lab 29 report

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Brooklyn College, CUNY *

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PHYS2100

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Physics

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Feb 20, 2024

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F = 1/ ((1/p) + (1/q)) Group 6: Lab 29: Mirror and Lenses Physics 120 Lab 11/13/23 Introduction In this lab, we explore the concept of mirrors and lenses to understand the principles behind the formation of images and measure their focal lengths. The lab consists of using an optical bench with carriages and holders, along with a variety of optical components, including an illuminated object, screens, mirrors, and lenses. The purpose of this lab was to understand the behavior of concave spherical mirrors, converging lenses, and diverging lenses to fully grasp the concept of the mirror and lens equations. Concave mirrors exhibit an inward curvature, focusing parallel light rays to a point and generating inverted images. The application of the mirror equation, 1/p + 1/q = 1/f, aids in predicting the placement of these images. Converging lenses, characterized by a thicker middle, converge distant light to form inverted images, paralleling the lens equation and sign conventions observed in concave mirrors. Finally, diverging lenses, thicker at the edges, cause light rays to diverge, resulting in upright images on the same side as the object. The sign conventions dictate that f is positive for concave mirrors or lenses, but negative for convex mirrors or lenses; p is positive for a real object and negative for a virtual object; and q is positive for a real image but negative for a virtual image. An illustration of this concept in our daily lives can be observed in telescopes and microscopes, instruments designed to enhance our view by magnifying objects that are either distant or small, making them more perceptible to the human eye. Theory Mirror equation; tells where the image will be formed: 1/p + 1/q = 1/f f - the focal length (distance from the focus to the mirror) p - the object distance (distance from the luminous object to the mirror) q - the image distance (distance from image to mirror) Magnification; how the relative size of the image depends on its relative position: {image size}/{object size} = {image distance}/{object distance} = q/p Lens equation; gives the position of the image: 1/p + 1/q = 1/f Sign Conventions: f - positive for concave mirror or lens, negative for convex mirror or lens p - positive for real object, negative for virtual object

F = 1/ ((1/p) + (1/q)) q - positive for real image, negative for virtual image Data/Calculations/Questions A. Compute the focal length of the concave mirror from the data in (1) and (2). B. Compute the focal length of the converging lens from the data in (3), (4), (5), (6) and (7). C. Compute the focal length of the diverging lens from the data in (8). D. For all the cases where image and object dimensions were measured, check the validity of Equation (2). Concave mirror: Arrow length object: 4.4 cm P Q Arrow-length image experimental Arrow-lengt h image calculated M F Step 1 40 cm 39.8 cm 4.4 cm 4.4 cm 1 19.95 cm Step 1 is inverted. Arrow length calculated M = q/p M = Arrow length/arrow length experimental 1 = arrow length/ 4.4 cm Arrow length calculated = 4.4 cm / 1 = 4.4 cm F = 1/ ((1/p) + (1/q)) F = 1/ ((1/40 cm) + (1/39.8 cm)) = 19.95 cm P Q Arrow-length image experimental Arrow-length image calculated M F Step 2 39.6 cm 20.3 cm 2.3 cm 2.2 cm 0.51 13.42 cm Step 2 is inverted.

F = 1/ ((1/p) + (1/q)) Converging lens P Q Arrow-length image experimental Arrow-length image calculated M F Step 3 (lens 1) 29.3 cm 27.8 cm 4.3 cm 4.18 cm 0.95 14.27 cm Step 3 (lens 2) 43.2 cm 45.1 cm 4.8 cm 4.58 1.04 22.06 cm Step 3 (lens 3) 56 cm 52.6 cm 4.5 cm 4.14 0.94 27.12 cm Lens 1 is the thinnest, lens 2 is the middle, and lens 3 is the thickest. All are inverted. P Q Arrow-length image experimental Arrow-length image calculated M F Step 4 (lens 1) 35.8 cm 50.2 cm 6 cm 6.16 cm 1.4 20.90 cm Step 4 (lens 2) 66.5 cm 48.3 cm 3.3 cm 3.21 cm 0.73 27.98 cm Step 4 (lens 3) 44 cm 23.3 cm 1.6 cm 2.33 cm 0.53 15.23 cm All are inverted. Step 5: The image becomes smaller as the lens is put farther away. When the lens is put closer to the object, the image is larger. The image is also inverted. Step 6: P Q Arrow-length image experimental Arrow-length image calculated M F Step 6 (lens 1) 20.6 cm 20 cm 4.4 cm 3.8 cm 0.97 10.15 cm The image is inverted. Diverging lens

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F = 1/ ((1/p) + (1/q)) P Q Arrow-length image experimental Arrow-length image calculated M F Step 7 (lens 1) 102.3 cm 124 cm 4.3 cm 5.37 cm 1.22 56.05 cm Step 7 (lens 2) 70 cm 38 cm 2.1 cm 2.38 0.54 24.63 cm Step 7 (lens 3) 76.3 cm 13.2 cm 1.3 cm 0.75 cm 0.17 11.25 cm The converging lens is at 50 cm from the luminous object. The diverging lens at 20 cm from the converging lens. Conclusion In this laboratory experiment, we determined the focal length of mirrors and lenses by applying the lens and mirror equations. Initially, we focused on calculating the focal length of a concave mirror. In the first step, we observed that the inverted image matched the object's height, a consequence of the mirror projecting an equally inverted image. The focal length, 19.95 cm, equaled half the distance from the object to the mirror. The measured experimental object height was 4.4 cm, while the calculated height was determined through the use of the M value. However human error possibly attributed to inaccurate ruler measurements in the dark room, thus leading to differences in the measured experimental image value and the calculated image value. In the second step, with the mirror placed farther away, it hit the screen at 20.3cm. The focal point was 13.42 cm away, and the magnification decreased from 1 to 0.51, evident in the smaller object height. The calculated height was 2.2 cm, compared to the experimental height of 2.3 cm, potentially due to measurement or calculation errors. For the second part of the experiment, we determined the focal length of three converging lenses. In the third step, the focal points for lenses 1, 2, and 3 were 14.27cm, 22.06cm, and 27.12cm, respectively. Lenses 1 and 3 exhibited a decrease in magnification and image height, while lens 2 showed an increase. Calculated and experimental heights for lens 1 were 4.18 cm and 4.3 cm, and for lens 3, 4.14 cm and 4.5 cm, respectively. The calculated values reflected the magnification decrease, but experimental values did not, potentially due to measurement errors. Lens 2 showed a calculated and experimental height of 4.58 cm and 4.8 cm, indicating a magnification increase. In the fourth step, focal lengths for lenses 1, 2, and 3 were 20.90 cm, 27.98 cm, and 15.23 cm, respectively, with magnification decreasing due to the change in object lens distance.

F = 1/ ((1/p) + (1/q)) Finally, in the seventh step, the focal length was 10.31 cm, with a magnification of 0.75, reflected in the experimental and calculated heights of 1.3 cm and 2.1 cm, respectively. In this experiment, we used the lens and mirror equations to determine the focal length and explore the image formation by mirrors and lenses. Our objective was to comprehend the inversion of images by lenses and mirrors. Discrepancies between the calculated and experimental object heights for the concave mirror may be attributed to inaccuracies in ruler measurements steaming from incorrect starting points, misperception due to angles, or due to the dark environment. By analyzing the distances between the object and the lens/mirror and between the mirror/lens and the resulting image, we gained insights into the calculation of focal length.

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