Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Question
Chapter 26, Problem 60P
To determine
Prove the lens maker’s formula for a given condition.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
In Bessel's method for measuring the focal length ƒ of a positive lens, a small object and
a white screen are set at a fixed separation L, where L > 4f. The lens is moved along a
line through the object perpendicular to the screen, and it is found that there are two lens
positions where a sharply focused image is produced on the screen, one magnified and
one demagnified. The separation between these two lens positions is then measured as
distance D.
Prove that the lens focal length is given by
L² - D²
f
4L
An object is placed to the left of a concave lens with focal length -10 cm such that the image produced by the lens is exactly half the size of the object.
In a neat and organized fashion, write out a solution which includes the following:
A sketch of the physical situation with all given physical quantities clearly labeled.
Draw a ray diagram showing the object, the lens, and the image.
Determine the location of the object and the image. Clearly show all steps, starting from generalized equations. Explain your mathematical work in words. Your explanation should cover both what you did and the thought process behind why you did that.
Evaluate your answer to determine whether it is reasonable or not. Consider all aspects of your answer (the numerical value, sign, and units) in your evaluation.
Please answer 1 and 2 only and thanks
Chapter 26 Solutions
Principles of Physics: A Calculus-Based Text
Ch. 26.1 - In the overhead view of Figure 26.4, the image of...Ch. 26.1 - Prob. 26.2QQCh. 26.2 - Prob. 26.3QQCh. 26.2 - Prob. 26.4QQCh. 26.4 - What is the focal length of a pane of window...Ch. 26.4 - Prob. 26.6QQCh. 26.5 - Prob. 26.7QQCh. 26 - Prob. 1OQCh. 26 - (i) When an image of an object is formed by a...Ch. 26 - Prob. 3OQ
Ch. 26 - (i) When an image of an object is formed by a...Ch. 26 - Prob. 5OQCh. 26 - If Joshs face is 30.0 cm in front of a concave...Ch. 26 - A converging lens made of crown glass has a focal...Ch. 26 - Two thin lenses of focal lengths f1 = 15.0 and f2...Ch. 26 - Lulu looks at her image in a makeup mirror. It is...Ch. 26 - Prob. 10OQCh. 26 - Prob. 11OQCh. 26 - Prob. 12OQCh. 26 - Prob. 1CQCh. 26 - Prob. 2CQCh. 26 - Prob. 3CQCh. 26 - Prob. 4CQCh. 26 - Prob. 5CQCh. 26 - Prob. 6CQCh. 26 - Suppose you want to use a converging lens to...Ch. 26 - Explain why a fish in a spherical goldfish bowl...Ch. 26 - Prob. 9CQCh. 26 - Prob. 10CQCh. 26 - Prob. 11CQCh. 26 - Prob. 12CQCh. 26 - Prob. 13CQCh. 26 - Prob. 14CQCh. 26 - Prob. 15CQCh. 26 - Prob. 1PCh. 26 - Prob. 2PCh. 26 - Prob. 3PCh. 26 - Prob. 4PCh. 26 - A person walks into a room that has two flat...Ch. 26 - Prob. 6PCh. 26 - Prob. 7PCh. 26 - Prob. 8PCh. 26 - A large hall in a museum has a niche in one wall....Ch. 26 - Prob. 10PCh. 26 - A concave spherical mirror has a radius of...Ch. 26 - Prob. 12PCh. 26 - Prob. 13PCh. 26 - (a) A concave spherical mirror forms an inverted...Ch. 26 - Prob. 15PCh. 26 - A concave mirror has a radius of curvature of 60.0...Ch. 26 - Prob. 17PCh. 26 - Prob. 18PCh. 26 - Prob. 19PCh. 26 - Prob. 20PCh. 26 - A dedicated sports car enthusiast polishes the...Ch. 26 - Prob. 22PCh. 26 - Prob. 23PCh. 26 - Prob. 24PCh. 26 - Prob. 25PCh. 26 - Prob. 26PCh. 26 - Prob. 27PCh. 26 - A goldfish is swimming at 2.00 cm/s toward the...Ch. 26 - Prob. 29PCh. 26 - Prob. 30PCh. 26 - Prob. 31PCh. 26 - A converging lens has a focal length of 20.0 cm....Ch. 26 - The left face of a biconvex lens has a radius of...Ch. 26 - Prob. 34PCh. 26 - Prob. 35PCh. 26 - The use of a lens in a certain situation is...Ch. 26 - Prob. 37PCh. 26 - In Figure P26.38, a thin converging lens of focal...Ch. 26 - Figure P26.39 diagrams a cross-section of a...Ch. 26 - Prob. 40PCh. 26 - Prob. 41PCh. 26 - An object is at a distance d to the left of a flat...Ch. 26 - Prob. 43PCh. 26 - A nearsighted person cannot see objects clearly...Ch. 26 - Prob. 45PCh. 26 - Prob. 46PCh. 26 - The accommodation limits for a nearsighted persons...Ch. 26 - Prob. 48PCh. 26 - Prob. 49PCh. 26 - Prob. 50PCh. 26 - Prob. 51PCh. 26 - Prob. 52PCh. 26 - Prob. 53PCh. 26 - Prob. 54PCh. 26 - Prob. 55PCh. 26 - Prob. 56PCh. 26 - Prob. 57PCh. 26 - Prob. 58PCh. 26 - Prob. 59PCh. 26 - Prob. 60PCh. 26 - Prob. 61PCh. 26 - Prob. 62PCh. 26 - Prob. 63PCh. 26 - Prob. 64PCh. 26 - Prob. 65PCh. 26 - Prob. 66PCh. 26 - The disk of the Sun subtends an angle of 0.533 at...Ch. 26 - Prob. 68PCh. 26 - Prob. 69PCh. 26 - Prob. 70PCh. 26 - Prob. 71PCh. 26 - Figure P26.72 shows a thin converging lens for...Ch. 26 - Prob. 73P
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- A converging lens made of crown glass has a focal length of 15.0 cm when used in air. If the lens is immersed in water, what is its focal length? (a) negative (b) less than 15.0 cm (c) equal to 15.0 cm (d) greater than 15.0 cm (e) none of those answersarrow_forwardWhat is the angular size of the Moon if viewed from a binocular that has a focal length of 1.2 cm for the eyepiece and a focal length of 8 cm for the objective? Use the radius of the moon 1.74106 m and the distance of the moon from the observer to be 3.8108m .arrow_forwardTwo thin lenses of focal lengths f1 = 15.0 and f2 = 10.0 cm, respectively, are separated by 35.0 cm along a common axis. The f1 lens is located to the left of the f2 lens. An object is now placed 50.0 cm to the left of the f1 lens, and a final image due to light passing though both lenses forms. By what factor is the final image different in size from the object? (a) 0.600 (b) 1.20 (c) 2.40 (d) 3.60 (e) none of those answersarrow_forward
- The left face of a biconvex lens has a radius of curvature of magnitude 12.0 cm, and the right face has a radius of curvature of magnitude 18.0 cm. The index of refraction of the glass is 1.44. (a) Calculate the focal length of the lens for light incident from the left. (b) What If? After the lens is turned around to interchange the radii of curvature of the two faces, calculate the focal length of the lens for light incident from the left.arrow_forwardIn Figure P26.38, a thin converging lens of focal length 14.0 cm forms an image of the square abcd, which is hc = hb = 10.0 cm high and lies between distances of pd = 20.0 cm and pa = 30.0 cm from the lens. Let a, b, c, and d represent the respective corners of the image. Let qa represent the image distance for points a and b, qd represent the image distance for points c and d, hb represent the distance from point b to the axis, and hc represent the height of c. (a) Find qa, qd, hb, and hc. (b) Make a sketch of the image. (c) The area of the object is 100 cm2. By carrying out the following steps, you will evaluate the area of the image. Let q represent the image distance of any point between a and d, for which the object distance is p. Let h represent the distance from the axis to the point at the edge of the image between b and c at image distance q. Demonstrate that h=10.0q(114.01q) where h and q are in centimeters. (d) Explain why the geometric area of the image is given by qaqdhdq (e) Carry out the integration to find the area of the image. Figure P26.38arrow_forwardIn Figure P35.30, a thin converging lens of focal length 14.0 cm forms an image of the square abed, which is he = hb = 10.0 cm high and lies between distances of pd = 20.0 cm and pa = 30.0 cm from the lens. Let a, b, c. and d represent the respective corners of the image. Let qa represent the image distance for points a and b, qd represent the image distance for points c and d, hb, represent the distance from point b to the axis, and hc represent the height of c. (a) Find qa, qd, hb, and hc. (b) Make a sketch of the image. (c) The area of the object is 100 cm2. By carrying out the following steps, you will evaluate the area of the image. Let q represent the image distance of any point between a and d, for which the object distance is p. Let h represent the distance from the axis to the point at the edge of the image between b and c at image distance q. Demonstrate that h=10.0q(114.01q) where h and q are in centimeters. (d) Explain why the geometric area of the image is given by qaqdhdq (e) Carry out the integration to find the area of the image. Figure P35.30arrow_forward
- Two converging lenses having focal lengths of f1 = 10.0 cm and f2 = 20.0 cm are placed a distance d = 50.0 cm apart as shown in Figure P35.48. The image due to light passing through both lenses is to be located between the lenses at the position x = 31.0 cm indicated. (a) At what value of p should the object be positioned to the left of the first lens? (b) What is the magnification of the final image? (c) Is the final image upright or inverted? (d) Is the final image real or virtual?arrow_forwardA man inside a spherical diving bell watches a fish through a window in the bell, as in Figure P23.26. If the diving bell has radius R = 1.75 m and the fish is a distance p = 1 00 m from the window, calculate (a) the image distance and (b) the magnification. Neglect the thickness of the window. Figure P23.26arrow_forwardPeople who do very detailed work close up, such as jewelers, often can see objects clearly at much closer distance than the normal 25 cm. (a) What is the power of the eyes of a woman who can see an object clearly at a distance of only 8.00 cm? (b) What is the image size of a 1.00-mm object, such as lettering inside a ring, held at this distance? (c) What would the size of the image be if the object were held at the normal 25.0 cm distance?arrow_forward
- What is the focal length of a pane of window glass? (a) zero (b) infinity (c) the thickness of the glass (d) impossible to determinearrow_forwardThe accommodation limits for a nearsighted persons eyes are 18.0 cm and 80.0 cm. When he wears his glasses, he can see faraway objects clearly. At what minimum distance is he able to see objects clearly?arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
University Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax
Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
Physics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Physics for Scientists and Engineers with Modern ...
Physics
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
Physics for Scientists and Engineers, Technology ...
Physics
ISBN:9781305116399
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Convex and Concave Lenses; Author: Manocha Academy;https://www.youtube.com/watch?v=CJ6aB5ULqa0;License: Standard YouTube License, CC-BY