Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 26, Problem 58P
To determine
Reason why a given situation is impossible.
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Why is the following situation impossible? Consider the lens–mirror combination as shown. The lens has a focal length of fL = 0.200 m, and the mirror has a focal length of fM = 0.500 m. The lens and mirror are placed a distance d = 1.30 m apart, and an object is placed at p = 0.300 m from the lens. By moving a screen to various positions to the left of the lens, a student finds two different positions of the screen that produce a sharp image of the object. One of these positions corresponds to light leaving the object and traveling to the left through the lens. The other position corresponds to light traveling to the right from the object, reflecting from the mirror and then passing through the lens.
A photographer is taking a portrait of her client using a 180mm lens on her 40mm camera. The orientation is such that the sensor will be 32mm tall and the field of view covers 540 mm of the field of view in the vertical direction. How far from the lens will the client have to be?
Problem 4: A person who is nearsighted has a far point of d = 3.9 m. She wears glasses that are designed to sit d = 2.2 cm from her eyes.
Randomized Variables
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d = 2.2 cm
Part (a) Write an expression for the focal length of the glasses which will allow her to see distant objects clearly.
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Hint
Part (b) Numerically, what is the focal length in m?
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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
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- In 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_forwardA 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_forwardFigure P26.39 diagrams a cross-section of a camera. It has a single lens of focal length 65.0 mm, which is to form an image on the CCD (charge-coupled device) at the back of the camera. Suppose the position of the lens has been adjusted to focus the image of a distant object. How far and in what direction must the lens be moved to form a sharp image of an object that is 2.00 m away? Figure P26.39arrow_forward
- Why is the following situation impossible? Consider the lensmirror combination shown in Figure P35.55. The lens has a focal length of fL = 0.200 m, and the mirror has a focal length of fM = 0.500 m. The lens and mirror are placed a distance d = 1.30 m apart, and an object is placed at p = 0.300 m from the lens. By moving a screen to various positions to the left of the lens, a student finds two different positions of the screen that produce a sharp image of the object. One of these positions corresponds to light leaving the object and traveling to the left through the lens. The other position corresponds to light traveling to the right from the object, reflecting from the mirror and then passing through the lens. Figure P35.55 Problem 55 and 57.arrow_forwardTwo 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_forwardTwo stars that are 109km apart are viewed by a telescope and found to be separated by an angle of 105 radians. If the eyepiece of the telescope has a focal length of 1.5 cm and the objective has a focal length of 3 meters, how far away are the stars from the observer?arrow_forward
- In 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_forwardTwo converging lenses having focal length of f1 = 10.0 cm and f2 = 20.0 cm are placed d = 50.0 cm apart, as shown in Figure P23.44. The final image is to be located between the lenses, at the position x = 31.0 cm indicated. (a) How far to the left of the first lens should the object be positioned? (b) What is the overall magnification of the system? (c) Is the final image uptight or inserted? Figure P23.44arrow_forwardA lamp of height S cm is placed 40 cm in front of a converging lens of focal length 20 cm. There is a plane mirror 15 cm behind the lens. Where would you find the image when you look in the mirror?arrow_forward
- A thin plastic lens with index of refraction n = 1.67 has radii of curvature given by R1 = 12 0 cm and R2 = 40.0 cm. Determine (a) the focal length of the lens, (b) whether the lens Ls converging or diverging and the image distances for object distances of (c) infinity, (d) 8,00 cm, and (e) 50.0 cm.arrow_forwardHow many times will the incident beam in Figure P34.33 (page 922) be reflected by each of the parallel mirrors? Figure P34.33arrow_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_forward
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