13. Optical Instruments*

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1 13. Optical Instruments* Objective: Here what you have been learning about thin lenses is applied to make a telescope. In the process you encounter general optical instrument design concepts. The learning objectives are the following: 1. To learn to use ray tracing to locate images, predict magnification. 2. To be able to analyze multi-lens systems with the thin lens formula. 3. To use the ray-through-the-center concept to calculate either lateral or angular magnification. 4. To see how the light passing through the real image produced by the an objective lens behaves as if it were coming from an actual object in its focal plane. 5. To see how an eyppiece lens can be added to an objective to form an astronomical telescope with an inverted image. 6. To learn how another lens can be added to make the final image erect. Reading assignment: Serway and Vuille (212): 23.2 Reflection and Refraction, 23.4 Images formed by Refraction 23.6 Thin Lenses. Serway and Jewett (252):36.3 Images Formed by Refraction, 36.4 Images Formed by Thin Lenses, 36.8 Simple Magnifier, The Telescope. Pre-lab exercises: Complete the following based on your reading before coming to laboratory. 1. A thin lens, either converging or diverging, has two focal points or foci. In general a focal point is not a point where the image will focus. Define the two focal points, the focal length, and the optical axis of the lens in the following space. 2. When light passes through a thin lens, certain rays are easy to trace. List four of these easyto-trace light rays. For each one, tell (a) how it enters the lens (i.e. parallel to what or through what) and (b) how it exits the lens. * William A Schwalm

2 Write down the thin lens formula, using the symbols p, q, f respectively for the object distance, the image distance and the focal length of the lens. Using the convention described in your textbook, indicate the conditions under which each of these quantities is positive or is negative. 3. Suppose two thin lenses are placed one after another along the same optical axis. Suppose to start with that they are both converging lenses with focal lengths f 1 and f 2 respectively, with lens 1 to the left of lens 2, and that the distance between them d is initially large. An object is placed a distance q 1 to the left of lens 1. (a) Draw a scaled diagram of this situation. (This means use a ruler to make the lines straight and the lengths proportional.) (b) Use the lens formula to find the position of the image formed by lens 1, and then using this image as an object for lens 2, locate the final image position. 13-2

3 (c) Now take a limit in your result that will bring the two lenses into contact and thus show that the final image distance q 2 measured to the right of lens 2 is such that p q f f What does this tell you about the 2-lens-in-contact combination? 4. Based on your reading, design an astronomical telescope using a cardboard tube two lenses: Lens 1 (Objective) focal length 45 cm, diameter 5 cm. Lens 2 (Eyepiece) focal length 5 cm, diameter 2 cm. (a) Make a scale drawing of the completed telescope, indicating the dimensions. (b) Find the angular magnification. Explain why the final image will be inverted. 13-3

4 (c) Modify your design to include another lens, identical to lens 2, so that the over all angular magnification remains the same but the final image is erect. How will this affect the length of the completed telescope? In class activity: 1. Make a drawing, including an optical axis, an eyeball and an object (indicated by an arrow) that will show how the angle subtended by the object as seen by the eye will depend on the distance from the object to the eye. Use the picture to derive a formula for the angular magnification, or ratio of the angular sizes, as the object moves from distance a to distance b. 2. Suppose you have a converging lens with focal length f. The lens is placed between a lighted object and a screen. The distance from the object to the screen is 50 cm. When the lens is 20 cm from the screen an image is formed. You will also find that an image is formed on the screen when the lens is at another position. What is the other position? What is the focal length f? Explain. 13-4

5 Equipment: Optical bench with lens holders, a set of lenses and mirrors that fit into the lens holders. A lighted object, a flashlight, a ruler or meter stick and a screen. You should have access to a view of a distant object. The lights will be dimmed during part of the period. Exploration of the equipment: Determine which of the lenses are converging and which are diverging. See how the lenses can be placed in the lens holders and figure out how to align lenses vertically and determine their relative position using the scale on the optical bench. Estimate the focal lengths of the converging lenses by forming images of a distant object. See if you can form an image of the lighted object on your optical bench on the screen using one of the converging lenses. Is this image real or virtual, and how do you know? Record your observations here. Problem 1 Your group is asked to create a procedure for measuring the focal length of a converging lens on the optical bench using only the lens, a screen, and a light source. You need to write a procedure and demonstrate it with some actual lenses. Of course, as always, your employer needs to know about the limits of accuracy of this method as well. Plan: Formulate your measurement plan and record it here. 13-5

6 Implementation: Cary out your plan for the converging lenses provided. Determine the focal lengths and provide a tolerance for your measured values. Record relevant data and necessary observations here. Analysis: Do the analysis described in your plan and provide results here. Conclusions: Draw conclusions about your method here. These should result from a brief discussion within your group. 13-6

7 Problem 2 Now you are asked to find a way to measure the focal length of a diverging lens by placing it in contact with converging lenses of known focal length. Plan: On conferring with your work group, devise a plan for making such a measurement. You will have to apply other things you have learned so far. Record your plan here and discuss it with your instructor before you begin. As always, you need to tell what you are going to do, what data you will collect, how you will analyze it to come up with the desired measurement, and how you will estimate the amount of error inherent in the method. Implementation: Take the necessary data, and record enough ancillary information to achieve the desired focal length measurement. Make it clear what each thing is with brief but clear notations. Analysis: Carry out the analysis described in your measurement plan and arrive at a value and an error analysis. 13-7

8 Problem 3 Observation of a real image. After discussion amongst your group members, describe here what the difference is between a real image and a virtual image, when either one can be formed by a converging lens. Following a procedure similar to that of the previous problem, set up an illuminated object and a converging lens with f of about 10 cm such that a real image is formed on a screen with the screen near the center of the optical bench. Is the image erect or inverted? Now remove the screen leaving the screen holder in place. Replace the screen by a pencil in such a way that the tip of the pencil points to the center of the real image. Look into the light coming through the lens from the light source. You should see the real image floating in space at the tip of the pencil. Be sure that everyone in your group observes the image floating in space where the screen was. Question: What observational method can you think of to find the location in space of the image? Now here s the problem: Figure out a way to add a second lens that will produce another real image on a screen, using the first image as an object. Write out a short description here of what you plan to do. Plan: (Do it.) Implementation: Carry out your plan. Report on the condition of the new image. Is it larger or small than the first one? Is it erect or inverted? Is it larger or smaller? Is it more or less intense? 13-8

9 Problem 4 An astronomical telescope affords a magnified (but upside down) view of distant objects. As you know from your reading, an objective lens creates a real image of the object and then an eyepiece lens acts as a magnifying glass to give a virtual image at infinity. You are asked to use the available equipment to make a prototype astronomical telescope on the optical bench. Plan: Design a telescope utilizing what you have available. Draw a diagram and calculate how far apart the lenses should be placed and what the resulting angular magnification should be.. Implementation: Construct the telescope. use it to observe a distant object. Let your instructor verify that it works. Modification: Suppose all of a sudden your employer learns that it will be necessary to come up with a terrestrial telescope in which the final image is not upside down. Plan: Make a design modification, using available lenses if possible, so that by adding an additional lens the final image will be erect. Figure out the spacing between each pair of lenses and the final magnification. You should provide a scaled diagram. Implementation: Create your telescope prototype on the optical bench if possible and demonstrate that it works. 13-9

10 Conclusion: On discussion with your group, describe the weak points of these telescope designs and suggest modifications that might improve them

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