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 13CQ
To determine
How the cornea should be reshaped to correct nearsightedness.
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During LASIK eye surgery (laser - assisted in situ keratomileusis), the shape of the cornea is modified by vaporizing some of its material. If the surgery is performed to correct for nearsightedness, how does the cornea need to be reshaped?
Problem 103.
A) How do the lenses in glasses designed to correct nearsighted eyes with no astigmatism differ from the lenses designed
to correct nearsighted eyes with astigmatism?
B) Why can reshaping the cornea with a laser correct the far vision of a nearsighted person?
The smallest object we can resolve with our eye is limited by the size of the light receptor cells in the retina. In order for us to distinguish any detail in an object, its image cannot be any smaller than a single retinal cell. Although the size depends on the type of cell (rod or cone), a diameter of a few microns (μm) is typical near the center of the eye. We shall model the eye as a sphere 2.50 cm in diameter with a single thin lens at the front and the retina at the rear, with light receptor cells 5.0 μm in diameter. (a) What is the smallest object you can resolve at a near point of 25 cm? (b) What angle is subtended by this object at the eye? Express your answer in units of minutes (1°=60 min), and compare it with the typical experimental value of about 1.0 min. (Note: There are other limitations, such as the bending of light as it passes through the pupil, but we shall ignore them here.)
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_forwardIf the lens of a person’s eye is removed because of cataracts (as has been done since ancient times), why would you expect an eyeglass lens of about 16 D to be prescribed?arrow_forwardFigure P26.72 shows a thin converging lens for which the radii of curvature of its surfaces have magnitudes of 9.00 cm and 11.0 cm. The lens is in front of a concave spherical mirror with the radius of curvature R = 8.00 cm. Assume the focal points F1 and F2 of the lens are 5.00 cm from the center of the lens. (a) Determine the index of refraction of the lens material. The lens and mirror are 20.0 cm apart, and an object is placed 8.00 cm to the left of the lens. Determine (b) the position of the final image and (c) its magnification as seen by the eye in the figure. (d) Is the final image inverted or upright? Explain.arrow_forward
- Figure P38.43 shows a concave meniscus lens. If |r1| = 8.50 cm and |r2| = 6.50 cm, find the focal length and determine whether the lens is converging or diverging. The lens is made of glass with index of refraction n = 1.55. CHECK and THINK: How do your answers change if the object is placed on the right side of the lens? FIGURE P38.43arrow_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_forwardA nearsighted man cannot see objects clearly beyond 20 cm from his eyes. How close must he stand to a mirror in order to see what he is doing when he shaves?arrow_forward
- An object viewed with the naked eye subtends a 2° angle. If you view the object through a 10 x magnifying glass, what angle is subtended by the image formed on your retina?arrow_forwardWhat is the magnification of a magnifying lens with a focal length of 10 cm if it is held 3.0 cm from the eye and the object is 12 cm from the eye?arrow_forwardThe disk of the Sun subtends an angle of 0.533 at the Earth. What are (a) the position and (b) the diameter of the solar image formed by a concave spherical mirror with a radius of curvature of magnitude 3.00 m?arrow_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_forwardUnder what circumstances will an image be located at the focal point of a spherical lens or mirror?arrow_forwardWhy is your vision so blurry when you open your eyes while swimming under water? How does a face mask enable clear vision?arrow_forward
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