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physics
modern physics

Physics 5th edition James S. Walker - Solutions

To focus its eyes, an octopus does not change the shape of its lens, as is the case in humans. Instead, an octopus moves its rigid lens back and forth, as in a camera. This changes the distance from the lens to the retina and brings an object into focus. (a) If an object moves closer to an
The actual light sensor size of a digital camera is 14.9 mm × 22.3 mm. You want to take a photo of your friend, who is 1.9 m tall. Your camera has a 55-mm-focal-length lens. How far from the camera should your friend stand in order to produce a 22-mm-tall image on the light sensor?
A patient receives a rigid IOL whose focus cannot be changed-it is designed to provide clear vision of objects at infinity. The patient will use corrective contacts to allow for close vision. Should the refractive power of the corrective contacts be positive or negative?
Referring to the previous problem, find the refractive power of contacts that will allow the patient to focus on a book at a distance of 23.0 cm. A. 0.0435 diopter B. 0.230 diopter C. 4.35 diopters D. 8.70 diopters
After a fixed IOL is installed, it is found to have the wrong focal length, so a piggyback IOL is installed as well. The piggyback IOL has a power of -1.50 diopters. What is its focal length and type? A. converging, 1.50 m B. converging, 66.7 cm C. diverging, 1.50 m D. diverging, 66.7 cm
Suppose a flexible, adaptive IOL has a focal length of 3.00 cm. How far forward must the IOL move to change the focus of the eye from an object at infinity to an object at a distance of 50.0 cm? A. 1.9 mm B. 2.8 mm C. 3.1 mm D. 3.2 mm
Suppose a person's eyeglasses have a focal length of -301 cm, are 2.00 cm in front of the eyes, and allow the person to focus on distant objects. (a) Is this person's far point greater than or less than 323 cm, which is the far point for glasses the same distance from the eyes and with a focal
In Example 27-4, a person has a far-point distance of 323 cm. If this person wears glasses 2.00 cm in front of the eyes with a focal length of -321 cm, distant objects can be brought into focus. Suppose a second person's far point is 353 cm. (a) Is the magnitude of the focal length of the
Suppose a person's eyeglasses have a refractive power of 2.75 diopters and that they allow the person to focus on an object that is just 25.0 cm from the eye. The glasses are 2.00 cm in front of the eyes. (a) Is this person's near point greater than or less than 57.0 cm, which is the near-point
Suppose a person's near-point distance is 67.0 cm. (a) Is the refractive power of the eyeglasses that allow this person to focus on an object just 25.0 cm from the eye greater than or less than 2.53 diopters, which is the refractive power when the near-point distance is 57.0 cm? The glasses are
(a) Find the ƒ-number of a telescope with an objective diameter of 8.3 cm and a focal length of 91 cm. (b) Find the aperture diameter of an ƒ/1.2 all-sky meteor camera lens with a focal length of 2.5 mm.
You are taking a photo of a poster on the wall of your dorm room, so you can't back away any farther than 3.0 m to take the shot. The poster is 0.80 m wide and 1.2 m tall, and you want the image to fit on the 15-mm × 22-mm image sensor in your camera. What is the longest focal length lens that
You are taking pictures of the beach at sunset. Just before the Sun sets, a shutter speed of 1/100 and an aperture of ƒ/11 produces a properly exposed picture. Shortly after the Sun sets, however, your light meter indicates that the scene is only one-quarter as bright as before. (a) If you don't
You are taking a photograph of a horse race. A shutter speed of 125 at ƒ/5.6 produces a properly exposed image, but the running horses give a blurred image. Your camera has ƒ-stops of 2, 2.8, 4, 5.6, 8, 11, and 16. (a) To use the shortest possible exposure time (i.e., highest shutter speed),
The 200-in. (5.08-m) diameter mirror of the Hale telescope on Mount Palomar has a focal length ƒ = 16.9 m. (a) When the detector is placed at the focal point of the mirror (the "prime focus"), what is the ƒ-number for this telescope? (b) The coudé focus arrangement uses additional mirrors
Two professors are stranded on a deserted island. Both wear glasses, though one is nearsighted and the other is farsighted. (a) Which person's glasses should be used to focus the rays of the Sun and start a fire? (b) Choose the best explanation from among the following: I. A nearsighted person
A clerk at the local grocery store wears glasses that make her eyes look larger than they actually are. Is the clerk nearsighted or farsighted? Explain.
The umpire at a baseball game wears glasses that make his eyes look smaller than they actually are. Is the umpire nearsighted or farsighted? Explain.
A police detective discovers eyeglasses with a focal length of -80.0 cm at a crime scene. (a) If the eyeglasses belong to the suspect, is the suspect nearsighted or farsighted? Explain. (b) A search of a person's home reveals an eyeglass prescription of −0.80 diopter. Is the person the suspect?
Your friend is 1.7 m tall. (a) When she stands 3.2 m from you, what is the height of her image formed on the retina of your eye? (Consider the eye to consist of a thin lens 2.5 cm from the retina.) (b) What is the height of her image when she is 4.2 m from you?
The cornea of a normal human eye has an optical power of +44.0 diopters. What is its focal length?
A myopic student is shaving without his glasses. If his eyes have a far point of 1.9 m, what is the greatest distance he can stand from the mirror and still see his image clearly?
An eyeglass prescription calls for a lens with an optical power of + 2.9 diopters. What is the focal length of this lens?
An optometrist prescribes contact lenses with a power of - 0.75 diopter for you. What is your far-point distance?
Two thin lenses, with ƒ1 = + 25.0 cm and ƒ2 = - 42.5 cm, are placed in contact. What is the focal length of this combination?
Two concave lenses, each with ƒ = - 15 cm, are separated by 7.5 cm. An object is placed 25 cm in front of one of the lenses. Find (a) The location (b) The magnification of the final image produced by this lens combination.
The focal length of a relaxed human eye is approximately 1.7 cm. When we focus our eyes on a closeup object, we can change the refractive power of the eye by about 16 diopters. (a) Does the refractive power of our eyes increase or decrease by 16 diopters when we focus closely? Explain. (b)
Double- crested cormorants (Phalacrocorax auritus) are extraordinary birds-they can focus on objects in the air, just like we can, but they can also focus underwater as they pursue their prey. To do so, they have one of the largest accommodation ranges in nature-that is, they can change the focal
A converging lens of focal length 9.000 cm is 18.0 cm to the left of a diverging lens of focal length -6.00 cm. A coin is placed 12.0 cm to the left of the converging lens. Find (a) The location (b) The magnification of the coin's final image.
Repeat Problem 28, this time with the coin placed 18.0 cm to the right of the diverging lens. In problem 28 A converging lens of focal length 9.000 cm is 18.0 cm to the left of a diverging lens of focal length -6.00 cm. A coin is placed 12.0 cm to the left of the converging lens. Find (a) The
Which forms the larger image on the retina of your eye: a 43-ft tree seen from a distance of 210 ft, or a 12-in. flower viewed from a distance of 2.0 ft?
Find the focal length of contact lenses that would allow a farsighted person with a near-point distance of 166 cm to read a book at a distance of 10.1 cm.
Find the focal length of contact lenses that would allow a nearsighted person with a 125-cm far point to focus on the stars at night.
What focal length should a pair of contact lenses have if they are to correct the vision of a person with a near point of 66 cm?
Reading glasses with a power of + 1.50 diopters make reading a book comfortable for you when you wear them 2.2 cm from your eye. If you hold the book 28.0 cm from your eye, what is your near-point distance?
A nearsighted person wears contacts with a focal length of -8.5 cm. If this person's far-point distance with her contacts is 8.5 m, what is her uncorrected far-point distance?
Without his glasses, Isaac can see objects clearly only if they are less than 3.8 m from his eyes. What focal length glasses worn 2.0 cm from his eyes will allow Isaac to see distant objects clearly?
A person whose near-point distance is 42.5 cm wears a pair of glasses that are 2.1 cm from her eyes. With the aid of these glasses, she can now focus on objects 25 cm away from her eyes. Find the focal length and refractive power of her glasses.
A pair of eyeglasses is designed to allow a person with a far-point distance of 2.50 m to read a road sign at a distance of 25.0 m. Find the focal length required of these glasses if they are to be worn(a) 2.00 cm(b) 1.00 cm from the eyes.
Your favorite aunt can read a newspaper only if it is within 15.0 cm of her eyes. (a) Is your aunt nearsighted or farsighted? Explain. (b) Should your aunt wear glasses that are converging or diverging to improve her vision? Explain. (c) How many diopters of refractive power must her glasses
The relaxed eyes of a patient have a refractive power of 48.5 diopters. (a) Is this patient nearsighted or farsighted? Explain. (b) If this patient is nearsighted, find the far point. If this person is farsighted, find the near point. (For the purposes of this problem, treat the eye as a
Approximating the eye as a single thin lens 2.70 cm from the retina, find the eye's near-point distance if the smallest focal length the eye can produce is 2.10 cm.
Without glasses, your Uncle Albert can see things clearly only if they are between 35 cm and 160 cm from his eyes. (a) What power eyeglass lens will correct your uncle's myopia? Assume the lenses will sit 2.0 cm from his eyes. (b) What is your uncle's near point when wearing these glasses?
A 2.05-cm-tall object is placed 30.0 cm to the left of a converging lens with a focal length ƒ1 = 20.5 cm. A diverging lens, with a focal length ƒ2 = -42.5 cm, is placed 30.0 cm to the right of the first lens. How tall is the final image of the object?
A simple camera telephoto lens consists of two lenses. The objective lens has a focal length ƒ1 = + 39.0 cm. Precisely 36.0 cm behind this lens is a concave lens with a focal length ƒ2 = -10.0 cm. The object to be photographed is 4.00 m in front of the objective lens. (a) How far behind the
With unaided vision, a librarian can focus only on objects that lie at distances between 5.0 m and 0.50 m. (a) Which type of lens (converging or diverging) is needed to correct his nearsightedness? Explain. (b) Which type of lens will correct his farsightedness? Explain. (c) Find the refractive
A person's prescription for her new bifocal glasses calls for a refractive power of - 0.445 diopter in the distance-vision part and a power of + 1.85 diopters in the close-vision part. What are the near and far points of this person's uncorrected vision? Assume the glasses are 2.00 cm from the
A person's prescription for his new bifocal eyeglasses calls for a refractive power of - 0.0625 diopter in the distance-vision part and a power of + 1.05 diopters in the close-vision part. Assuming the glasses rest 2.00 cm from his eyes and that the corrected near-point distance is 25.0 cm,
Two lenses, with Æ’1 = +20.0 cm and Æ’2 = + 30.0 cm, are placed on the x axis, as shown in FIGURE 27-28. An object is fixed 50.0 cm to the left of lens 1, and lens 2 is a variable distance x to the right of lens 1. Find the lateral magnification and location of the final image relative to
A converging lens with a focal length of 4.0 cm is to the left of a second identical lens. When a feather is placed 12 cm to the left of the first lens, the final image is the same size and orientation as the feather itself. What is the separation between the lenses?
Two magnifying glasses are for sale at a store. Magnifying glass 1 has a 4-in. diameter with a long focal length, and glass 2 has a 1-in. diameter with a short focal length.(a) Which magnifying glass should you purchase if you wish to examine tiny insects? Explain.(b) Which glass should you
The Moon is 3476 km in diameter and orbits the Earth at an average distance of 384,400 km.(a) What is the angular size of the Moon as seen from Earth?(b) A penny is 19 mm in diameter. How far from your eye should the penny be held to produce the same angular diameter as the Moon?
Approximating the eye as a single thin lens 2.70 cm from the retina, find the focal length of the eye when it is focused on an object at a distance of (a) 255 cm (b) 25.5 cm?
A magnifying glass is a single convex lens with a focal length of ƒ = +14.0 cm. (a) What is the angular magnification when this lens forms a (virtual) image at -∞? How far from the object should the lens be held? (b) What is the angular magnification when this lens forms a (virtual) image at
Calculate the focal length of a magnifying lens designed to produce an angular magnification of 8.50 while producing the image at the standard near-point distance of 25.0 cm.
A student has two lenses, one of focal length ƒ1 = 5.0 cm and the other with focal length ƒ2 = 13 cm.(a) When used as a simple magnifier, which of these lenses can produce the greater magnification? Explain.(b) Find the maximum magnification produced by each of these lenses.
A beetle 4.93 mm long is examined with a simple magnifier of focal length ƒ = 10.1 cm. If the observer's eye is relaxed while using the magnifier, and has a near-point distance of 26.0 cm, what is the apparent length of the beetle?
To engrave wishes of good luck on a watch, an engraver uses a magnifier whose focal length is 8.75 cm. If the image formed by the magnifier is at the engraver's near point of 24.6 cm, find (a) The distance between the watch and the magnifier (b) The angular magnification of the engraving. Assume
A jeweler examines a diamond with a magnifying glass. If the near-point distance of the jeweler is 22.8 cm, and the focal length of the magnifying glass is 7.70 cm, find the angular magnification when the diamond is held at the focal point of the magnifier. Assume the magnifying glass is directly
In Problem 55, find the angular magnification when the diamond is held 5.59 cm from the magnifying glass. In Problem 55, A jeweler examines a diamond with a magnifying glass. If the near-point distance of the jeweler is 22.8 cm, and the focal length of the magnifying glass is 7.70 cm, find the
A person with a near-point distance of 25 cm finds that a magnifying glass gives an angular magnification that is 1.5 times larger when the image of the magnifier is at the near point than when the image is at infinity. What is the focal length of the magnifying glass?
You have two lenses: lens 1 with a focal length of 0.45 cm and lens 2 with a focal length of 1.9 cm. If you construct a microscope with these lenses, which one should you use as the objective? Explain.
Microscope objective A is labeled 15 × and objective B is labeled 25 ×. (a) Which objective has the longer focal length? Explain. If the image formed by the objective is designed to be 16.3 cm from the lens, calculate the focal length of the (b) 15 × (c) 25 × objectives.
Find the far-point distance of a person whose relaxed eye has a focal length of 2.68 cm, treating the eye as if it were a single thin lens 2.71 cm from the retina.
A compound microscope has an objective lens with a focal length of 2.2 cm and an eyepiece with a focal length of 5.4 cm. If the image produced by the objective is 12 cm from the objective, what magnification does this microscope produce?
A typical red blood cell subtends an angle of only 1.9 × 10-5 rad when viewed at a person's near-point distance of 25 cm. Suppose a red blood cell is examined with a compound microscope in which the objective and eyepiece are separated by a distance of 12.0 cm. Given that the focal length of the
(a) If you treat a 10 × eyepiece of a microscope as a magnifying glass that produces an image at infinity, what is its focal length? (b) The microscope is designed for an image distance of 163 mm from the objective, and the objective is marked 25 ×. What is its focal length?
The medium-power objective lens in a laboratory microscope has a focal length ƒobjective = 3.75 mm. (a) If this lens produces a magnification of - 50.0, what is its "working distance"; that is, what is the distance from the object to the objective lens? (b) What is the focal length of an
A compound microscope has the objective and eyepiece mounted in a tube that is 18.0 cm long. The focal length of the eyepiece is 2.62 cm, and the near-point distance of the person using the microscope is 25.0 cm. If the person can view the image produced by the microscope with a completely relaxed
The barrel of a compound microscope is 15 cm in length. The specimen will be mounted 1.0 cm from the objective, and the eyepiece has a 5.0-cm focal length. Determine the focal length of the objective lens.
A compound microscope uses a 75.0-mm lens as the objective and a 2.0-cm lens as the eyepiece. The specimen will be mounted 122 mm from the objective. Determine(a) The barrel length and(b) The total magnification produced by the microscope.
The "tube length" of a microscope is defined to be the difference between the (objective) image distance and objective focal length: L = di - ƒobjective. Many microscopes are standardized to a tube length of L = 160 mm. Consider such a microscope whose objective lens has a focal length ƒobjective
Two telescopes of different lengths produce the same angular magnification. Is the focal length of the long telescope's eyepiece greater than or less than the focal length of the short telescope's eyepiece? Explain.
A grade school student plans to build a 35-power telescope as a science fair project. She starts with a magnifying glass with a focal length of 7.5 cm as the eyepiece. What focal length is needed for her objective lens?
Four camera lenses have the following focal lengths and Æ’-numbers:Rank these lenses in order of increasing aperture diameter. Indicate ties where appropriate
A 75-power refracting telescope has an eyepiece with a focal length of 5.0 cm. How long is the telescope?
An amateur astronomer wants to build a small refracting telescope. The only lenses available to him have focal lengths of 5.00 cm, 10.0 cm, 20.0 cm, and 30.0 cm.(a) What is the greatest magnification that can be obtained using two of these lenses?(b) How long is the telescope with the greatest
A pirate sights a distant ship with a spyglass that gives an angular magnification of 22. If the focal length of the eyepiece is 11 mm, what is the focal length of the objective?
A telescope has lenses with focal lengths ƒ1 = +30.0 cm and ƒ2 = +5.0 cm. (a) What distance between the two lenses will allow the telescope to focus on an infinitely distant object and produce an infinitely distant image? (b) What distance between the lenses will allow the telescope to focus on
Jason has a 25-power telescope whose objective lens has a focal length of 120 cm. To make his sister appear smaller than normal, he turns the telescope around and looks through the objective lens. What is the angular magnification of his sister when viewed through the "wrong" end of the telescope?
A professor shipwrecked on Hooligan's Island decides to build a telescope from his eyeglasses and some coconut shells. Fortunately, the professor's eyes require different prescriptions, with the left lens having a power of +5.0 diopters and the right lens having a power of +2.0 diopters. (a) Which
Galileo's first telescope used a convex objective lens and a concave eyepiece, as shown in FIGURE 27-29. When this telescope is focused on an infinitely distant object, it produces an infinitely distant image.(a) What is the focal length of the eyepiece of a Galilean telescope that has an objective
The Moon has an angular size of 0.50° when viewed with unaided vision from Earth. Suppose the Moon is viewed through a telescope with an objective whose focal length is 68 cm and an eyepiece whose focal length is 17 mm. What is the angular size of the Moon as seen through this telescope?
A telescope is 275 mm long and has an objective lens with a focal length of 257 mm. (a) What is the focal length of the eyepiece? (b) What is the magnification of this telescope?
The focal length for light that strikes near the center of a spherical convex lens is 15 cm. Referring to Figure 27-23, will the focal length for light that strikes near the edge of the lens be greater than, less than, or equal to 15 cm?In figure 27-23
The focal length of the human eye is approximately 1.7 cm. (a) What is the ƒ-number for the human eye in bright light, when the pupil diameter is 2.0 mm? (b) What is the ƒ-number in dim light, when the pupil diameter has expanded to 7.0 mm?
The focal length for red light that strikes a spherical concave lens is -15 cm. Referring to Figure 27-26, will the magnitude of the (negative) focal length for blue light be greater than, less than, or equal to 15 cm?In figure 27-26
An intracorneal ring is a small plastic device implanted in a person's cornea to change its curvature. By changing the shape of the cornea, the intracorneal ring can correct a person's vision. (a) If a person is nearsighted, should the ring increase or decrease the cornea's curvature? (b) Choose
The lens in a normal human eye, with aqueous humor on one side and vitreous humor on the other side, has a refractive power of 15 diopters. Suppose a lens is removed from an eye and surrounded by air. In this case, is its refractive power greater than, less than, or equal to 15 diopters? Explain.
When the lens in a person's eye becomes clouded by a cataract, the lens can be removed with a process called phacoemulsification and replaced with a man-made intraocular lens. The intraocular lens restores clear vision, but its focal length cannot be changed to allow the user to focus at different
Galileo's original telescope (Figure 27-29) used a convex objective and a concave eyepiece. Use a ray diagram to show that this telescope produces an upright image when a distant object is being viewed. Assume that the eyepiece is to the right of the object and that the right-hand focal point of
For each of the following cases, use a ray diagram to show that the angular sizes of the image and the object are identical if both angles are measured from the center of the lens. (a) A convex lens with the object outside the focal length. (b) A convex lens with the object inside the focal
You have two lenses, with focal lengths ƒ1 = +2.60 cm and ƒ2 = +20.4 cm.(a) How would you arrange these lenses to form a magnified image of the Moon?(b) What is the maximum angular magnification these lenses could produce?(c) How would you arrange the same two lenses to form a magnified image of
The eye is actually a multiple-lens system, but we can approximate it with a single-lens system for most of our purposes. When the eye is focused on a distant object, the optical power of the equivalent single lens is +41.4 diopters. (a) What is the effective focal length of the eye? (b) How far
When a patient is being fitted with contact lenses, the curvature of the patient's cornea is measured with an instrument known as a keratometer. A lighted object is held near the eye, and the keratometer measures the magnification of the image formed by reflection from the front of the cornea. If
A rare 1918 "Jenny" stamp, depicting a misprinted, upside-down Curtiss JN-4 "Jenny" airplane, sold at auction for $525,000. A collector uses a simple magnifying glass to examine the "Jenny," obtaining a linear magnification of 2.5 when the stamp is held 2.76 cm from the lens. What is the focal
A camera with a 65-mm-focal-length lens has aperture ƒ-numbers of 2.8, 4, 8, 11, and 16. (a) Which setting has the largest aperture diameter? (b) Calculate the five possible aperture diameters for this camera.
The largest eye ever to exist on Earth belonged to an extinct species of ichthyosaur, Temnodontosaurus platyodon. This creature had an eye that was 26.4 cm in diameter. It is estimated that this ichthyosaur also had a relatively large pupil, giving it an effective aperture setting of about
Consider a Galilean telescope, as illustrated in Figure 27-29, constructed from two lenses with focal lengths of 75.6 cm and -18.0 mm.In figure 27-29(a) What is the distance between these lenses if an infinitely distant object is to produce an infinitely distant image? (b) What is the angular
A farsighted person uses glasses with a refractive power of 3.6 diopters. The glasses are worn 2.5 cm from his eyes. What is this person's near point when not wearing glasses?

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