EXPERIMENT NO. 6 Converging Lens: Image and Object Relationships OBJECTIVE To identify the focal length of a converging

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EXPERIMENT NO. 6 Converging Lens: Image and Object Relationships OBJECTIVE To identify the focal length of a converging lens (i.e., magnifying glass). • To establish the relationship between object and image formation through a converging lens. BACKGROUND Given a lens of any shape and index of refraction, you could determine the shape and location of the images it forms based only on the Law of Refraction. You need only to apply the law along with some of the ray tracing techniques. However, for spherical lenses (and for spherical mirrors as well), there is a more general equation that can be used to determine the location and magnification of an image. This equation is called the Fundamental Lens equation: 1 1 1 +-= do di f where f is the focal length of the lens, and d, and d, are the distance from the mirror to the image and object, respectively (see Fig. 1). The magnification of the image is given by the equation: di do In this experiment, you will have an opportunity to test and apply these equations. NOTE: Instead of the above equation, you may have learned the Fundamental Lens Equation as So Si = f², where So and Si are the distances between the principle focus of the lens and the object and image, respectively. If so, notice that So= d.- f, and Si= di- f (see Fig. 1). Using these equalities, convince yourself that 1/do + 1/d = 1/f and So Si = f² are different expressions of the same relationship. m
object (arrow) S₂ d₂ "the objects here are unscaled PROCEDURE Preliminary: Fig. 1. Equipment setup. MATERIALS / TOOLS Mobile phone (to project the object) Magnifying glass → Measuring tape Room that can be darkened well enough d S₁ viewing screen (bond paper) * Adhesive tape (to secure your bond paper) → Clamp for the magnifying glass (to make the magnifying glass vertical) Phone holder (optional; for a stable measurement) > Box (to hold the bond paper(s) in vertical position) • Download the image file from the link below and save to your mobile phone. =sharing. • Be sure to charge your phone before this experiment or at least have your mobile phone charger available since you are going to display the object at the maximum brightness setting of your phone. 1. Using your mobile phone, open the "arrow" image you have downloaded and put the brightness setting of your mobile phone to its maximum level. 2. Measure the height of the arrow on your mobile phone's screen and record this as h.. Be careful not to zoom in/out the image while you are measuring. 3. Setup the equipment as shown in Fig. 1.
• You may use a box or any object that will hold your bond paper(s) in vertical position. This serves as your viewing screen. • Place the measuring tape in such a way that will make it easier for you to read the distance between viewing screen, magnifying glass and mobile phone. It would be more convenient to position the zero mark of your measuring tape at your mobile phone. 4. Notice that from the Fundamental Lens equation that as d, goes to infinity, d, goes to the focal length of the lens. Use the lens to focus an image of a very distant object on the screen (d, should be greater than two meters - preferably much longer). Measure the image distance, d,; it will be approximately equal to the focal length of the lens. Record this as the focal length of the lens in Table 1. 5. Now set the d, to the values (in millimeters) listed in Table 1. At each set of do, locate the image by sliding the viewing screen at the other side of the lens until the displayed image is "projected" clearly onto the paper, and measure the distance as d.. • Make sure that the bond paper is perpendicular to the optical path of the light. 6. Also measure the height of the image, h, on your viewing screen. 7. Repeat #s 5-6 for all the values of d, in Table 1 and record your measurement. REFERENCE E. Pitkin, Experiment 7: Converging Lens: Image and Object Relationships. In D. Griffith (Ed.). The PASCO scientific Model OS-8500 Introductory Optics System Manual. PASCO Scientific.
Names: Date Performed: Course Code & Section: DATA SHEET do (mm) 500 450 400 350 300 250 200 di (mm) mm h (mm) f= = Table 1. Data. h₂ = Focal Length f do di do + di mm Calculations % diff M = ho Magnification M = d₁ do % diff QUESTIONS 1. From your result, is the image magnified or reduced? Is the image upright or inverted? 2. Based on your table of data, can you say that your results are in complete agreement with the Fundamental Lens Equation? If not, to what do you attribute the discrepancies?
3. For what values of d, where you unable to focus and image onto the screen? Use the Fundamental Lens Equation to explain why. 4. For a lens of focal length f, what value of d, would give an image with a magnification of one? 5. Is it possible to obtain a non-inverted image with a converging spherical lens? Explain. 6. For a converging lens of focal length f, where would you place the object to obtain an image as far away from the lens as possible? How large would the image be?