6m_lab6

6m_lab6 - EXPERIMENT 6M-7: GEOMETRIC OPTICS As we will...

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Unformatted text preview: EXPERIMENT 6M-7: GEOMETRIC OPTICS As we will discuss in lecture during the final week, light rays which pass from one transparent material to another are bent, or “refracted”, as they pass through the plane of transition. We can take advantage of this phenomenon to build lenses, devices which focus incoming light to a single image point. ' We will deal with two types of lenses today: Converging lenses, which appear as a convex, tear-shaped piece of transparent material, can take light ways which were originally parallel and cause them to converge to a single point: EACM?V\9 The point where the light rays converge is called the image poinf. The idea of an image is that if you were to place your eyes “downstream” of the image point, and look at the pattern of light reaching your eyes, the light would seem to originate from the image point. This pattern of light can “fool” your brain’s depth perception into thinking the light originated from the image point, when it really originated from some distance source. Any other optical device can also be “fooled”; for example, a camera held downstream oif the image point can bring the image into focus as if there were an actual physical object there. ' The type of image shown above — where the light rays really did pass through the image point, just as a “downstream” eye or camera will think they did w is called a real image. If the incoming light rays were all parallel, then the distance. from the plane of the lens to the image point is called the focal length of the lens. Diverging lenses, which appear as a concave piece of transparent material, can take light rays which were originally parallel and cause the rays to “fan out” like this: e may if s \i‘o‘l Vlirfrwmk J (2)7 M90”? ‘i Q CLOwngiW/(fitm \W‘q7a ‘ I 976%“; _ - — - r . . * ~ E e .,_ r . [iriww‘lrg ' ‘ l '6 I I _ lewfifi'h , - - ’“locm F H, 2 , At first, the lens shown above may seem not to cast an image at all; after all, its rays never come together to a point. But if you were to place your eye or a camera downstream of the lens, the light rays still seem to originate from a common point to the left of the lens, as shown by the dotted lines above. Once again, if the incoming rays are parallel, then the distance from the plane of the lens to the image point is called the lens’s focal length. (Although by convention, the focal length of a diverging lens is considered negative. So the lens in the above picture, for example, would have a focal length of —10 cm.) The type of image shown in the above picture — and the type most commonly cast by any diverging lens -- is called a virtual image. To an eye or to a camera, this image will appear every bit as convincingly “real” as the other kind...however, most of the light rays never actually passed through the image point. One way to tell the difference between a real and a virtual image is this: if you were to place a “screen” (such as a piece of paper, or just your hand) at a real image point, you would see a sharp point of light projected on the screen. But if you place the screen at the virtual image point, you would not see any image point appear on the screen, since the light rays don’t actually pass through this point. Experiment #1: Convergine lens On your lab bench you have a ray box, which uses a mask with slits in it to throw a bundle of parallel light rays across the surface of the table. Adjust the ray box so that the light rays it casts are parallel — play around with it for a moment; you’ll figure out how this works. Then place a converging lens in the path of _ the rays. (You will know it is a convergine lens by its convex shape.) Sketch the patterns of rays that you see on both sides of the lens — it should resemble Figure 1 above fairly closely. Measure and record the focal length f of this lens. Try actually placing-your eyes downstream of the image point r you may have to lift the whole setup off the bench for this step. Does the light that passed through the lens seem to come from a single point? Can you estimate (using your depth perception) roughly where this point seems to lie? Now try sending parallel light beams through the lens at an angle from its central “optical axis” as shown below. The light should still converge to a point. If the lens is “perfect”, then the distance from the plane a. the lens to the image point will still be equal to f, the lens’s focal length. Era, 3 Try it and see: does the light still form an image point? Is the distance from the plane of the lens to the image the same as before? (The answers to both theses questions might change as you tilt the light beams at more extreme angles off the optical axis.) ‘ We mentioned above that a real image can be projected onto a screen. Place a piece of paper (or your hand) at the image point. Do you see a sharp point of light on this screen? Note: as you attempt to explain your observations, it can be very heipful to place a piece of paper on your lab bench and actually trace the lens and the light rays. You can then refer directly to this sketch (placed in your lab book or your partner‘s) to explain your observations. Experiment #2: Divergine Lens Now take a divergine lens — you will know it by its concave shape, and by the fact that it produces a pattern of light similar to figure 2 above — and repear all the same observations you made in part 1 for a converging lens. You will have to trace the outgoing rays backwards to find the image point — so more than ever, it will be helpful to trace the rays onto a piece of paper and then use a straightedge to locate the virtual image. Let Figure 2 be your guide in this. As you explain your results, make sure to detail both the similarities and the differences between the behavior of a converging and a diverging lens. Experiment #3: Mirrors. In addition to the lenses you have been working with, you have two pieces of reflective metal that can act as mirroirs w one flat, and one curved. For now, take a look at the curved mirror. Both sides of it are shiny, so you can use either the concave surface or the convex surface as a mirror: i--§- —-—-9 ._—9— 3 WlAc-i‘l‘ lac-1 WS in eacln cage? \ it P, i Try placing each side of mirror in turn in the path of the rays from the the ray box. Sketch (or trace directly onto a piece of paper) the pattern of incoming and outgoing (reflected) light rays in each case. Let the experiments you performed in part 1 guide you as you play around with the mirrors. You don’t have to repeat every single observation, but try to find the paralleis between the behavior of a lens and a curved mirror. Do the mirrors cast images? In each case, would you call the image real or virtual? Which shape of mirror (concave or convex) would you call a converging mirror, and which shape is a diverging mirror? Experiment #4: Compound Optical Systems Many types of optical devices — microscopes, telescopes, even a pair of eyeglasses plac ed over the lens of your own eye — use two or more lenses or mirrors together; the light passes through each lens (or reflects off each mirror) in turn. The principle we use to analyze these devices is simple: the image of one lens (or mirror) becomes the object (the light source) of the next lens or mirror. As a first example of this, team up with the group across from you (or just borrow a lens from them) so that you have two converging lenses. Use the first lens to cast a real image just as you did in Experiment 1. Then place the second lens “downstream” of this image, so that it “catches” the light emerging from the real image: LEN} 351 As you move the second lens closer or further away from its object point, you will notice something interesting: the second lens will sometimes cast a real image of its own, sometimes a virtual image. If you adjust the second lens’s position just right, you can make the outgoing light rays from this lens parallel — We say the ima e is at infinity, since these rays would have to travel infinitely far before they converge. l s Ma g (60! 1 fi{ Adjust the position of lens #2 until its outgoing rays are parallel. Measure the distance between lens #2 and its object point (which is also the image point of lens #1.) Do you notice anything remarkable about thi 5 distance? (Hint: within reasonable meansurement limitations, it should be exactly the same as another distance you measured earlier.) Experiment #5: The thin lens equation You now have all the ingredients you need to explore the relationship between the position of any lens’s object (again, the source of the light that enters the lens) and the image that the lens casts. One simple way to do this geometrically is the method of principle rays. For a converging lens, it works like this: 1) Draw the lens, and mark the optical axis running through its center. 2) Along the optical axis, mark the focal points of the lens, an equal distance to each side. (This distance is the focal length.) 3) Mark the position of the object. it should be off the optical axis. (Even if the actual object is on—axis, move it off—axis for this diagram to find the image distance.) 4) The object (which can be an actual luminous object, or can be the image cast by a previous lens) sends light rays in all directions. But there are three rays which are particularly easy to trace; we call these the principle rays: . g - Draw a ray leaving the object and running parallel to the axis. You saw in experiment #1 that after passing through the lens, this ray will pass through the len’s focal point on the far side. a, - Draw a second ray leaving the object and passing through the focal point. You saw in experiment #4 what this ray will do: it will pass through the lens and emerge parallel to the optical axis. ' Draw a third ray leaving the object and passing through the center of the lens. You saw in the later parts of experiment #1 what this ray will do: it will continue straight through the lens without bending. If you’ve done this right, all three rays will converge at a point: this is the location of the real image. (Or sometimes, all three rays will seem to diverge from a common point, allowing you to locate a virtual image.) I - i iloml leffi’lA?‘ imagg ([i‘9+quq_ l .Ta fl: . i Mined“ cits-lan 90 For a diverging lens, you will do exactly the same thing...except.that ray #1 should be “aimed” toward the focal point on the far side of the lend, and will emerge parallel to the axis. Ray #2, which goes in parallel to the axis, emerges from the lens traveling directly away from the left-hand focal point. Ray #3 still passes through the center of the lens without bending. Again, thesgibehaviors match what you have seen in previous experiments today. ' i5-- §o"'—-> As you can imagine, it is not always convenient to draw principle every time you want to analyze a lens system. Fortunately, after a bit of similar—triangle geometry on the diagrams above, we can come up with the thin lens equation, which predicts the distance from the plane of the lens to the image: where so is the object distance (measured from the object to the plane of the lens), 51' is the image distance (from the image to the plane of the lens and f is the iens’s focal length. Note that f is a constant for each iens; it depends on the shape of the lens and the type of material it is made of, but does not change as you ‘ move the object and image points around. (Sign conventions: - f is positive for a converging lens, negative for a diverging lens. - s,- is positive if the image is real, negative if it is virtual. (So often, solving the thin lens equation for ,i and noting whether it comes out positive or negative is how you predict whether the image will be real or virtual.) Play around for a while with the ideas of images and objects: arrange the lenses and mirrors in different configurations, remembering that the image cast by one lens or mirror becomes the object of the next one. Watch how the position of a lens’s image changes as you change the object distance. Sketch a few of the more interesting configurations you observe. Can you again verify the behavior of the three principle rays described above? Some other things you may want to try: Measure the object distance of a lens, and then use the thin lens equation to predict its image distance. (Remember, you already know the focal lengths of all your lenses.) Measure the image distance; does it agree reasonably well with your calculation? Can you find a way to make a converging lens cast a virtual image? (Fairly easy; in fact, you have already seen it happen at least once in the lab so far.) How about a way to make a diverging lens cast a real image? (Trickier, but can be done.) Sketch the configurations if you find them! Pre—Lab question: (As discussed in Monday’s lecture.) Suppose you have a converging lens with focal length f = 20 sm. You place an object at a distance 30 = 30 cm from the lens. Use two different methods to predict where the lens’s image will be cast, and whether this image will be real or virtual: 1) Draw a scale diagram of the situation and sketch the three principle rays (as explained in lecture or in experiment #5 above.) 2) Solve the thin-lens equation for 5;. ...
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This lab report was uploaded on 04/16/2008 for the course PHYS 6M taught by Professor Graham during the Winter '07 term at UCSC.

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6m_lab6 - EXPERIMENT 6M-7: GEOMETRIC OPTICS As we will...

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