SIMPLE LENSES. To measure the focal lengths of several lens and lens combinations.

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1 SIMPLE LENSES PURPOSE: To measure the ocal lengths o several lens and lens combinations. EQUIPMENT: Three convex lenses, one concave lens, lamp, image screen, lens holders, meter stick. INTRODUCTION: Combinations o lenses are used extensively or many optical devices ranging rom ordinary spectacles to powerul microscopes and telescopes. In this exercise, you will study some o the undamental principles incorporated in the design o these instruments. Lenses are described by their geometric shape. Those thicker at the center than at the edges are convex. Concave lenses are thicker at the edge than at the center. Various combinations o these types are used. They include plano convex, double convex, plano concave, double concave, and meniscus. Sophisticated lenses oten consist o combinations o these orms to correct or various image deects called aberrations. Figure Most lenses are made o glass, but modern technology has made it possible to produce acceptable ones o plastic at much less cost. All lenses utilize the principle o reraction; changing the direction o light rays as they pass rom air into the lens, and again as they pass rom the lens back into air. An easy point to remember is that as rays pass through a lens they are "bent" toward the thicker part o the lens. Thus, convex lenses are reerred to as converging lenses while concave ones are reerred to as diverging lenses (opticians reer to convex lenses as positive while concave are designated as negative). The "strength" o these lenses is measured in diopters - a term whose deinition you might want to look up. Figure 2 Revised Summer 200

2 I parallel rays o light pass through a convex lens, they are reracted in such a manner that they all intersect at one point, called the principal ocus o the lens. (This statement is true only or those rays that pass through the lens along a path that is rather limited as to direction and point o entrance and exit rom the lens. It is also true only or rays o light o a single wavelength. Aberrations result rom the act that all rays o light do not meet these reuirements. You might be interested in inding out more about chromatic aberration, spherical aberration, astigmatism, and coma. The distance rom the principal ocus to the lens is an important property o the lens, its ocal length (see Fig. 2). This property is determined by the geometry (shape) o the lens and the index o reraction o the material o which is made. In the case o a concave lens, the parallel rays diverge, but i the reracted rays are projected backward, they appear to come rom a point, the virtual ocus, and the distance rom this point to the lens is the ocal length o the lens. (see Fig. 3). Using the idea o parallel rays o light implies that their source was a point at an ininite distance away, each point on the source will be transmitting light in all directions, and the eect o the lens on those that pass through it will be to orm an image o the source at a distance which is related to the distance rom the lens by the simple lens euation: p Figure 3 () where is the ocal length o the lens, p is the distance rom the lens to the source (object distance) and is the distance rom the lens to the image (image distance). Using a little algebra, Euation () becomes: Note that i p is large, 0 p the ocal length. and p p or simply = ; that is, the image distance euals (2) PROCEDURE: We shall deine your lenses as ollows: Lens A: Lens B: Lens C: Lens D: one that is double convex, at with a small diameter one that is also double convex, but thinner than A, with a small diameter double convex, almost lat, large diameter double concave, small diameter For an object, we will use the wire mesh. The image is the shadow o the wire mesh. Revised Summer 200

3 A. To ind the ocal lengths o Lens A and Lens B. Set up your simple optical bench as in Figure 4. Using lens A irst move the lens and/or screen on the meter stick until the sharpest image possible is ormed on the screen. Record the position on the Data Sheet. Repeat this procedure two more times or dierent object distances. Now insert lens B and record the positions o the lens and screen or 3 trials. Figure 4 Now calculate p,, and. Put answers on the data sheet. B. On the meter stick, place a lens and the screen, Use an object ar away, like a door, window, or music building, and adjust the screen until a sharp image is ormed. Record the distance,, between the lens and the screen. Repeat twice more. Do this part using lens A, B, and C. Since the object is so ar away rom the lens, p is very large. Thereore, /p is very small and nearly zero. So in Euation, we can ignore /p and it becomes / = /. Thereore, in Part B, you ound which is actually because the object was so ar away. This is a simple way o inding the ocal length o a lens although not a very accurate way. C. Using masking tape, asten lens A and B together so that they are in contact. The tape may cover most o the lens but try to leave the center clear. Use the arrangement o Figure 4, ind p, and the ocal length o the combination. D. Repeat part C using lens A and C. (optional) E. Put lens A and D in contact. Find the ocal length o the combination. Then calculate the ocal length o lens D using the ollowing ormula. D A AD A AD You will get a negative number. F. Repeat part E using Lens B and D. (optional) D B BD B BD Revised Summer 200

4 Part A Data Sheet Lens A: Object Lens Screen P Trial Trial 2 Trial 3 Average = Lens B: Object Lens Screen P Trial Trial 2 Trial 3 Part B o Lens A o Lens B Average = o Lens C Trial Trial 2 Trial 3 Average = Revised Summer 200

5 Data Sheet Part C From Part A New Data A = B = p = AB = = Part D From Part B New Data A = C = p = AC = = Part E From Part A New Data A = p = AD = D = = Part F From Part A New Data B = p = BD = D = = Average D = From Part E and F Revised Summer 200

6 QUESTIONS:. What is the relationship between the curvature o lens A, B, and C and their ocal lengths? (Hint: look at Fig. and draw Lenses A, B, and C. Mark the ocal length under the drawing.) 2. Describe the images you saw in part B. 3. When a simple convex lens is used as a "burning glass" by ocusing bright sunlight on dry leaves to set them aire, what is the bright spot o light called? O what is the bright spot an image? 4. In part C, how does the ocal length o the two lenses together compare with either lens alone? 5. In part D, how does the ocal length o the combination compare to the ocal length o either lens alone? 6. Why didn't you ind the ocal length o lens D in the same way as you did or A, B, and C? Revised Summer 200