Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 35, Problem 12P
To determine
The radius of curvature of the cornea.
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You are training to become an optician’s assistant. One day, you are learning how to fit a contact lens to a patient’s eye. You make a measurement with a keratometer, which is used to measure the curvature of the eye’s front surface, the cornea. This instrument places an illuminated object of known size at a known distance p from the cornea. The cornea reflects some light from the object, forming an image of the object. The magnification M of the image is measured by using a small viewing telescope that allows comparison of the image formed by the cornea with a second calibrated image projected into the field of view by a prism arrangement. As part of your training, the optician has required that you do not use the automatic calculator associated with the machine, but must perform the calculations yourself. You must determine the radius of curvature R of the cornea for the measurements you make for the patient: p = 30.0 cm and M = 0.013 0.
A keratometer is a device used to measure the curvature of the cornea of the eye, particularly for fitting contact lenses. Light is reflected from the cornea, which acts like a convex mirror, and the keratometer measures the magnification of the image. The smaller the magnification, the smaller the radius of curvature of the cornea. If the light source is 12 cm from the cornea and the image magnification is 0.032, what is the radius of curvature of the cornea?
A keratometer is a device used to measure the curvature of the cornea, particularly for fitting contact lenses. Light is reflected from the cornea, which acts like a convex mirror, and the keratometer measures the magnification of the image. The smaller the magnification, the smaller the radius of curvature of the cornea. If the light source is 15.0 cm from the cornea and the image’s magnification is 0.0430, what is the cornea’s radius of curvature? Express your answer in 3 decimal places. No unit required.
Chapter 35 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 35.1 - Prob. 35.1QQCh. 35.2 - You wish to start a fire by reflecting sunlight...Ch. 35.2 - Consider the image in the mirror in Figure 35.14....Ch. 35.3 - Prob. 35.4QQCh. 35.3 - Prob. 35.5QQCh. 35.4 - What is the focal length of a pane of window...Ch. 35.6 - Prob. 35.7QQCh. 35 - (a) Does your bathroom mirror show you older or...Ch. 35 - Two flat mirrors have their reflecting surfaces...Ch. 35 - A periscope (Fig. P35.3) is useful for viewing...
Ch. 35 - Prob. 4PCh. 35 - Prob. 5PCh. 35 - Prob. 6PCh. 35 - An object of height 2.00 cm is placed 30.0 cm from...Ch. 35 - Prob. 8PCh. 35 - Prob. 9PCh. 35 - A concave spherical mirror has a radius of...Ch. 35 - Prob. 11PCh. 35 - Prob. 12PCh. 35 - Prob. 13PCh. 35 - Prob. 14PCh. 35 - Prob. 15PCh. 35 - Prob. 16PCh. 35 - One end of a long glass rod (n = 1.50) is formed...Ch. 35 - Prob. 18PCh. 35 - Prob. 19PCh. 35 - Figure P35.20 (page 958) shows a curved surface...Ch. 35 - To dress up your dorm room, you have purchased a...Ch. 35 - You are working for a solar energy company. Your...Ch. 35 - Prob. 23PCh. 35 - An objects distance from a converging lens is 5.00...Ch. 35 - Prob. 25PCh. 35 - Prob. 26PCh. 35 - A converging lens has a focal length of 10.0 cm....Ch. 35 - Prob. 28PCh. 35 - Prob. 29PCh. 35 - In Figure P35.30, a thin converging lens of focal...Ch. 35 - Prob. 31PCh. 35 - Prob. 32PCh. 35 - Two rays traveling parallel to the principal axis...Ch. 35 - Prob. 34PCh. 35 - Prob. 35PCh. 35 - Prob. 36PCh. 35 - Prob. 37PCh. 35 - Prob. 38PCh. 35 - Prob. 39PCh. 35 - The intensity I of the light reaching the CCD in a...Ch. 35 - Prob. 41PCh. 35 - Prob. 42PCh. 35 - A simple model of the human eye ignores its lens...Ch. 35 - Prob. 44APCh. 35 - Prob. 45APCh. 35 - The distance between an object and its upright...Ch. 35 - Prob. 47APCh. 35 - Two converging lenses having focal lengths of f1 =...Ch. 35 - Two lenses made of kinds of glass having different...Ch. 35 - Prob. 50APCh. 35 - Prob. 51APCh. 35 - Prob. 52APCh. 35 - Prob. 53APCh. 35 - In many applications, it is necessary to expand or...Ch. 35 - Prob. 55APCh. 35 - A zoom lens system is a combination of lenses that...Ch. 35 - Prob. 57CPCh. 35 - Prob. 58CP
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- 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_forwardAn observer to the right of the mirror-lens combination shown in Figure P36.89 (not to scale) sees two real images that are the same size and in the same location. One image is upright, and the other is inverted. Both images are 1.50 times larger than the object. The lens has a focal length of 10.0 cm. The lens and mirror are separated by 40.0 cm. Determine the focal length of the mirror.arrow_forwardFigure P36.95 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 filial image and (c) its magnification as seen by the eye in the figure. (d) Is the final image inverted or upright? Explain.arrow_forward
- 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_forwardYou are working in an optical research laboratory. Your supervisor requests that you build her a beam expander with specifications required by her experiment. A beam expander is a series of two lenses on the same principal axis. A beam of laser light covers the total area of the first lens, which focuses the parallel rays at its focal point. A second lens with a longer focal length and a larger radius is placed on the axis so that the rays expanding from the focal point of the first lens cover the area of the second lens. The outgoing rays of the second lens are parallel. The net result is that the diameter of the outgoing laser beam is larger than the original beam. Your supervisor provides you with a lens of focal length f₁ = 1.30 cm. Its diameter matches that of an incoming laser beam of diameter d₁ = 0.150 cm. She wants the beam expanded to a diameter of d₂ = 0.690 cm. She asks you to find the following. (a) the focal length ₂ necessary for the second lens (in cm) cm (b) the…arrow_forwardA keratometer is a device used to measure the curvature of the cornea, particularly for fitting contact lenses. Light is reflected from the cornea, which acts like a convex mirror, and the keratometer measures the magnification of the image. The smaller the magnification, the smaller the radius of curvature of the cornea. If the light source is 12.0 cm from the cornea and the image’s magnification is 0.0320, what is the cornea’s radius of curvature?arrow_forward
- You have a slab of diamond that is attached to a slab of sapphire. A laser beam starts off in the diamond (index of refraction =2.42) and then exits into sapphire (index of refraction =1.77). The beam makes an angle of 30 degrees with the normal in the diamond. What is the maximum angle of incidence that the laser will refract into the sapphire?arrow_forwardA plano-convex lens is made up of glass with an index of refraction equal to 1.5. Its curved surface has a radius of 2 cm. What is the focal length of the lens?arrow_forwardYou need to record an image on a flat array of CCDs (charge coupled devices—basically a detector). You have two convex lenses mounted in a tube to which you will also attach the CCD plane. The first lens has a focal length of 15 mm and is positioned 25 mm from the sample to be imaged. The second lens, with a focal length of 10 mm, is closer to the CCDs and is 50mm from the first lens. How far away from the second lens will you mount the CCD plane? You must solve this problem using a good diagram and geometry. It is not permissible to use the lens/mirror equation, except to check your answer. Please show all work, and do not copy from chegg.arrow_forward
- In this experiment, the distances are p = xL - xO and q = xS - xL. They satisfy the thin-lens equation, when the image is focused on the screen: 1/p+1/q=1/f If you place the screen at a different position, you get a blurry image. The three objects are at the following three positions, and the image is focused on the screen. Calculate the focal length of the lens, f, in mm. xL = 316 mm xO = 165 mm xS = 508 mmarrow_forwardA convex lens made of glass (n = 1.50) has a focal distance of 20 cm. An identical looking piece of plastic with same shape and thickness has a focal distance of 15 cm. Which of the following could be the index of refraction of the plastic? 1.6 1.0 1.4 1.5arrow_forwardA laser beam is reflected by a plane mirror. It is observed that the angle between the incident and reflected beams is 25°. If the mirror is now rotated so that the angle of incidence increases by 6.0°, what is the new angle between the incident and reflected beams? Group of answer choices 29° 13° 21° 37°arrow_forward
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Convex and Concave Lenses; Author: Manocha Academy;https://www.youtube.com/watch?v=CJ6aB5ULqa0;License: Standard YouTube License, CC-BY