Physics 2020 Lab: Lenses and Telescopes page 1 of 9 University of Colorado at Boulder, Department of Physics Lab: Lenses & Telescopes INTRODUCTION AND BACKGROUND: In this experiment, you will study converging lenses and the lens equation. You will make several measurements of the focal length of lenses and you will construct a simple astronomical telescope. When a bundle of parallel light rays enters a converging lens, the rays are focused at a point in space a distance f, the focal length, from the lens. A converging lens is convex in shape, that is, thick in the middle and thin at the edges. A diverging lens is concave in shape, i.e. thin in the middle and thicker near the edges. A converging lens can be used to form an image of an object on a screen. The lens equation relates the focal length f of a lens, the object distance do and the image distance di : 11 1fd doi=+. (1) (This equation can used for both converging and diverging lens; the only difference is that the focal length f is positive for converging lenses, negative for diverging lenses.) In the diagram above, the points labeled F are the focal points of the lens – the distance from the lens to either of the points F is the lens focal length. fConverging lens, convexfDiverging lens, concavedodiimageobjectFFhohioptic axisdihidohoPhysics 2020 Lab: Lenses and Telescopes page 2 of 9 University of Colorado at Boulder, Department of Physics The magnification m of the image is defined as oihhm =. From the diagram above, one can use similar triangles to show that m can also be written as oiddm =. In the preceding figure, there are two important points to note: First, notice that the distance from the lens to the image is not the focal length of the lens, but is related to it through equation 1. Secondly, note that light is being reflected off of the object in many directions. The amazing thing about lenses is that all of the light rays that originate at some specific point on the object (radiating outward in all different directions) and then go through the lens are redirected to arrive at a single point on the image. Re-draw a simplified version of the preceding drawing, but without the lens. Namely, draw the arrow-shaped object, and draw rays of light coming from the tip of the object going out in many directions. Now draw rays of light coming from the middle of the object going out in many directions. If you were to expose a piece of photographic film to this mess of rays at some distance away (with no lens present), what would it look like? Would it form an image? Re-sketch the same drawing, but now with the lens in place. Duplicate the drawing with the object, the lens, and 5 different rays coming from the tip of the object through the lens, and converging at the image location. Draw 3 rays coming from the middle of the object and converging at the image location. (Draw carefully and precisely, or your drawing will be a mess…) If you were to expose a piece of film to the rays that arrive at the image location, what would it look like? Would it form a picture?Physics 2020 Lab: Lenses and Telescopes page 3 of 9 University of Colorado at Boulder, Department of Physics In this lab, you will use three different techniques to measure focal lengths. Method I: How can you use equation (1) to determine the focal length (f) of a lens, if you can measure di and do? Method II: If di were set to ∞ in equation (1), and we could measure do, how could we determine the focal length f? What would the rays of light look like near the lens if the rays converged to an image “at infinity”? Make a diagram, indicating the lens, the rays which emerge from a point at a distance do on the left side and then form an image “at infinity” on the other. Indicate the focal length f on the figure. Method III: If a point source and a lens have been set up to produce a collimated beam (i.e. parallel rays), then the focal length of another lens can be easily measured. The second lens (lens B) is placed in the collimated beam, and the place where the rays are brought to focus is measured. The distance from lens B to the focal point is fB, the focal length of lens B. How is equation (1) used in this situation to determine fB ? pointsource lens Alens Bscreen fA fBPhysics 2020 Lab: Lenses and Telescopes page 4 of 9 University of Colorado at Boulder, Department of Physics PART I: MEASURING FOCAL LENGTH BY METHOD I: IMAGE FORMATION In this lab, you will use an optics bench, which is simply a rail on which lenses are placed, with a ruler on the side for measuring distances. The other equipment includes a small bright light, which acts almost like a point source, and three converging lenses labeled A, B, and C. There is a frosted glass screen, labeled "I", on which you can view images. Finally, there is a metal plate with an aperture (a hole) in the shape of an arrow. The hole is covered with a frosted, translucent material (scotch tape). When this aperture is placed in front of the light source, it forms a convenient object for image-forming experiments. Place the light source at the end of the optics bench and attach it with the thumbscrew in the slot. Place the arrow aperture on the front of the light source; there is a magnet to hold it in place. It will save a little trouble in your calculations if you position the source so that the object (the frosted arrow) is exactly beside an integer mark (e.g. 2.0 cm) on the scale of the bench. Gently tighten the thumbscrew to secure the source, and record the position of the object. Turn on the light source. Place the frosted screen, I, at the far end of the bench. Again, it will save some trouble if you locate it a convenient integer mark, like 90.0 cm or 92.0 cm. Record its position, as indicated by the ring inscribed on the housing. Now put lens B on the bench close to the object (the arrow) and move it slowly away from the source until you see a clear image on the screen. The image is most easily seen looking through the screen towards the light source, but it can also be seen from the other side. Adjust the position of the lens to give the sharpest image and record the position of the lens (as indicated by the ring on the housing). Draw a sketch of the setup, labeling the appropriate parts. Measure do and di . From equation (1), calculate the focal length fB. If the image is not centered
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