added to a color, the less saturated it is. We can distinguish about 20 steps of saturation for a given wavelength of light. 2-2 Additive Color Mixing Brightness, or luminance, refers to how many photons are reflected from an object. We can distinguish about 500 steps of brightness for every hue and grade of saturation. A totally color-blind person (like the colorblind painter) can also distinguish levels of brightness but not differences in hue or saturation. Thus, a totally color-blind person can distinguish about 500 grades of brightness in differentiating an object from the background. In contrast, a person with normal color vision can distinguish 200 hues X 20 grades of saturation X 500 steps of brightness = 2 million gradations of hue, saturation and brightness combined! (Is this how many colors there are? Can we distinguish this many? Can we name them all?) COLOR MIXING WITH SLIDE PROJECTORS Try to come up with a set of rules for mixing red, green, and blue light, in pairs and all together. Use the filters provided, and shine the lights onto a white surface, overlapping them as appropriate. R + G = R + B = G + B = R + G + B = After you have a set of basic rules, make some predictions based on those rules. For example, what do you expect to see upon mixing red and cyan? Use this page to take notes. Light and Everything Lab Manual 3-1 Lab 3. Color Mixing on the Computer Screen prerequisites: Lab 2 lab credits: 1 We will use a program written by Bill Kaiser in the psychology department that allows us to mix 643 different colors on a color monitor. [Note: If there is only one computer available, it is very important that everyone gets to see, especially with the magnifying glass. If you find yourself walking away unsatisfied, you can do the mixing exercise on any networked PC (not Mac) by following the instructions in the appendix.] USING THE PROGRAM. • Open “COLORS.EXE” by double clicking on it. The numbers at the bottom represent the intensities of the red, the blue, and the green circles. (See Appendix, 34 if you are not in the observatory) • Type “r”, “b”, or “g” to reduce the intensity of the red, blue, and green, respectively (to a minimum of 0). • Type “R”, “B”, or “G” to increase the intensity of the red, blue, and green, respectively (to a maximum of 63). • “Enter” exits the program (sorry about that). BASIC COLOR MIXING. Set all three (R,G,B) at their maximum intensity, and write down (or tabulate or draw) the apparent rules for color mixing on the computer screen. By varying the settings, try to see how the red, green, blue, cyan, magenta, and yellow relate to each other. Use the table below to get started R 63 Intensity of B 63 G 63 0 63 63 63 0 63 63 0 63 resulting color HOW’D THEY DO THAT? Examine the screen close up with a hand lens or magnifying glass. What do you see? If your socks haven’t been knocked off, you haven’t looked closely enough! 3-2 Color Mixing on the Computer Screen BLACK AND WHITE: What color do you see when you set all three colors at their maximum? minimum? At the same intermediate setting? Tabulate your results. R 63 Intensity of B 63 G 63 0 0 0 At their resulting color Write a one sentence exposition on black, white, and gray. CHANGING PROPORTIONS Yellow and orange Start with this setting: 63 - 0 - 63. Hold down the “g” key and watch what happens to the overlap area. What is the difference between yellow and orange? Try going the other way (keeping green high and reducing red). What happens? What is the primary change: hue, intensity, or saturation? R 63 Intensity of B 0 G 63 63 0 31 resulting color Write a one sentence exposition on the color mixing rules for yellow and orange. Light and Everything Lab Manual 3-3 Other mixtures Try some other mixtures. Make purple, for example, and write down the settings. R Intensity of G B resulting color purple PASTELS AND TINTS: Start with 32 - 32 - 32. Watch the overlap color as you raise one color. What is changing, hue, saturation, or intensity? Try to make some other pastel colors in the middle (such as salmon or lavender). Write down the settings. R 32 Intensity of B 32 G 32 resulting color Write a one sentence exposition on pastel color. BROWN: What is brown? Test the theory that brown is a dim orange. If brown is dim orange, is that a difference (from orange) of hue, intensity, or saturation? Write down some settings that produce brown. R Intensity of B G resulting color 3-4 Color Mixing on the Computer Screen APPENDIX Getting into “Colors” on any networked IBM-type computer First, map a network drive. There are two ways to do this: Get a MSDOS prompt (C:\>) Right click on “My Computer” Type Choose “Map network Drive” net use m: \\www\courses%yourid Enter your email password when asked, even if it first says your password is invalid. Type the path: \\www\courses%yourid Enter your email password when asked It should say the command was successfully Do not check “reconnect at logon” completed. Get into the drive you just mapped. There are also two ways to do this: While you are still in DOS “My Computer” Type “Courses%yourid on ‘Www’ (N:) cd: n: You are in drive N if it says N:\> kdorfman Type cd: kdorfman: colors Type cd: colors: colors.exe Type colors Light and Everything Lab Manual 4-1 Lab 4. Subtractive Color Mixing prerequisites: Lab 1 lab credits: 1 Most color printers use cyan, magenta, yellow and black ink. We have both the inks and materials printed with these inks in lab. INK MIXING Try to produce red, green, blue, and neutral gray by mixing the cyan, magenta, and yellow inks together. [Don’t be overly fussy about the volume of liquid; the inks have been diluted to different degrees.] Be aware that you are making and testing hypotheses, and try to articulate your ideas to each other before you start stirring everything together. What do you expect and why? Does everyone in your group predict the same thing? Tabulate your results. approximately equal amounts of C + prediction (and reasoning) C + Y = C + M = Y + M = Y + M = result 4-2 Subtractive Color Mixing COLOR MIXING ON THE OVERHEAD PROJECTOR Starting with cyan, yellow, and magenta filters, see what you get by combining them. Tabulate or diagram your results. Draw a diagram showing why this works, by figuring out what part of the white light passes through each filter, for example: a red filter might be thought of as working like this: R G B R Light and Everything Lab Manual 5-1 Lab 5. Color naming prerequisites: none lab credits: ½ HOW WELL DO WE AGREE ON THE COLORS OF THE SPECTRUM? Look in the color boundary device as instructed. Turn the dial until the black line is exactly as indicated below, and have your partner record the wavelength. Enter your data on the sheet provided The data will be compiled and made available so you can compare the results for different students.. first visible edge of violet best violet best blue best green best yellow best orange best red last visible red Light and Everything Lab Manual 6-1 Lab 6. Color Printing prerequisites: Lab 2, Lab 4 lab credits: 1 Examine the various printed materials with your naked eye (i.e., without microscope — glasses and contacts are OK). Some especially good examples of large areas of a uniform color are marked for you. Some cheap printed materials, such as the Sunday comics and most cereal boxes, have a registration, a small pattern showing boxes or circles of pure inks, somewhere outside the picture. Find a registration and see what the cyan, magenta, yellow, and black inks look like unmixed. When you watch a color printer at work, you see that it prints the picture 4 times, once with each ink. Cheaply printed materials often do not have perfect registration of the four inks, allowing us to look around the margins of color images to see which inks were used. Look more closely at the printed materials, using a dissecting microscope. If you have never used one before, have the instructor show you how. How are the colors mixed on the page? What does it look like magnified? Observe the edges of a colored region carefully, where poor alignment of inks actually makes it easier to figure out what how it works. The actual work of a pigment is to absorb light. (The light that is transmitted through the pigment has not interacted with it.) Think about each ink, and what part of the visible light it absorbs. What light is left to return to your eye? When the inks do not completely overlap on the page, what part of the spectrum returns to your eye. 6-2 Color Printing Find a marked example of each of the following colors, and see how it is composed. Are the inks completely mixed, for example, or can you see one on top of another? Do you see the white paper between ink marks? Is one ink laid down solidly, and another patterned? Is the pattern uniform? color on the ink(s) used how arranged page (C,Y,M,K) green purple red pink dark blue orange (look at a yellow-tored gradient)) Why do you suppose there is any need for black ink? Light and Everything Lab Manual 6-3 Explain the printing of the following colors in terms of light, in a single sentence each: what is the source of the light, what does each ink do to it, what part of the light actually makes it back to your eye? Green Pink Orange Light and Everything Lab Manual 7-1 Lab 7. Reflections in a Spectrum prerequisites: Lab 1, and (Lab 2 or Lab 4) lab credits: 1 Newton wrote, The rays to speak properly are not coloured. In them there is nothing else than a certain Power and Disposition to stir up a Sensation of this or that Colour. … Colours in the Object are nothing but a Disposition to reflect this or that sort of Rays more copiously than the rest … (See “The Rays Are Not Coloured”, Selected Readings.) HOW DO OBJECTS OF DIFFERENT COLORS LOOK IN DIFFERENT PARTS OF THE SPECTRUM? For this, we need a spectrum projected in a much darker room, where we can project a big spectrum onto a screen, and move various objects across it. A collection of some very instructively colored objects is to be used for this purpose. Color of object in white light Color of object in each part of the spectrum V B G Y O R Light and Everything Lab Manual 8-1 Lab 8. Color Vision and the Retina prerequisites: Lab 2 lab credits: 1 The essay, The Case of the Colorblind Painter by Oliver Sacks, from his book, An Anthropologist on Mars is an insightful, haunting description of a painter who lost his color vision, probably due to a stroke, when he was in his sixties. The essay gives us an appreciation of our sense of color, and some background about the study of color vision. This lab provides an opportunity to explore of some of the phenomena of color vision described in lecture, and in your reading. You and one to three partners may do these demonstrations in almost any order. While you are doing the cone vision exercises, put the card with the glow-in-the-dark dot(s) on it under a desk lamp to activate it. IN THE LIGHT: CONE VISION Where is our sharpest vision? Stare at the circle in the middle of this line - and see whether you can read the words at the margins without moving your eyes. If you can, try the same exercise with a larger piece of written material. (E.g., stare at the gutter in the middle of an open book and try to read the text at the outer margins.) Are the red, green, and blue cones equally represented in the fovea? The very central region of the retina is called the fovea. This is the region where your color vision is most acute. The entire image of a small or distant object can fit entirely in your fovea. Have your buddy hang (or hold) the yellow card with 4 dots on it at eye level somewhere (like at the end of a well-lit hallway) where you can stand 20 or 30 feet away from it, then walk toward it. From across the room, the image of each dot is quite small, and it falls entirely on the fovea. As you get closer to the card, the image takes up a larger and larger portion of your retina. Monitor the colors of the dots as you walk slowly to or from the cards. (If you see nothing change, try the other size dots.) Are all colors equally detectable at all distances? What can you conclude about the relative numbers of R, G, and B cones in the fovea? (Remember that the designations R, G, and B refer to the type of light absorbed.) Where on our retina are our cone cells found? Ophthalmologists use a device for mapping the retina called a visual field perimeter. The subject sits at the center of a hemisphere, along whose various circumferences tiny red, green, blue, or white lights can be blinked. From the subject’s responses (seeing something, knowing its color), the technician constructs a map of the retina. We will use the basic idea behind the perimeter, without measuring the actual angles. 8-2 Color Vision and the Retina Work with a buddy. Find a place with uniform, not too bright lighting (not facing a desk lamp or a window in daytime). Sit or stand where you have room to spread both arms. Find a point to stare at. (Pick something small and distinct.) To do this properly, you must absolutely keep your eyes on this point! You will not experience the effect if you turn your eyes or head! Close or cover one eye. Stare at your spot with the open eye. Extend your arm on that side straight out from the shoulder. You shouldn’t be able to see it, even if you wiggle your fingers. Slowly bring your outstretched arm toward the front, keeping it parallel to the floor, while you wiggle your fingers. (Don’t cheat! Stare at your spot!) At some point, you will be able to detect the movement. This gives you a sense of the extent of your visual field. Here’s where the buddy comes in. Hold your arm out to your side, as before. Have your buddy put a card in your hand, without telling you what color dot is on it. Wiggle the card slightly as you slowly bring your arm toward the front. (Stare straight ahead! Don’t move your eyes!) When do you know what color it is? The color may go away if you stop wiggling the card. Have your buddy make estimates of the angle (or mark the floor directly below your hand). Repeat this for the other cards. Your buddy should hand you the same card more than once, so anticipation won’t influence your perception (e.g., “This must be blue, since that’s the only one I haven’t seen yet!”). This gives you a sense of the extent of your color vision. Repeat one last time, with the card that has all the dots. Be honest, now. Are all the colors detectable at the same angle? Which do you see furthest out in the periphery? Which needs to be closest to the middle of your visual field? Switch roles, and let your buddy investigate her peripheral vision. What can you conclude about the distributions of the red, green, and blue cone cells (named not for the color they appear, but the type of light they absorb) on the retina from these observations? Light and Everything Lab Manual 8-3 Find your blind spot You may have found a location during the previous exercise where the dot disappears altogether. This is your blind spot. To demonstrate this phenomenon more clearly, follow the instructions below. Cover your left eye and look at the diagram below with your right eye. Hold the paper at arm’s length and stare at the dot on the left, but pay attention to the cat on the right. Slowly bring the paper toward you, and note what happens to the cat. (You may test your left eye, too, by turning the paper upside down.) What anatomical feature of your eye causes this? l ö IN THE DARK: ROD VISION Where in the retina are our rod cells found? Rod cells are more sensitive to dim light than cone cells; in fact, cone cells require bright light, and bright light swamps the rods. In dim light, therefore, we are using our rods rather than our cones. In this exercise, you will experience the difference between rod vision and cone vision with respect to color and fine focus. Have you ever looked at a night sky and seen a star out of the corner of your eye, but when you turn to look at that star directly, it disappears? We’ll try to set up a similar situation in a dark room. First, collect the things you’ll need: cards with dots, the card with fine print, and the card with the circle of glow-in-the-dark paint. Read all the directions before you begin, as you cannot read them after you have started! Find a really dark, but safe, place. The floor of a closet might do, if you put a rolled up towel covering the crack under the door, and a dark towel or coat draped over your head. Sitting under your blankets on your bed with the room lights out is another possibility. You should be able to see nothing when you begin. If you can see right after you close the door or get under the covers, there is too much light. Wait until your eyes are completely adapted to the dark. This can take 10 minutes, so maybe a radio or walkman would be a welcome companion. Hold the glow-in-the-dark dot at arm’s length. Look at it directly, and out of the corner of your eye. (To do this, hold the card in front of you, and direct your gaze to the right or left of the dot, perhaps at your hand.) Try looking back and forth between the dot and somewhere to the side of it. Is it equally bright in both orientations? What can you conclude from this about the distribution of the rod cells in the retina? 8-4 Color Vision and the Retina Can we see color with our rods? Examine the card with multiple dots on it. Don’t cheat by holding the card in the brightest light leak you can find! The dots will be hard to distinguish. Think about why this happens. In dim light, how do normally sighted individuals distinguish objects from each other and from the background? Why do you suppose color vision is important to have? I.e., what advantage does it give to animals that have it? What disadvantage? Can we see fine detail with our rods? Examine the card with the printing on it. What is the smallest line you can make out? How do color and focus change as we gradually add light? Return to the light gradually so your eyes can adapt slowly. Watch as the colors of the dots become apparent. Watch as the fine print becomes more distinguishable. YOUR REPORT: 1. Answer each of the following questions, and provide specific supporting evidence from this exercise. • What photoreceptors are most numerous in the fovea? • Where are rods most common? • Where is your sharpest vision, and which receptors do you use for it? 2. Why don’t we see color with our rods? Light and Everything Lab Manual 9-1 Lab 9. Color Vision, Part II Anatomy of the Eye Colorblindness prerequisites: Lab 8 lab credits: 1 ANATOMY Examine the model of the eye and find: • the retina • the fovea • the optic nerve • the pupil • the lens Draw a diagram. COLOR BLINDNESS Color vision improves our ability to distinguish an object from its background. When we talk about color vision, we are really talking about three sensibilities: hue, saturation and brightness. Hue is what most people think of as color. Hue distinguishes red from yellow from blue and so on. While we name only a small number of them, we can actually distinguish about 200 different hues. Colored yarns: These are one of the color matching tests referred to in The case of the colorblind painter. If you have normal color vision, matching these is easy. Try it looking through a filter! Test charts: These are the standard charts that you may have seen at the doctor's office. They consist of patterns of differently colored dots, of matched intensity. If you are not colorblind, you will see that the patterns of dots form numbers. Examine the plates, taking care to keep them clean. Touch them only with the paint brush provided; Do not use your fingers or your pen. Use the key in Table 9-1. Some of the plates have been photocopied. Compare the copy with the original. Consider the plates that are read differently by normal and color-deficient individuals. What parts of the spectrum are reflected by the dots in each image? Use filters to remove certain parts of the spectrum to help you answer this. (You’ll have to review the color mixing rules to choose the appropriate filter.) For at least one plate, try to figure out which hues are apparently indistinguishable to the colorblind person, but which let you see the figure. Which filter would be appropriate to look through to simulate red blindness (protanopia)? Green blindness (deuteranopia)? For at least one plate that lets the clinician distinguish between these two conditions, try to figure out some hues that can be distinguished by a person with each type of colorblindness, but not the other. 9-2 Color Vision, Part II Table 9-1: Key to Ishihara Plates Total Color Blindness 12 *3 * * * * * * * * * * * Plate # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Normal vision 12 8 29 5 3 15 74 6 45 5 7 16 73 * * 16 17 18 26 42 purple-red line 19 20 * bluish green line Red-Green Deficiency 12 3 70 2 5 17 21 * * * * * * 5 45 4 Protan Deutan5 Strong Mild Strong Mild 6 (2) 6 2 2 (6) 2 (4) 2 4 4 (2) purple both red both line lines; line lines; purple red easier easier can trace the line * 21 orange line * * connect the bluish-green & purple * connect purple & bluish-green all can trace the line * 22 23 24 connect the bluish-green & yellowish-green connect purple & orange 3 * Cannot be distinguished 4 Blindness to red (the first color) 5 Blindness to green (the second color) * * Light and Everything Lab Manual 9-3 YOUR REPORT: • Draw a map of a human retina. (Start by drawing a large circle.) Indicate which eye it is, and which side the nose is on. By means of careful labeling, show the approximate locations of the fovea, the blind spot, and the area covered by each type of photoreceptor, using your notes from your homework exercise. • What hues are difficult for a person with red-green deficiency to distinguish? • How do people with protanopia differ from those with deuteranopia? Light and Everything Lab Manual 10-1 Lab 10. There’s More to this than Meets the Eye Interaction of Color by Josef Albers a Macintosh computer exersize prerequisites: Lab 8 lab credits: 1 Josef Albers (1811-1976) was an influential German-American artist and educator who studied spatial and color illusions. “I am particularly interested in the psychic effect, an esthetic experience that is evoked by the interaction of juxtaposed colors. … Every perception of color is an illusion. … We do not see colors as they really are. In our perception they alter one another. For example, two different colors can look the same or two identical colors can look different. … This is the ‘play’ of colors; this change in identity is the object of my concern.” quoted on page 11 in World Artists, 1950-1980, by Claude Marks, H.W.Wilson, NY, 1984 Albers taught at the Bauhaus in Germany, then immigrated to the USA in 1933 to teach at Black Mountain College. He taught courses at Harvard’s Graduate School of Design, and in 1950 was appointed chairman of Yale University’s Department of Design. His famous color course and the resulting text, Interaction of Color, have influenced generations of students. Originally published in 1963 as a limited edition of text and color plates, Interaction of Color has been reissued over the years in various formats, including paperback in 1971, a revised text in 1975, and a CD-ROM version for the Macintosh in 1994. A FEW TERMS Hue: Color (e.g., red, orange, yellow, etc.) Saturation: Degree of difference of a hue from gray (or white) of the same brightness. Red is saturated, pink is unsaturated. Simultaneous color contrast: A color looks most intense against a background of its complement. (Red against green, blue against yellow) Receptive field: The retina is organized into layers of cells: photoreceptors at the back, sending information to the ganglion cells at the front, via the bipolar cells in the middle. The axons of the ganglion cells are bundled together to form the optic nerve, sending information from the retina to the brain. Each ganglion cell receives input only from photoreceptors in a small, circular area of the retina, its receptive field. The receptive fields of different ganglion cells overlap, permitting more than one kind of information to be extracted from the same general region of the retina. (See How Neurons Work, from the Selected Readings.) 10-2 There’s More to this than Meets the Eye Most ganglion cells are double-opponent nerve cells, that is, their receptive fields consist of two concentric circles, as illustrated in Figure 10-1. A double-opponent cell gets excitatory input from different photoreceptors in the inner and outer circles of its receptive field. When the cell is excited, it sends nerve impulses to higher centers in the brain. Some respond to differences between the center and the surround in brightness, and others, to differences in hue (in particular, red vs. green, blue vs. yellow). Color opponency: Figure 10-1 shows how a blue center/yellow surround double opponent cell works. When blue light falls on the center of the receptive field and yellow light on the surround, the two colors enhance the response of the cell. In any other combination, the inhibitory input received by the double opponent cell from one kind of receptor cancels out the excitatory input from the other two, and the cell does not respond with nerve impulses. individual photoreceptors RGB receptive field RGB Retina to higher brain levels blue center/yellow surround double opponent ganglion cell Figure 10-1. Color Opponency. This cell is excited by blue in the center of the receptive field, red and green in the outer circle of the receptive field; inhibited by red and green in the center, blue in the surround. Light and Everything Lab Manual 10-3 There are four types of double-opponent cells involved in color vision: green center/red surround; red center/green surround; blue center/yellow surround; yellow center/blue surround. In each case, the color that causes excitatory impulses from the center causes inhibitory impulses from the surround, and vice versa. The blue/yellow double opponent cells are stimulated most strongly by the contrast between blue and yellow colors located in adjacent points in space. Similarly, red/green double opponent cells are stimulated most strongly by the contrast between red and green colors located in adjacent points in space. Thus, blue looks bluer next to yellow (and vice versa) and red looks redder next to green (and vice versa). USING THE PROGRAM Getting into Interaction of Color Logistics: This homework is done entirely on the Macintosh computer. You may use the program on any networked Macintosh on campus (Dwight is the best location). Help sessions with an instructor will be announced. The very best way to do this is with a friend. You will each contribute to the other’s appreciation and understanding of the phenomena demonstrated. You will also be more inclined to laugh when you share the experience with someone than when you do it by yourself. This is a fun program! Before you launch IoC, pull down the menu, get control panel, then general controls, and, under Documents, set it to open folders set by application. Please set this back when you are finished. Finding Interaction of Color: The program is in Lab Shared Software / Instruction / Unity of Science. You can get to Lab Shared Software in four different ways, depending on the location of the computer. • It may be on the launcher. • It may be on the desktop. • It may be in • You may have to get it by this route: /recent servers. menu chooser AppleShare Dwight Computer Lab zone Dwight Lab Server Lab Shared Software (on the list of items you want to use) Sign in as a Guest with no password. Open Interaction of Color by double-clicking on it. 10-4 There’s More to this than Meets the Eye Navigating within Interaction of Color: Use the Controller, as illustrated in Figure 10-2. You can use the arrows on the righthand border of any window to scroll up or down. (You can also move the little “elevator” box up and down.) Keyword search Next/previous Find Sub-parts Path Topics Introduction Notes Intro Parts list I Color recollection Color reading II Drag this lower corner down to enlarge the box. Figure 10-2: The Controller. Optional reading and color studies: Your homework assignment asks you to explore only three of the many color illusions presented in this program. However, there is a great deal of information here. Feel free to explore to your heart’s content. Read the written portion, for example, for insight into Albers’ ideas about color and color interactions. Look at as many studies as you wish. Introduction. This was written by Josef Albers for his 1963 book about his famous color course. (In the Controller box, click on the icon marked Introduction. A box with scrolling text will appear. You can stop the scrolling by clicking on the black rectangle in the upper right corner of the box.) Read this if you are interested. Notes. If you want to read Albers’ ideas on any of the studies, click on the Notes icon [$]. He wrote these notes to accompany his original color studies on colored paper. The first time you do this, a dialog box may appear. Click on Open Notes…. Choose Interaction of Color, then Open. (If you did not set open folders set by application at the start of your session, you may have to jump through some extra hoops here. When it asks where the notes are, tell it: desktop/lab shared software/instruction/unity of science/Interaction of Color/Interaction of Color Notes.) You can keep the notes window open as you change studies, although you may have to reposition it. Dark/light contrast. Studies V.1.2 and V.2.3 illustrate the dark/light contrast Sue Barry described in class. Explore these to review this phenomenon. Your brain loves edges! Afterimages. You may enjoy the afterimage in Study VIII-1. (If “delete” doesn’t work, use Edit/Cut. Hold the button down 30 seconds, then release.) Read the topic text. Light and Everything Lab Manual 10-5 Find the error(s) in Albers’ explanation of color vision at the level of the retina. Remember, this text was written in 1963. ASSIGNMENT: Do an example Topic VI. One color appears as two. Click on the sub-parts icon [ ] to go directly to the color studies. Select Study VI-3.1. You should now see something like what is shown in Figure 10-3. yellow background blue background yellow X blue X Figure 10-3. Study VI-3.1. VI-3.1 The X’s appear yellowish on the blue (lavender) background and blueish (lavender) on the yellow background. Moving the X’s around will confirm that they are a single color. Since there is no color that can be both blue and yellow (if you mix blue and yellow light, you get white!), some illusion must be going on here! Enlarge the study window, then grab the X with the cursor and drag it to the white background. Against the white, it seems sort of beige. While you have the X’s selected, drag Colors from the menu bar to somewhere on your desktop. The color of the selected shape is highlighted on the palette. Double click on that color. If you are looking at a multi-colored circle, get more choices so you can pick Apple RGB. This tells you the proportions of the red, green, and blue phosphors of the display. You can do this for every color in the study. (Just leave the palette on the desktop.) The settings for Study IV-3.1 are given in Table 10-1. Table 10-1. RGB settings for Study VI-3.1 color blue background X’s yellow background R(%) 60 80 100 G(%) B(%) 60 80 80 60 100 40 10-6 There’s More to this than Meets the Eye The color of the X design is created by setting the red and green phosphors at 60% of their maximum intensity, and the blue at 80%. [These 0-100 settings are comparable to the 0-63 settings on our color mixing program.] According to color mixing rules, the X’s are unsaturated yellow (equal amounts of red and green, less blue); the blue (lavender) background is unsaturated blue, and the yellow background is (more saturated) yellow. (Think of lavender as an unsaturated violet, and violet as part of the blue third of the spectrum.) The X’s differ from the blue background in the relative contributions of B vs. R+G. The X has less blue and more red and green compared to the background, so we see it as yellow, because the yellow-blue contrast is enhanced. Similarly, the X has more blue and less R+G than the yellow background, so the yellowblue contrast is enhanced in the opposite direction: we see the X as blue on the yellow background. As you proceed through the various color studies, always choose “Don’t Save” when the program asks about saving changes. It won’t save them even if you ask it to, and you’ll spare yourself some waiting time, while it reconsiders whether it should have asked you in the first place. Examine two studies Examine Studies VI-2.2 and VI-3.2, using the techniques described above for VI-3.1. These are especially good illusions. Worksheets are provided on the following pages. Write a report For whichever of these two you prefer: • Draw a diagram, labeled as the colors appear to you. • Tabulate the RGB settings for background and design(s), and indicate what the colors “should” be by color mixing rules. • Identify the contrast at work here (i.e., blue/yellow, red/green, dark/light). Writing neatly and clearly, explain, using the RGB color settings and the color mixing rules, how the illusion works. Light and Everything Lab Manual 10-7 STUDY VI-2.2 Table _____________________________________ part of diagram apparent color left background design on left design on right right background Describe & explain: R(%) G(%) B(%) color by mixing rules 10-8 There’s More to this than Meets the Eye STUDY VI-3.2 Table _____________________________________ part of diagram left background design on left design on right right background apparent color R(%) G(%) B(%) color by mixing rules Light and Everything Lab Manual 11-1 Lab 11. Making Waves (Light is a wave!) prerequisites: none lab credits: 2 PROPERTIES OF WAVES In this lab you will have the opportunity to explore the properties of waves, and to view for yourself the evidence that light is a wave. A wave is a rhythmic fluctuation. It can be described by its frequency, its wavelength, its amplitude, and its speed. Figure 11-1 illustrates some of these properties. amplitude wavelength (one cycle) frequency (cycles per second) Figure 11-1. A wave Frequency is usually given in hertz, or cycles per second. The first wave illustrated in Figure 11-2 has a higher frequency than the second. Wavelength is the length of one cycle, or the distance (in meters, for example) between crests. The first wave in Figure 11-2 has a shorter wavelength. Amplitude is the height of the crests above the midline. This would be the loudness of the sound, the height of the water, or the brightness of the light. The first wave illustrated in Figure 11-2 has a uniform amplitude; the second varies. Speed is the distance the wave travels per unit time (meters per second, for example): how far one crest travels in a second. Sound travels 344m/sec in air at standard temperature and pressure; light travels 300,000,000m/sec in a vacuum. 11-2 Making Waves Figure 11-2. Two waves Frequency, wavelength, and speed are related to one another. If two waves travel at the same speed (the speed of light, for example), the one with the higher frequency will produce more cycles per second, and they will be closer together (i.e., have shorter wavelength) than the one with the lower frequency. See Figure 11-3. long wavelength short wavelength low frequency high frequency long wavelength short wavelength 4 cycles from center to outer boundary 8 cycles from center to outer boundary Figure 11-3. Relationship between frequency and wavelength. A wave with longer wavelength has a lower frequency Light and Everything Lab Manual 11-3 Mathematically, this relationship can be expressed as follows: frequency x wavelength = speed cycles sec x m cycle = m sec Note: Frequency (i.e., hertz) is often referred to as s-1 (1/sec). Similarly, wavelength is given as meters or nanometers. In both cases, “cycles” are implied. Thus, frequency x wavelength = speed s-1 x m = m sec Waves can interfere with one another. When two waves meet such that their crests and troughs coincide, the amplitudes of the two waves are added together. In this situation, the water would rise higher, the sound would be louder, or the light would be brighter, depending on the type of wave. This is known as constructive interference. Destructive interference, on the other hand, occurs when two waves meet such that the crest of one coincides with the trough of the other, bringing the combined amplitude to zero. In this situation, the water would be level, there would be silence, or it would be dark. This is illustrated in Figure 11-4. wave 1 sum = 0 wave 2 Figure 11-4. Destructive interference between 2 waves. The crests of one wave exactly coincide with the troughs of the other. They add up to zero. In water and in light, two point sources of waves will create constructive and destructive wave fronts at an angle to the direction of the original waves, as described in Snippets on the Wave Theory of Light. At certain angles to the original direction, the waves will add constructively, and at others, destructively. In Figure 11-5, the original direction of the waves is straight across horizontally. Note the fan-shaped pattern of lines of constructive and destructive interference, and the angle made by each line of destructive interference (labeled C, D, E, F) with respect to the horizontal. (Where you can see distinct blackand-white lines, you are seeing the crests and troughs; where you see more nearly uniform gray, the crests and troughs have negated each other.) 11-4 Making Waves Figure 11-5. A two-slit interference pattern viewed from above (from Thomas Young). A and B are the two sources (the two slits), and C, D, E, and F are where we see destructive interference. The angle at which two waves interfere depends on the wavelength and the distance between the two sources of waves. In the statement below, S (the Greek letter lambda) stands for wavelength, d stands for the distance between the sources, and P (the Greek letter theta) stands for the angle at which the interference occurs. λ is directly proportional to θ d The angle at which interference occurs is larger for longer wavelengths, and smaller for greater distances between the sources. THE WAVE TABLE The relationship between wavelength and frequency. Set up the wave table so that there is one point source of waves. (I.e., let only one knob touch the water surface.) Turn on the motor to a “slowish” frequency. Raise the frequency. (Should this increase or decrease the wavelength?) Compare the wavelengths for the two frequencies. Do they relate as expected? (It may be useful to look at Figure 11-3 again.) The effect of frequency (and hence wavelength) on the interference pattern. Set the wave table up with 2 point sources, close together. Choose a frequency that allows you to see the interference pattern. You should see something like the pattern in Figure 11-6. Light and Everything Lab Manual minima (destructive interference) 11-5 central maximum first order maximum (constructive interference) second order maximum Figure 11-6. Water wave interference pattern set up by two point sources. At the lines of destructive interference, the water surface is smooth, and the image on the screen below the tank looks uniform. At the lines of constructive interference, the water surface looks rippled, and the light shining through the water creates stripes on the screen below the tank. Without moving the point source knobs, vary the frequency of the motor. Sketch a high frequency pattern and a low frequency pattern. How does the interference pattern change? Does the angle from central maximum to 1st order minimum get wider or narrower? Is this as expected? 11-6 Making Waves The effect of the distance between point sources on the interference pattern. Set the wave table up with 2 point sources, close together. Choose a frequency that allows you to see the interference pattern. Without touching the frequency setting, increase the distance between the point sources. Draw sketches that show the difference between point sources close together and farther apart. Label the central and the first (and any higher) order maxima. What happens to the bending angle (the angle between the central maximum and the first order maximum) when the distance gets larger? (Does the pattern get wider or narrower?) Is this as expected? Compare this to the pattern laser light makes when it passes through two slits. Why is using two point sources the equivalent of letting one wave go through two slits? The effect of multiple sources. Imitate a diffraction grating by putting all the knobs down, equally spaced. Sometimes, if you do this just right, you can see a wave front coalescing and moving off at an angle to the main wave. Light and Everything Lab Manual 11-7 YOUNG’S TWO-SLIT EXPERIMENT Observe the interference pattern created by projecting laser light through two slits. Which slits give you the wider pattern, slits close together or far apart? Draw what you observe. Now see for yourself the interference pattern created by white light, as Thomas Young would have seen it. Hold one of the glass plates right up to your eye, with the slits vertical, and look through the slits toward the long filament bulb. Stand so you see the filament as straight (it waves in one plane). There should be a pattern of vertical stripes of dark and light in the image, something like that shown in Figure 11-7. Ignore “fringes” Compare the width and spacing of the lines in the middle Figure 11-7. Two slit interference pattern. After you have gotten a good look at the interference pattern, try another glass plate, with slits farther apart or closer together than your first slits. How does the pattern change? Is this consistent with your observations at the wave table? (If you haven’t been to the wave table yet, simply make 2 sketches of the patterns, labeled “slits close together” and “slits farther apart.”) Light and Everything Lab Manual 12-1 Lab 12. Sound Interference prerequisites: Lab 11 lab credits: 1 OUR APPARATUS This apparatus consists of a tube with a speaker at one end hooked up to a tone generator and a plunger with a microphone attached at the other, as shown in Figure 12-1. An oscilloscope provides a visual indicator of what the microphone is detecting. Plunger Tone generator Oscilloscope Microphone Speaker Figure 12-1. Our sound interference device Generate a pure tone with the tone generator, and change its frequency. Describe what happens to the sound. How does what you hear relate to what you see on the oscilloscope? 12-2 Sound Interference HOW TO READ THE FREQUENCY ON THE OSCILLOSCOPE The oscilloscope screen has a grid on it, as shown in Figure 12-2. The grid is 10 cm across, and each cm on the screen represents the amount of time given on the time dial. If the oscilloscope is set to 1msec/cm, one sweep across the screen represents 10 msec. In Figure 12-2, there are 6 complete cycles per sweep, so the frequency is 6 cycles/10 msec, or 600 cycles/sec. (1 sec = 1000 msec) Figure 12-2. An oscilloscope screen HOW TO CREATE SOUND INTERFERENCE The sound waves generated by the speaker travel to the plunger, where they are reflected. At certain locations along the length of the tube, the reflections are such that they cancel the incoming waves (i.e., produce destructive interference). This is illustrated in Figure 12-3. Light and Everything Lab Manual barrier reflects wave at the neutral point incoming wave reflected wave out of phase with incoming wave 12-3 barrier reflects wave at a crest incoming wave reflected wave in phase with incoming wave Figure 12-3. Interference by reflected waves. When the barrier reflects the wave at the neutral point, the reflected wave cancels out the original, incoming wave. When the barrier reflects the wave at a crest or at a trough, the reflected wave is in phase with the incoming wave, creating constructive interference. One complete cycle (one wavelength) goes from crest to crest (or trough to trough), so to find the wavelength, you must find 3 consecutive maxima or (3 consecutive minima). Figure 12-4 illustrates this for minima. At each of the three positions, the barrier reflects the sound at the neutral position, so the reflected wave interferes destructively with the incoming wave. With the barrier at any of these points, the volume of the sound should be at its lowest. Reflector positions that produce destructive interference one wavelength Figure 12-4. Three consecutive reflector positions let you find one wavelength. 12-4 Sound Interference Measure the wavelength of sounds at 3 different frequencies: find the locations where the sound is maximized (or canceled, whichever is easier). Measure the distance between a node and two nodes away, and calculate the speed of sound inside the apparatus, using the formula below. (At sea level, and at standard temperature and pressure, the speed of sound is 344 m/sec.) cycles m m × = sec cycle sec Frequency wavelength speed Light and Everything Lab Manual 13-1 Lab 13. The Wavelength of Light Measuring the wavelength of light with diffraction grating and a tape measure. Really! prerequisites: Lab 1, Lab 11 lab credits: 1 Look at the spectrum created by a piece of diffraction grating. Edmond Scientific, the manufacturer of the cardboard framed diffraction gratings, claims that the film has 23,000 grooves per inch. Calculate how many nm (nanometers) this is per groove (this will be “d” in our wavelength calculation). (1 inch = 2.54 x 107 nm; 1 nm = 10–9 m). d = __________nm View the linear filament incandescent bulb through the grating. Try turning the grating different directions, until you get a clear, bright, wide, horizontal spectrum. This is illustrated in . Try wiggling a finger on your free hand in front of the image of the filament, and noting what happens to the image. You might wish to interpose a filter between the bulb and the grating. What do you expect to happen to the spectrum? Stand so that a line from you to the bulb makes a right angle with the blackboard behind the table the lamp sits on. (This would be ‘A’ in Figure 13-1. Position your partner at the red end of the spectrum. Have her mark the blackboard. You stay put. Do it again for the violet end. Measure the distance from the mark to the lamp, and from you to the mark. (These would be ‘B’ and ‘C’ from Figure 13-1 , respectively.) Enter your data in the table below. (See page 13-3 for help with calculations.) RED VIOLET λ B C (calculations on p. 13-3) apparent color of λ (from color naming spectrometer) B C λ apparent color of λ Wavelength of Light incident light 13-2 B light source zero order (central) maximum Diffraction grating θ1 A spectrum C θ diffraction grating θ2 θ=0 A. What happens to the light as it B. Where the spectrum appears to be in passes through the grating space apparent location of spectrum in space Source viewed directly light source Source viewed by diffracted rays B blackboard B Note: this “big” triangle (ABC) is similar to C the small triangle (abc) The triangle abc is too small to see directly, but it is the same shape as the big triangle ABC. So if we see ABC, we “see” abc! R A diffraction grating θ c θ a R location of spectrum on retina B b The shape of the triangle abc is fixed by the grating space and by the wavelength retina C. Why your brain interprets the D. Using similar triangles to understand spectrum as out in space. the apparent angle. Figure 13-1. The spectrum created by diffraction grating. As the light passes through the diffraction grating, it creates spectra by constructive interference (A). You experience this as if the spectrum were projected in front of you (B), because your brain interprets the image on the retina as if the light had entered the eye from a distant point on the line from the pupil to the image on the retina (C). Similar triangles can be used to show why this works (D). Light and Everything Lab Manual 13-3 Calculate the wavelength of far red and far violet light, using the formula given in Snippets on the Wave Theory of Light, B λ = , C d where λ (the Greek letter lambda) stands for wavelength, d stands for the distance between the sources, (in this case, the slit-to-slit distance) and θ (the Greek letter theta) stands for the angle at which the interference occurs (in this case, where the red or violet light appears in the spectrum you see through the diffraction grating) with respect to the source. If B λ = , λ= C d Add your calculated wavelengths to the data table on page 13-1, and to the class data sheet provided at the station. Check yourself with the spectrophotometer (the color boundary device we used in a previous lab). Set the dial on the spectrophotometer to the wavelength you calculated, and look in the chamber to see what color light is at that wavelength. How’d you do? Young calculated 423 nm for violet and 705 nm for red (actually 1/36,000 inch and 1/60,000 inch, respectively); how did he do? Compare the wavelengths calculated by different students. Every measurement comes with some degree of uncertainty. It is instructive to consider the many possible sources of variation in our measurement technique. Later on in the semester, your instructor will have a list of the answers calculated by all students for you to examine. Light and Everything Lab Manual 14-1 Lab 14. Electricity An Introduction to Ohm’s Law prerequisites: none lab credits: 1 OBJECTIVES This lab is designed to help you become familiar with basic concepts of electricity, some simple electrical equipment, and the use of graphs to confirm relationships between things we can measure. This familiarity will be of great benefit to you in upcoming labs on photoelectric effect and neuromuscular activity. BASIC EQUIPMENT Before beginning, take a moment to look at the equipment and devices on the lab bench. Identify the following devices: The power supply. Notice this has a gauge indicating the voltage being supplied. Also notice the terminals marked positive and one negative. It supplies direct current. The ammeter. This displays the current. Resistors. (These look like small metal blocks or ceramic cylinders with wires coming out of the ends.) Diodes. (You have two kinds: a light emitting diode (LED) and a glass signal diode that looks a bit like a resistor.) RESISTANCE AND OHM’S LAW Set up the circuit. Turn off the power supply, and turn the knob regulating the voltage all the way down. Plug the red ammeter lead (the banana plug) in the 10 ADC slot. Plug the black lead into the COM slot. Set the meter to the 10A range. Using alligator clips as necessary, connect up a circuit as shown in Figure 14-1 with resistor #1 and an ammeter in series. power supply Adjust voltage here ammeter resistor Figure 14-1. How to set up your circuit 14-2 Electricity See how it works. Turn on the power supply and slowly increase the voltage until you are supplying ten volts. What happens to the current (the reading on the ammeter) as you increase the voltage? Without changing the voltage, turn the resistor around in the circuit. What happens to the current? Measure the current through your resistors. For each of your three resistors, measure the current in the circuit at three different voltages, and write it in the data sheet provided. You will get greater accuracy if your ammeter displays more than one significant digit (e.g., 0.10 or more), so very low voltages may not be the best choices. The two cylindrical resistors, however, tend to get hot at the higher voltages, or if left in the circuit too long, so aim for the lowest voltage that gives two digits, and turn off the power supply after you have taken your readings. Use the data table below to enter the voltage and current of each resistor. (The other values will be calculated after data collection.) Calculate the resistance of each resistor using Ohm’s law. Ohm’s law says that current (I) is equal to voltage (V) divided by resistance (R). I= Resistor # 1 2 3 V I V V , so R = R I R slope (m) intercept (b) equation of the line Light and Everything Lab Manual 14-3 Graph your results. Draw a graph of voltage against current for your three resistors. The variable we manipulate is called the independent variable, and is put by convention on the X-axis. Which ought to be on the X-axis (the independent variable) and which on the Y-axis (the dependent or response variable)? Current Current Plot your points. (If you are uncertain how to do this, please check with your instructor.) With a ruler, fit the best straight line to these points. [Should your line go through the origin? What is the current when the voltage is 0?] Your points ought to sit on your straight line. Do they? Is one point way off? Check your plotting, then see whether you can fix it by repeating some measurements. Figure 14-2 illustrates fitting a line to points. The points are your raw data, in all their genuine, honest raggedness, but your line is your interpretation of your data, showing the relationship between the variables in its idealized form. Voltage Put in your line like this, Voltage not like this. Figure 14-2 Fitting the best straight line to the points The equation for a straight line is Y = mX + b. See Appendix 1: Lines, on page 14-4. The constant ‘b’ in this equation is near zero for the graph you have drawn. Explain in one sentence how you know this. The constant ‘m’ is the slope, or rise over run. Calculate its value using your graph and write it down. How is your constant ‘m’ related to resistance? Write down the formula. DIODES Put a diode in the circuit in series with your highest value resistor. (Diodes conduct current in one direction only.) Check the current in one direction, then reverse the diode and check it in the other direction. Do this for both your diodes. Write down a brief description of what a diode does. Old fashioned devices that did this were called ‘valves’. Write a sentence saying why. If you have time, go on to Lab 15 now. 14-4 Electricity APPENDIX 1: LINES Y axis Y intercept Rise X axis Run Figure 14-3. Anatomy of a line The notation m b Y = mX + b What it is slope of a line Y-intercept Equation of a line How to do it In Figure 14-3: the rise divided by the 6/3, or 2. The line rises run * 2 units for every horizontal unit where the line crosses 1 the Y axis; the value of Y when X is 0 to find Y, multiply X by multiply X by 2 and add m, then add b 1. ∗(Measure these at convenient locations on your graph, that is, at places where your line neatly runs through an intersection of grid lines. The longer the rise or run you choose, the more accurate your slope calculation will be.) Light and Everything Lab Manual 14-5 10 8 6 4 Y = 2X + 0 Y = 1X + 0 Y = -1X + 0 Y = -2X + 0 2 0 -2 0 2 4 6 8 10 -4 -6 -8 -10 Figure 14-4. The effect of changing the slope (m). As seen in Figure 14-4, • Larger slopes make steeper lines. • Positive slopes make lines point up to the right • Negative slopes make lines point down to the right 20 18 16 14 12 10 Y = 2X + 2 Y = 2X + 0 Y = 2X - 2 8 6 4 2 0 -2 0 2 4 6 8 10 -4 Figure 14-5. The effect of changing the Y intercept (b) As shown in Figure 14-5, lines with larger Y intercepts cross the vertical axis higher up. Light and Everything Lab Manual 15-1 Lab 15. Electrical Resistance prerequisites: Lab 1 lab credits: 1 COMBINING RESISTORS IN SERIES Put your two lowest value resistors (from Lab 1) in series, following the diagram in Figure 15-1. What is their combined resistance? Take several measurements of voltage and current, and calculate the total resistance of the circuit, as you did in Lab 1. R1 R2 Figure 15-1. Two resistors in series Voltage Current Resistance What is the apparent relationship between the resistance of the individual resistors and the combined resistance in the circuit? (E.g., the average of the two, the ratio of the smaller to the larger, etc.) 15-2 Electrical Resistance COMBINING RESISTORS IN PARALLEL In Figure 15-2, Two resistors (R1 and R2) are put in parallel into a circuit from A to B. When a voltage is applied across A and B, a current (I) flows between them. Part of the current (I1) goes through resistor 1 and the rest (I2) goes through resistor 2. The voltage is the same across each resistor. A I I1 I2 R1 B R2 Figure 15-2. Two resistors in parallel Ohm’s law says that current is equal to voltage divided by resistance: I = V . R The current through the first resistor must be equal to the voltage divided by its resistance, and the current through the second resistor must be equal to the voltage divided by its resistance (and the voltage is the same for both): I1 = V V and I 2 = R1 R2 The total current is equal to the current through the first resistor plus the current through the second resistor: I = I1 +I2 . So the current must be equal to: I = 1 1 V V . + , or V × + R1 R 2 R1 R 2 The individual resistances are related to the combined resistance like this: 1 1 1 = + . R R1 R 2 Light and Everything Lab Manual 15-3 Connect the same two resistors in parallel. Draw a diagram illustrating your circuit. Now what is their combined resistance? How close is the measured current to the current predicted by the formula? 1 R 1 1 1 = + R R1 R 2 predicted Measured Resistance 1 V Voltage current actual R= R I I V predicted current 1 1 + I = V × R1 R2 Why do these two ways of combining resistors produce such different results? Sometimes a grocery store analogy is helpful: suppose there are a certain number of shoppers (aka electrons) and a certain number of checkout clerks (aka resistors). The shoppers will check out faster if each clerk takes few of them, especially if each shopper goes to the next available clerk, so the slowest one doesn’t hold everybody up. On the other hand, if each shopper had to check out with each clerk (say, one for produce, another for canned goods, etc.), the flow of shoppers out of the store and into the parking lot would be very slow indeed. We will return to the concept of combined resistance when we discuss neurons. Light and Everything Lab Manual 16-1 Lab 16. Photoelectric Effect Light is a particle! prerequisites: Lab 7, Lab 11, Lab 1 lab credits: 3 SUMMARY OF EINSTEIN’S THEORY Einstein’s theory of photons (contained in section 8 of his 1905 paper) offers the following explanation for the photoelectric effect. The energy in a beam of light is carried in indivisible packets called photons, each of which carries an amount of energy hν, where h is a constant (Planck’s constant) to be determined from our experiment, and ν (the Greek letter nu) is the frequency of the light. (In sections 3-6 of the paper he “present[s] the line of thought ... which led [him] to this view.”) When one of these “energy quanta” strikes a metal surface, it may (if it has enough energy) knock an electron loose from the metal; if there is energy left over the electron will go flying off at high speed. If there is an electrode to collect these flying electrons, a current will flow between the metal surface (the photocathode) and the collecting electrode. If we think of this speed in terms of “kinetic energy,” KE, we must have KE = hν – W (1) (equation 1 of Einstein’s paper). W is the amount of energy required to knock an electron free from the metal surface; it is a property of the surface. Only if hν > W is an electron actually liberated. If you use a battery to apply a positive charge to the metal plate (or a negative charge to the collecting electrode) you will interfere with this process, by making it harder for an electron to be ejected from the plate (or collected by the collecting electrode). A large enough charge should in fact completely inhibit the photoelectric effect from occurring. In courses on electricity, students learn that a voltage multiplied by a charge corresponds to an energy; if the voltage is allowed to accelerate the charge, then V x charge is equal to the kinetic energy gain of the accelerated charge. In our case, we use a field which decelerates the charge, and V x charge therefore measures the loss of kinetic energy. 16-2 Photoelectric Effect In light of the above, Einstein concludes that equation (1) can be written VSe = hν - W. (2) VS is the “stopping voltage”: in a real experiment, the reading of a voltmeter attached between the two electrodes when the photoelectric effect just barely stops; and VSe is the corresponding energy of one of the electrons. This relationship is illustrated in Figure 16-1. Vse VSe = hν - W ν W Figure 16-1. A graphical representation of the relationship between stopping voltage and frequency (VSe = hν ν - W). Physicists define a unit of energy, called the “electron Volt”, symbol eV, to be the kinetic energy of an electron accelerated by one volt; thus, the reading of our volt meter is directly the electron energy, in units of electron volts. OUR GOALS IN THIS LABORATORY Einstein’s model thus predicts two things: that the voltage required to stop the photoelectric effect from occurring should be independent of the intensity of the light, and that we should obtain a linear relation between the stopping voltage, VS, and the frequency, U, of the light with which we illuminate the photocathode Our lab has four goals: 1. We wish to demonstrate the photoelectric effect. 2. We wish to test whether the light intensity affects the stopping voltage. 3. We wish to test whether the relationship between the stopping voltage VS and the frequency, U, is indeed linear – i.e., whether it is possible to draw a straight line through a graph of our data points, with due allowance for experimental error and the peculiarities of our commercial (not ideal) photocell. Light and Everything Lab Manual 16-3 4. We wish to determine the two constants h and W from the graph of our data. If Einstein’s model is correct, then h is a fundamental constant of nature, and W is a property of the particular metal contained in our photocathode. Figure 16-2 shows the general appearance of the device we’ll be using; Figure 16-3 is a circuit diagram of its electronic inner workings. dial to adjust voltage applied to phototube switch (set this to V to read voltage or mA to read current) light source light strikes phototube inside here, generating current ammeter (voltmeter) read V or µA here (depending on switch setting) Figure 16-2. Photoelectric apparatus. The light shines through the aperture and onto the phototube. If the switch is set to m A, the current shows on the ammeter. The dial allows you to apply a voltage to the photocell, stopping the current. When the switch is set to V, the voltage shows on the ammeter. 16-4 Photoelectric Effect V I I Current meter (Amps) V Voltmeter (Volts) Variable Resistor Photocell Battery photocathode anode Figure 16-3. Circuit diagram of photoelectric effect apparatus. When the switch is set to V, the ammeter shows the voltage between the photocathode and the anode. When the dial is turned, the variable resistor changes the voltage applied to the photocell by the battery. When the switch is set to m A, the ammeter shows the current caused by the light striking the photocathode. A high enough voltage will prevent the electrons from crossing the vacuum between cathode and anode, and thus stop the current. DOING THE WORK 1. First, confirm that the photoelectric effect occurs with our apparatus. Set the switch to V, and use the dial to set the applied voltage to zero. Cover the aperture, change the switch to µA and read the current. (There should be none.) Now shine the light into the opening. What happens? 2. Observe the effect of changing the intensity of the light. Use the screen provided to reduce the light entering the photocell. What happens to the current? Stop the current by applying a voltage to the photocathode. Increase the voltage until the current just barely stops, being careful not to overshoot. Read the voltage. Repeat this with and without the screen in place. I Full intensity Partly screened Vs Light and Everything Lab Manual 16-5 3. Observe the effect on the stopping voltage of varying the wavelength (or the frequency) of light. Our small interference filters each have a very narrow bandpass; they admit light only within 5 nm of the specified wavelength. The wavelengths of our filters are: 405, 430, 480, 520, 549, 589, 656, and 694 nm. Use at least 5 different wavelengths across the visible spectrum, getting as wide a spread as the filters will allow. Insert one of the filters into the aperture, and shine the light in. Apply voltage until the current just stops, and record how much voltage was required. Repeat this process for the other filters. You should obtain a set of measurements of stopping voltage through each of the filters, some of them repeated several times (to give you an idea of your own repeatability), and some of them made personally by you. Each such experiment is a measurement of the stopping voltage VS at a particular ν. λ (nm) (color)6 ν (Hz)7 Vs 6 Look at a very bright light through the very center of the filter. Make sure you are seeing light transmitted through the filter, rather than light reflected off its surface. 7 Calculate these after you have collected your data (see fix your units on page 16-6) 16-6 Photoelectric Effect 4. Analyze your data (to find h and W). First, fix your units. Our filters transmit at varying wavelengths between 405 and 694 nm (nanometers: 1nm = 10-9 meter, i.e., 1 meter = 109 nm). But Einstein’s theory is formulated in terms of the frequency, U. Therefore, before you plot any data, convert the wavelengths to frequencies. Recall the relationship between frequency and wavelength from Making Waves: frequency cycles sec x wavelength or m cycle x = speed = m sec In terms of light, this can be represented by the equation: c = λν, where c is the speed of light (c = 3 x 108 m/sec), λ is the wavelength, and ν is the frequency. This equation can be rewritten for our purposes (dividing both sides by λ): í = c , or ë cycles dist cycle = × sec sec dist Note, however, that we must make all the units match. One technique is to convert c from units of m/sec to units of nm/sec. 1m = 109 nm, so nm m = 10 9 × sec sec Plot your data for VS (vertically) as a function of U (horizontally). [Think about why they are plotted this way.] Your graph should go all the way to 0 on the frequency axis, even though your data are all positive frequencies; a sensible choice would be to let the horizontal axis range from 0 x 1014 Hz to 8 x 1014 Hz. (Figure 16-1 suggests the way to set up the axes.) Determine h and W from your graph. To do this, first draw a single straight line which “best represents” all the data points (as you did in the electricity lab). Except by a miracle (or fudging of the data) this line will not pass through all the points; but estimate by eye the line which does as good a job as possible “on the average”. Extend (extrapolate) this line all the way to zero frequency even though you do not have data there. Even though this extension of the line has no meaning in terms of your experiment, it does have mathematical significance; for it is the line which we hypothesize to be a graph of equation (2). Light and Everything Lab Manual 16-7 Read off your graph the ordinate (VS) at ν = 0; this is –W. To determine h, find the slope of your line. You may use the technique from Lab 1: find convenient places where your line (not your points!) neatly runs through an intersection of grid lines, and measure the rise and run (take care with the units on your axes!). Another technique is to pick a point on the line (not a data point) near the upper right end; read off VSe and ν. Substitute these two numbers into equation (2) (including now the numerical value of W) to find h. According to current reference works, h = 4.1356692 x 10-15 eV s, with an estimated uncertainty of 12 units in the last decimal place. How well did we do? (A percentageerror calculation suggests itself!) [Note: in an ideal photocathode, the slope of the line is an accurate measure of h. Commercial photocells, however, are made to emphasize sensitivity at the expense of ideal response. Therefore, although the qualitative effect can be clearly seen, and a reasonable estimate of h obtained, the line may not be completely straight, and its slope not necessarily a precise measure of h.] 5. Think about what it means. How does changing the intensity of the light affect the current? Why? (Think blizzard, not tidal wave.) Why doesn’t changing the intensity affect the stopping voltage? Which photons have more energy, those in blue light or those in red light? Which requires a higher stopping voltage? 16-8 Photoelectric Effect Generally speaking, what is the relationship between the frequency of light causing the current and the voltage necessary to stop that current? What is the relationship between wavelength and stopping voltage? Why is the stopping voltage so similar for white and far blue light, even though the white light has about 100 times as much light as the light through any of the filters? How does the photoelectric effect in general, and your data in particular, demonstrate the quantized nature of light? What property of waves we used in today’s experiment demonstrating the quantized nature of light (i.e., the existence of photons)? YOUR REPORT Using your notes in this manual as your guide, complete the work sheet provided in class, attach your graph to it, and hand it in.