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HARVARD PHYS E-1B - Geometric Optics

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1 Physics E-1b Expt 4: Geometric Optics Spring 2007 Introduction Preparation: Before coming to lab, read the lab handout and Chapter 23 in Giancoli. Then complete the pinhole experiments in Part I and answer the bold numbered questions that appear throughout this handout. Answers to these pre-lab questions are to be handed in at the beginning of your lab. See the Lab Companion, page 3, for further information. Be sure to bring to lab, writing paper, a ruler, a calculator and your copy of the Lab Companion. Graph paper will be supplied. Post Lab Questions: At the start of your lab section, you will be given an additional handout with a series of questions to be answered during the lab and handed in at the end of the experiment. Try to answer these questions with one or two concise sentences. Experimental Setup Part I of the experiment is to be done on your own. However aluminum foil and needles are available in the help room for you to make a pinhole. Parts II, III, and IV are performed in the lab. A water filled aquarium and a laser light source are used in the first experiment. A thin double convex lens is used in Part II while a thick spherical lens made from a water filled glass flask is used in Part III. In Part IV you combine these two lenses to build a microscope. Candles and samples of text (fine print) are available to be used as objects for all of the experiments. Objective: In this lab you study the magnification properties of a pinhole. You observe the bending or refracting of light in water and determine the index of refraction of the water. The behavior of a thin double convex glass and thick spherical water lens are studied and compared to calculated results obtained with the thin-lens formula. The lens makers formula is used to find the index of refraction of water in your thick lens. Finally you utilize your data from these experiments to construct a microscope with the thin and thick lenses.2 Part I: Pinhole Imaging Pinhole Magnifier First check and note how close you can bring this printed page to your eye before you can no longer focus, and the print becomes fuzzy. Next, take a piece of aluminum foil and make in it a pinhole of about 1/2-mm diameter or less. Hold it close in front of your eye. Now look at the well-illuminated printed page through the pinhole. (If you wear glasses, take them off. You don’t need them and they won’t do any good.) Bring the page up closer and closer to your eye. Notice that the word you are looking at stays “in focus” and is magnified as it is brought closer! (It finally gets fuzzy because your pinhole is not small enough.) You have made a pinhole camera using your eye (a) The magnification is easily calculated if you make some assumptions about the distance between the pinhole and the retina of your eye. 1→ Draw a ray diagram that explains how your pinhole magnifier works and derive a formula for the lateral magnification. Do you really see things upside down? (b) Here is a way you can convince yourself that the image on your retina is inverted. Look through your pinhole at a broad light source (like the bright sky or ceiling fluorescent lamps). Hold a pencil point in front of the pinhole and look at its shadow on your retina. Everything behaves as expected. Now reverse the order and put the pencil point between the pinhole and your eye. Move the pencil and notice the direction of motion of the shadow! 2→ Make a sketch and explain what’s happening. Exercising the pupils... (This part is just to do and notice - nothing to measure.) When you look at a broad light source through your pinhole, you see a bright circle. That circle is the projection of your pupil on your retina, not the outline of the pinhole. You can study the dilation and contraction of your pupil by covering and uncovering your other eye, the eye that is not looking through the pinhole. When you uncover the other eye so that light enters it, its pupil contracts. So does the pupil of the eye looking through the pinhole! You can easily see these “sympathetic” pupil contractions. Notice that it takes a time of the order of 1/2 sec for the pupil to contract or dilate when the light intensity is suddenly changed.1 1Eye-pupil size and mental activity. If someone shows you a picture of a good-looking individual of the opposite sex, your eye-pupil diameter may increase by as much as 30%, according to Eckhard H. Hess, Scientific American p. 46 (April 1965). This large a change is very easy to detect in your own pupil by using this pinhole technique. You may wish to try this: Perhaps by just thinking, you can vary your pupil size, depending on what you think about. Have someone read to you. (Concentrate on listening, not on the pupil size.)3 Part II: Index of Refraction of Water In this experiment you will measure the index of refraction of water by measuring heights and applying the small angle approximation. Refer to the sketch below. !idhMedium 1(Air)h'Medium 2(Water or Air)CLaser Light Source!r Begin with the aquarium tank that is full of water. Mount the laser pointer in the clamp and adjust it so that the ray strikes the bottom edge of the tank as shown in the diagram. Use masking tape to locate the position of the tank on the lab bench. Measure the distances d and h. Arrange the geometry so that d/h is about 3/4 — this value is not critical. Replace the filled tank with the empty one, carefully positioning it in the location determined by the masking tape. Without moving the laser, locate the point on the face of the tank where the ray strikes (a piece of masking tape will help) and measure h’. Place the full tank in its original position. Adjust the laser so that d/h is now about 1/5. Repeat the measurements. Calculate the values of h/h’ for the two sets of measurements. Be sure to include the uncertainties. The index of refraction, n, of the water is approximately equal to the ratio of the height h to the height h’. 3→ Show that the ratio h/h’ approaches the value of the index of refraction as d becomes smaller. To prove this, relate h/h’ to the tangents of the angles of

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