Explanation Given info: The distance between an object and its upright image is d , the magnification is M . Write the equation for magnification. M = − q p q = − M p (1) Here, M is the magnification. q is the distance between an image and the lens. p is the distance between an object and the lens. Here, the image is given upright. So, for a single lens the object and its image must on the same side of the lens. It means the distance between an object and the lens is negative q < 0 and the magnification M is positive. The distance between an object and its upright image, when the image is in between the object and the lens is, d = p − | q | d = p − ( − q ) ( q < 0 ) d = p + q q = d − p Substitute ( d − p ) for q in the equation (1). ( d − p ) = − M p d p − 1 = − M d p = 1 − M p = d 1 − M Write the thin lens equation. 1 p + 1 q = 1 f (2) Here, f is the focal length of the lens. Substitute − M p for q in equation (2) to get the focal length of the lens. 1 p + 1 ( − M p ) = 1 f M M p − 1 M p = 1 f ( M − 1 ) M p = 1 f f = M p M − 1 (3) Substitute ( d 1 − M ) for p in equation (3) to get the focal length of the lens. f = M ( d 1 − M ) M − 1 = M M − 1 ( d 1 − M ) = − M d ( 1 − M ) 2 Thus, the focal length of the lens when the image is in between the object and the lens is − M d ( 1 − M ) 2

Physics for Scientists and Engineers (AP Edition)

9th Edition

ISBN: 9781133953951

Author: Raymond A. Serway, John W. Jewett

Publisher: Cengage Learning

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Chapter 36, Problem 36.74AP

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The focal length of the lens.

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Chapter 36, Problem 36.73AP

Chapter 36, Problem 36.75AP

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Chapter 36 Solutions

Physics for Scientists and Engineers (AP Edition)

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The focal length of the lens.

Solution Summary: The author explains how to determine the focal length of the lens. The distance between an object and its upright image is d.

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The focal length of the lens.

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Chapter 36 Solutions