Physics Laboratory Manual · Loyd LABORATORY 41 Focal Length of Lenses OBJECTIVES Investigate the properties of converging and diverging lenses. Determine the focal length of converging lenses both by a real image of a distant object and by finite object and image distances. Determine the focal length of a diverging lens by using it in combination with a converging lens to form a real image. EQUIPMENT LIST • Optical bench, holders for lenses, a screen to form images, meter stick, tape • Lamp with object on face (illuminated object), three lenses (f=+20, +10,–30 cm) THEORY When a beam of light rays parallel to the central axis of a lens is incident upon a converging lens, the rays are brought together at a point called the focal point of the lens. The distance from the center of the lens to the focal point is called f the focal length of the lens, and it is a positive quantity for a converging lens. When a parallel beam of light rays is incident upon a diverging lens the rays diverge as they leave the lens; however, if the paths of the outgoing rays are traced backward, the rays appear to have emerged from a point called the focal point of the lens. The distance from the center of the lens to the focal point is called the focal length f of the lens, and it is a negative quantity for a diverging lens. In Figure 41-1 two common types of lenses are pictured. In general, a lens is converging or diverging depending upon the curvature of its surfaces. In Figure 41-1 the radii of curvature of the surfaces of the two lenses are denoted as R1 and R2. The relationship that determines the focal length f in terms of the radii of curvature and the index of refraction n of the glass of the lens is called the lens makers equation. It is 1 (n-1) R1 (Eq. 1) COPYRIGHT © 2008 Thomson Brooks/Cole For the converging lens shown in Figure 41-1(a) the radius Ry is positive and the radius R2 is negative, but for the diverging lens of part (b), the radius Ry is negative and the radius R2 is positive. The signs of these radii are determined according to a sign convention that is described in all elementary textbooks. THOMSON © 2008 Thomson Brooks/Cole, a part of The Thomson Corporation. Thomson, the Star logo, and Brooks/Cole are trademarks used herein under license. ALL RIGHTS RESERVED. No part of this work covered by the copyright hereon may be reproduced or used in any form or by any means—graphic, electronic, or mechanical, including photocopying, recording, taping, web distribution, information storage and retrieval systems, or in any other manner—without the written permission of the publisher. BROOKS/COLE 413 414 Physics Laboratory Manual Loyd R R2 R2 R For the converging lens shown in Figure 41-1(a) the radius Rį is positive and the radius R2 is negative, but for the diverging lens of part (b), the radius Ry is negative and the radius R2 is positive. The signs of these radii are determined according to a sign convention that is described in all elementary textbooks. THOMSON © 2008 Thomson Brooks/Cole, a part of The Thomson Corporation. Thomson, the Star logo, and Brooks/Cole are trademarks used herein under license. ALL RIGHTS RESERVED. No part of this work vw covered by the copyright hereon may be reproduced or used in any form or by any means—graphic, electronic, or mechanical, including photocopying, recording taping. web distribution, information BROOKS/COLE storage and retrieval systems, or in any other manner—without the written permission of the publisher. 413 414 Physics Laboratory Manual Loyd R2 R1 R2 R1 (a) (b) Figure 41-1 Ray diagram for converging and diverging lenses showing the definition of the focal length for both the converging case and the diverging case. As an example, consider a double convex lens like the one shown in part Figure 41-1(a) made from glass of index of refraction 1.60 with radii of curvature Rị and R2 of magnitude 20.0 and 30.0 cm, respectively. According to the sign convention given above, that would mean Rı= +20.0 cm and R2=-30.0 cm. Putting those values into Equation 1 gives a value for the focal length f of +20.0 cm. Essentially, Equation 1 indicates that a lens that is thicker in the middle than at the edges is converging, and a lens that is thinner in the middle than at the edges is diverging. A lens can be classified as converging or diverging merely by taking it between one's fingers to see if it is thicker at the center of the lens than it is at the edge of the lens. Lenses are used to form images of objects. There are two possible kinds of images. The first type, called a real image, is one that can be focused on a screen. For a real image, light actually passes through the points at which the image is formed. The second type of image is called a virtual image; light does not actually pass through the points at which the image is formed, and the image cannot be focused on a screen. Diverging lenses can form only virtual images, but converging lenses can form either real images or virtual images. If an object is farther from a converging lens than its focal length, a real image is formed. If the object is closer to a converging lens than the focal length, the image formed is a virtual one. Whenever a virtual image is formed, ultimately it will serve as the object for some other lens system to form a real image. Often the other lens system is the human eye, and the real image is formed on the retina of the eye. In the process of image formation, the distance from an object to the lens is called the object distancep, and the distance of the image from the lens is called the image distance q. The relationship between the object distance p, the image distance q, and the focal length of the lens f is 1 1 1 +-= P 9 (Eq. 2) Equation 2 is valid both for converging (positive f) and for diverging (negative f) lenses. Normally the object distance is considered positive. In that case a positive value for the image distance means that the image is on the opposite side of the lens from the object, and the image is real. A negative value for the image distance means that the image is on the same side of the lens as the object, and that the image is virtual. If a lens is used to form an image of a very distant object, then the object distance p is very large. For that case, the term 1/p in Equation 2 is negligible compared to the other terms 1/9 and 1/f in that equation. For the case of a very distant object, Equation (2) becomes Laboratory 41 Focal Length of Lenses 415 PRE-LABORATORY ASSIGNMENT 1. Mark the following statements about lenses as true or false. _a. Incident parallel light rays converge if the lens's focal length is negative. _b. If the path of converging light rays is traced backward, the rays appear to come from a point called the focal point _c. A double convex lens has a negative focal length. _d. The focal length of a lens is always positive. 2. A double convex lens is made from glass with an index of refraction of n=1.50. The magnitudes of its radii of curvature R, and R are 10.0 cm and 15.0 cm, respectively. What is the focal length of the lens? Show your work. cm 3. What is a real image? What is a virtual image? 4. For a diverging lens, state what kinds of images can be formed and the conditions under which those images can be formed. 417 418 Physics Laboratory Manual Loyd 5. For a converging lens, state what kinds of images can be formed and the conditions under which those images can be formed. 6. A lens has a focal length of f= +10.0 cm. If an object is placed 30.0 cm from the lens, where is the image formed? Is the image real or virtual? Show your work. 7. An object is 16.0 cm from a lens. A real image is formed 24.0 cm from the lens. What is the focal length of the lens? Show your work. 8. One lens has a focal length of +15.0 cm. A second lens of focal length +20.0 cm is placed in contact with the first lens. What is the equivalent focal length of the combination of lenses? Show your work. 4. For a diverging lens, state what kinds of images can be formed and the conditions under which those images can be formed. © 2008 Thomson Brooks/Cole 417 418 Physics Laboratory Manual Loyd 5. For a converging lens, state what kinds of images can be formed and the conditions under which those images can be formed. 6. A lens has a focal length of f=+10.0 cm. If an object is placed 30.0 cm from the lens, where is the image formed? Is the image real or virtual? Show your work. 7. An object is 16.0 cm from a lens. A real image is formed 24.0 cm from the lens. What is the focal length of the lens? Show your work. 8. One lens has a focal length of +15.0 cm. A second lens of focal length +20.0 cm is placed in contact with the first lens. What is the equivalent focal length of the combination of lenses? Show your work. 9. Two lenses are in contact. One of the lenses has a focal length of +10.0 cm when used alone. When the two are in combination, an object 20.0 cm away from the lenses forms a real image 40.0 cm away from the lenses. What is the focal length of the second lens? Show your work. r Tenets of a Technical Report Technical Reports are of various kinds. However, the following components are always prevalent and must be demonstrated in what constitutes "Technical Report” of any kind especially those that are: laboratory reports, case study reports and academic research studies. 1. Title of Paper or Report 2. Name(s) of Author(s) and their affiliations 3. Abstract or Executive Summary: brief report of the study objectives, approach utilized and the results got. 4. Introduction: should capture and highlight the goals, objectives and specific aims of a given study. 5. Literature Review: summary of what has been done and the results got or achieved by other people in a similar study. 6. Methodology: how the experiment was done or modified to achieve objectives. 7. Results and Discussion: results got, their comparison and evaluation with other similar work. 8. Conclusion: based on the accomplishment of objectives and evaluation results 9. References: literature referred to in the compilation of the report. 10. Acknowledgement(s): teams and individuals who helped in the accomplishment of the task. 8 าL <
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