The focal length of the human eye is approximately

Octopus EyesTo 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 octopus, must the octopus move its lens closer to or farther from its retina to keep the object in focus? (b)Choose the best explanation from among the following: I. The lens must move closer to the retinathat is, farther away from the objectto compensate for the object moving closer to the eye. II. When the object moves closer to the eye, the image produced by the lens will be farther behind the lens; therefore, the lens must move farther from the retina.

Your friend is 1.9 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?

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. ower viewed from a distance of 2.0 ft?

Approximating the eye as a single thin lens 2.60 cm from the retina, nd the eyes near-point distance if the smallest focal length the eye can produce is 2.20 cm.

Referring to Problem 4, what is the focal length of the eye when it is focused on an object at a distance of (a) 285 cm and (b) 28.5 cm?

Four camera lenses have the following focal lengths and f-numbers:Rank these lenses in order of increasing aperture diameter. Indicate ties where appropriate.

The focal length of the human eye is approximately 1.7cm.(a)What is the f-number for the human eye in bright light, when the pupil diameter is 2.0 mm? (b) What is the f-number in dim light, when the pupil diameter has expanded to 7.0 mm?

Acamera with a 55-mm-focal-length lens has aperture settings of 2.8, 4, 8, 11, and 16. (a) Which setting has the largest aperture diameter? (b) Calculate the ve possible aperture diameters for this camera.

The actual frame size of 35-mm lm is . You want to take a photograph 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 36-mmtall image on the lm?

To completely fill a frame of 35-mm lm, the image produced by a camera must be 36 mm high. If a camera has a focal length of 150 mm, how far away must a 2.0-m-tall person stand to produce an image that lls the frame?

You are taking a photograph of a poster on the wall of your dorm room, so you cant 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 t in the frame of the lm in your camera. What is the longest focal length lens that will work?

Aphotograph is properly exposed when the aperture is set to and the shutter speed is 125. Find the approximate shutter speed needed to give the same exposure if the aperture is changed to .

You are taking pictures of the beach at sunset. Just before the Sun sets, a shutter speed of 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 dont change the aperture, what approximate shutter speed is needed for your second shot? (b) If, instead, you keep the shutter speed at , what approximate f-stop will be needed for the second shot?

You are taking a photograph of a horse race. A shutter speed of 125 at produces a properly exposed image, but the running horses give a blurred image. Your camera has f-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), which f-stop should you use? (b) What is the shortest exposure time you can use and still get a properly exposed image?

The Hale Telescope The 200-in. (5.08-m) diameter mirror of the Hale telescope on Mount Palomar has a focal length . (a) When the detector is placed at the focal point of the mirror (the prime focus), what is the f-ratio for this telescope?(b)The coud focus arrangement uses additional mirrors to bend the light path and increase the effective focal length to 155.4 m. What is the f-ratio of the telescope when the coud focus is being used? (Coudis French for elbow, since the light path is bent like an elbow. This arrangement is useful when the light needs to be focused onto a distant instrument.)

Two professors are stranded on a deserted island. Both wear glasses, though one is nearsighted and the other is farsighted. (a) Which persons glasses should be used to focus the rays of the Sun and start a re? (b)Choose the best explanation from among the following: I. A nearsighted person can focus close, so that persons glasses should be used to focus the sunlight on a piece of moss at a distance of a couple inches. II. Afarsighted person cant focus close, so the glasses to correct that persons vision are converging. Aconverging lens is what you need to concentrate the rays of the Sun.

Aclerk 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.

Construct a ray diagram for Active Example 272.

The cornea of a normal human eye has an optical power of diopters. What is its focal length?

A myopic student is shaving without his glasses. If his eyes have a far point of 1.6 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 diopters. What is the focal length of this lens?

Two thin lenses, with and , are placed in contact. What is the focal length of this combination?

Two thin lenses have refractive powers of diopters and diopters. What is the refractive power of the two if they are placed in contact? (Note that these are the same two lenses described in the previous problem.)

Two concave lenses, each with , are separated by 6.0 cm. An object is placed 24 cm in front of one of the lenses. Find(a)the location and (b)the magnication of the nal 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 close-up 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) Calculate the focal length of the eye when we focus closely.

Diopter Change in Diving Cormorants Doublecrested cormorants (Phalacrocorax auritus) are extraordinary birdsthey 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 rangesin nature that is, they can change the focal length of their eyes by amounts that are greater than is possible in other animals. When a cormorant plunges into the ocean to catch a sh, it can change the refractive power of its eyes by about 45 diopters, as compared to only 16 diopters of change possible in the human eye.(a)Should this change of 45 diopters be an increase or a decrease? Explain. (b)If the focal length of the cormorants eyes is 4.2 mm before it enters the water, what is the focal length after the refractive power changes by 45 diopters?

Aconverging lens of focal length 8.000 cm is 20.0 cm to the left of a diverging lens of focal length . Acoin is placed 12.0 cm to the left of the converging lens. Find (a) the location and (b) the magnication of the coins nal image.

Repeat Problem 28, this time with the coin placed 18.0 cm to the right of the diverging lens.

Find the focal length of contact lenses that would allow a farsighted person with a near-point distance of 176 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 135-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 56 cm?

A nearsighted person wears contacts with a focal length of . If this persons 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 4.5 m from his eyes. What focal length glasses worn 2.1 cm from his eyes will allow Isaac to see distant objects clearly?

Aperson whose near-point distance is 49 cm wears a pair of glasses that are 2.0 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.

Apair of eyeglasses is designed to allow a person with a farpoint 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 or (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 have if they are worn 2.00 cm from the eyes and allow her to read a newspaper at a distance of 25.0 cm?

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, nd the far point. If this person is farsighted, nd the near point. (For the purposes of this problem, treat the eye as a single-lens system, with the retina 2.40 cm from the lens.)

You are comfortably reading a book at a distance of 24 cm. (a) What is the refractive power of your eyes? (b) Does the refractive power of your eyes increase or decrease when you move the book farther away? Explain. (For the purposes of this problem, treat the eye as a single-lens system, with the retina 2.40 cm from the lens.)

Without glasses, your Uncle Albert can see things clearly only if they are between 25 cm and 170 cm from his eyes. (a) What power eyeglass lens will correct your uncles myopia? Assume the lenses will sit 2.0 cm from his eyes. (b) What is your uncles 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 . Adiverging lens, with a focal length , is placed 30.0 cm to the right of the rst lens. How tall is the nal image of the object?

Asimple camera telephoto lens consists of two lenses. The objective lens has a focal length . Precisely 36.0 cm behind this lens is a concave lens with a focal length . The object to be photographed is 4.00 m in front of the objective lens. (a) How far behind the concave lens should the lm be placed? (b) What is the linear magnication of this lens combination?

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 power needed for each part of the bifocal eyeglass lenses that will give the librarian normal visual acuity from 25 cm out to innity. (Assume the lenses rest 2.0 cm from his eyes.)

With unaided vision, a physician 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 her nearsightedness? Explain. (b) Which type of lens will correct her farsightedness? Explain. (c) Find the refractive power needed for each part of the bifocal contact lenses that will give the physician normal visual acuity from 25 cm out to innity.

Apersons prescription for her new bifocal glasses calls for a refractive power of diopter in the distance-vision part, and a power of diopters in the close-vision part. What are the near and far points of this persons uncorrected vision? Assume the glasses are 2.00 cm from the persons eyes, and that the persons near-point distance is 25.0 cm when wearing the glasses.

A persons prescription for his new bifocal eyeglasses calls for a refractive power of diopter in the distance-vision part and a power of 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, determine the near and far points of this persons uncorrected vision.

Two lenses, with and , are placed on the x axis, as shown in Figure 2722. An object is xed 50.0 cm to the left of lens 1, and lens 2 is a variable distancexto the right of lens 1. Find the lateral magnication and location of the nal image relative to lens 2 for the following cases: (a) ; (b) ; (c) . (d) Show that your result for part (c) agrees with the relation for the effective focal length of two lenses in contact, .

Aconverging 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 rst lens, the nal image is the same size and orientation as the feather itself. What is the separation between the lenses?

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) Apenny is 19 mm in diameter. How far from your eye should the penny be held to produce the same angular diameter as the Moon?

A magnifying glass is a single convex lens with a focal length of . (a) What is the angular magnication when this lens forms a (virtual) image at ? How far from the object should the lens be held? (b)What is the angular magnication when this lens forms a (virtual) image at the persons near point (assumed to be 25 cm)? How far from the object should the lens be held in this case?

Astudent has two lenses, one of focal length and the other with focal length . (a) When used as a simple magnier, which of these lenses can produce the greater magnication? Explain. (b) Find the maximum magnication produced by each of these lenses.

Abeetle 4.73 mm long is examined with a simple magnier of focal length . If the observers eye is relaxed while using the magnier, and has a near-point distance of 25.0 cm, what is the apparent length of the beetle?

To engrave wishes of good luck on a watch, an engraver uses a magnier whose focal length is 8.65 cm. If the image formed by the magnier is at the engravers near point of 25.6 cm, nd (a) the distance between the watch and the magnier and (b) the angular magnication of the engraving. Assume the magnifying glass is directly in front of the engravers eyes.

A jeweler examines a diamond with a magnifying glass. If the near-point distance of the jeweler is 20.8 cm, and the focal length of the magnifying glass is 7.50 cm, nd the angular magnication when the diamond is held at the focal point of the magnier. Assume the magnifying glass is directly in front of the jewelers eyes.

In Problem 54, nd the angular magnication when the diamond is held 5.59 cm from the magnifying glass.

A person with a near-point distance of 25 cm nds that a magnifying glass gives an angular magnication that is 1.5 times larger when the image of the magnier is at the near point than when the image is at innity. 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.

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 magnication does this microscope produce?

A typical red blood cell subtends an angle of only when viewed at a persons 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 eyepiece is 2.7 cm, and the focal length of the objective is 0.49 cm, nd the magnitude of the angle subtended by the red blood cell when viewed through this microscope.

The medium-power objective lens in a laboratory microscope has a focal length . (a) If this lens produces a lateral magnication of , 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 eyepiece lens that will provide an overall magnication of 125?

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 eye, and the magnication is , what is the focal length of the objective?

In Problem 61, what is the distance between the objective lens and the object to be examined?

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.

Acompound 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 magnication produced by the microscope.

The tube length of a microscope is dened to be the difference between the (objective) image distance and objective focal length: . Many microscopes are standardized to a tube length of . Consider such a microscope whose objective lens has a focal length . (a)How far from the object should this lens be placed? (b)What focal length eyepiece would give an overall magnication of ?(c)What focal length eyepiece would give an overall magnication of ?

Two telescopes of different length produce the same angular magnication. Is the focal length of the long telescopes eyepiece greater than or less than the focal length of the short telescopes eyepiece? Explain.

To construct a telescope, you are given a lens with a focal length of 32 mm and a lens with a focal length of 1600 mm. (a)On the basis of focal length alone, which lens should be the objective and which the eyepiece? Explain. (b)What magnication would this telescope produce?

Agrade 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 5.0 cm as the eyepiece. What focal length is needed for her objective lens?

A55-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 magnication that can be obtained using two of these lenses? (b) How long is the telescope with the greatest magnication?

Apirate sights a distant ship with a spyglass that gives an angular magnication of 22. If the focal length of the eyepiece is 11 mm, what is the focal length of the objective?

Atelescope has lenses with focal lengths and . (a) What distance between the two lenses will allow the telescope to focus on an innitely distant object and produce an innitely distant image? (b)What distance between the lenses will allow the telescope to focus on an object that is 5.0 m away and to produce an innitely distant image?

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 magnication of his sister when viewed through the wrong end of the telescope?

Roughing It with Science A professor shipwrecked on Hooligans Island decides to build a telescope from his eyeglasses and some coconut shells. Fortunately, the professors eyes require different prescriptions, with the left lens having a power of diopters and the right lens having a power of diopters.(a)Which lens should he use as the objective? (b)What is the angular magnication of the professors telescope?

Galileos Telescope Galileos rst telescope used a convex objective lens with a focal length and a concave eyepiece, as shown in Figure 2723. When this telescope is focused on an innitely distant object, and produces an innitely distant image, its angular magnication is . (a) What is the focal length of the eyepiece? (b) How far apart are the two lenses?

The Moon has an angular size of 0.50when viewed with unaided vision from Earth. Suppose the Moon is viewed through a telescope with an objective whose focal length is 53 cm and an eyepiece whose focal length is 25 mm. What is the angular size of the Moon as seen through this telescope?

In Problem 76, an eyepiece is selected to give the Moon an angular size of 15. What is the focal length of this eyepiece?

Atelescope 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 magnication of this telescope?

CEPredict/ExplainBIOIntracorneal RingAn intracorneal ring is a small plastic device implanted in a persons cornea to change its curvature. By changing the shape of the cornea, the intracorneal ring can correct a persons vision. (a) If a person is nearsighted, should the ring increase or decrease the corneas curvature? (b) Choose the best explanation from among the following: I. The intracorneal ring should increase the curvature of the cornea so that it bends light more. This will allow it to focus on light coming from far away. II. The intracorneal ring should decrease the curvature of the cornea so its atter and bends light less. This will allow parallel rays from far away to be focused.

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.

An optical system consists of two lenses, one with a focal length of 0.50 cm and the other with a focal length of 2.3 cm. If the separation between the lenses is 12 cm, is the instrument a microscope or a telescope? Explain.

An optical system consists of two lenses, one with a focal length of 50 cm and the other with a focal length of 2.5 cm. If the separation between the lenses is 52.5 cm, is the instrument a microscope or a telescope? Explain.

Predict/ExplainBIOTreating CataractsWhen the lens in a persons eye becomes clouded by a cataract, the lens can be removed with a process called phacoemulsication 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 distances. In most cases, the intraocular lens is adjusted for viewing of distant objects, and corrective glasses are worn when viewing nearby objects. (a)Should the refractive power of the corrective glasses be positive or negative? (b) Choose the best explanation from among the following: I. The refractive power should be positiveconverging because the intraocular lens will make the person farsighted. II. A negative refractive power is required to bring the focal point of the intraocular lens in from innity to a nite value.

The greatest refractive power a patients eyes can produce is 44.1 diopters. (a) Is this patient nearsighted or farsighted? Explain. (b) If this patient is nearsighted, nd the far point. If this person is farsighted, nd the near point. (For the purposes of this problem, treat the eye as a single-lens system, with the retina 2.40 cm from the lens.)

You are observing a rare species of bird in a distant tree with your unaided eyes. (a) What is the refractive power of your eyes? (b) Does the refractive power of your eyes increase or decrease when you shift your view to the guidebook in your hands? Explain. (For the purposes of this problem, treat the eye as a single-lens system, with the retina 2.40 cm from the lens.)

Galileos original telescope (Figure 2723) 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 the eyepiece is just to the left of the objectives right-hand focal point. In addition, assume that the focal length of the eyepiece has a magnitude that is about one-quarter the focal length of the objective.

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) Aconvex lens with the object outside the focal length. (b) A convex lens with the object inside the focal length. (c)Aconcave lens with the object outside the focal length. (d) Given that the angular size does not change, how does a simple magnier work? Explain.

You have two lenses, with focal lengths and . (a)How would you arrange these lenses to form a magnied image of the Moon? (b)What is the maximum angular magnication these lenses could produce? (c) How would you arrange the same two lenses to form a magnied image of an insect? (d) If you use the magnier of part (c) to view an insect, what is the angular magnication when the insect is held 2.90 cm from the objective lens?

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 diopters. (a) What is the effective focal length of the eye? (b) How far in front of the retina is this equivalent lens located?

Fitting Contact Lenses with a KeratometerWhen a patient is being tted with contact lenses, the curvature of the patients cornea is measured with an instrument known as a keratometer. A lighted object is held near the eye, and the keratometer measures the magnication of the image formed by reection from the front of the cornea. If an object is held 10.0 cm in front of a patients eye, and the reected image is magnied by a factor of 0.035, what is the radius of curvature of the patients cornea?

Pricey Stamp Arare 1918 Jenny stamp, depicting a misprinted, upside-down Curtiss JN-4 Jenny airplane, sold at auction for $525,000. Acollector uses a simple magnifying glass to examine the Jenny, obtaining a linear magnication of 2.5 when the stamp is held 2.76 cm from the lens. What is the focal length of the magnifying glass?

Aperson needs glasses with a refractive power of diopters to be able to focus on distant objects. (a) Is this person nearsighted or farsighted? Explain. (b) What is this persons (unaided) far point?

A Big Eye 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 . (a) Assuming its pupil was one-third the diameter of the eye, what was the approximate focal length of the ichthyosaurs eye? (b)When the ichthyosaur narrowed its pupil in bright light, did its f-number increase or decrease? Explain.

Consider a Galilean telescope, as illustrated in Figure 2723, constructed from two lenses with focal lengths of 75.6 cm and . (a) What is the distance between these lenses if an18 innitely distant object is to produce an innitely distant image? (b) What is the angular magnication when the lenses are separated by the distance calculated in part (a)?

Aconverging lens forms a virtual object 12 cm to the right of a second lens that has a refracting power of 3.75 diopter. (a) Where is the image? (b)Is the image real or virtual? Explain.

Afarsighted person uses glasses with a refractive power of 3.6 diopters. The glasses are worn 2.5 cm from his eyes. What is this persons near point when not wearing glasses?

Landing on an Aircraft Carrier The Long-Range Lineup System (LRLS) used to ensure safe landings on aircraft carriers consists of a series of Fresnel lenses of different colors. Each lens focuses light in a different, specic direction, and hence which light a pilot sees on approach determines whether the plane is above, below, or on the proper landing path. The basic idea behind a Fresnel lens, which has the same optical properties as an ordinary lens, is shown in Figure 2724, along with a photo of the LRLS. Suppose an object (a lightbulb in this case) is 17.1 cm behind a Fresnel lens, and that the corresponding image is a distance in front of the lens. If the object is moved to a distance of 12.0 cm behind the lens, the image distance doubles to . In the LRLS, it is desired to have the image of the lightbulb at innity. What object distance will give this result for this particular lens? (a)Alens causes light to refract at its surface; therefore, the interior glass can be removed without changing its optical properties. This produces a Fresnel lens, which is much lighter than the original lens. (b) If an airplane is on the correct approach path, the pilot will see an amber light, called the meatball, in line with the row of blue lights.

When using a telescope to photograph a faint astronomical object, you need to maximize the amount of light energy that falls on each square millimeter of the image on the lm. For a given telescope and object, the total light that falls on the lm is proportional to the length of the exposure, so a long exposure will reveal fainter objects than a short exposure. Show that for a given length of exposure, the brightness of the image is inversely proportional to the square of the f-number of the telescope system.

A Cassegrain astronomical telescope uses two mirrors to form the image. The larger (concave) objective mirror has a focal length . Asmall convex secondary mirror is mounted 43.0 cm in front of the primary. As shown in Figure 2725, light is reected from the secondary through a hole in the center of the primary, thereby forming a real image 8.00 cm behind the primary mirror. What is the radius of curvature of the secondary mirror?

Aconvex lens is placed 10.0 cm in front of a plane mirror. Amatchstick is placed 25.0 cm in front of the lens, as shown in Figure 2726.(a)If you look through the lens toward the mirror, where will you see the image of the matchstick? (b)Is the image real or virtual? Explain. (c) What is the magnication of the image? (d)Is the image upright or inverted?

Repeat Problem 100 for the case where the converging lens is replaced with a diverging lens with . Everything else in the problem remains the same.

Repeat Problem 47 for the case where lens 1 is replaced with a diverging lens with . Everything else in the problem remains the same.

The diameter of a collimated laser beam can be expanded or reduced by using two converging lenses, with focal lengths and , mounted a distance from each other, as shown in Figure 2727. What is the ratio of the two beam diameters, , expressed in terms of the focal lengths?

Consider three lenses with focal lengths of 25.0 cm, , and 11.0 cm positioned on the x axis at , and , respectively. An object is at . Find (a)the location and (b)the orientation and magnication of the nal image produced by this lens system.

Because a concave lens cannot form a real image of a real object, it is difcult to measure its focal length precisely. One method uses a second, convex, lens to produce a virtual object for the concave lens. Under the proper conditions, the concave lens will form a real image of the virtual object! Astudent conducting a laboratory project on concave lenses makes the following observations: When a lamp is placed 42.0 cm to the left of a particular convex lens, a real (inverted) image is formed 37.5 cm to the right of the lens. The lamp and convex lens are kept in place while a concave lens is mounted 15.0 cm to the right of the convex lens. A real image of the lamp is now formed 35.0 cm to the right of the concave lens. What is the focal length of each lens?

Aperson with a near-point distance N uses a magnifying glass with a focal length f. Show that the greatest magnication that can be achieved with this magnier is

A patient receives a rigid IOL whose focus cannot be changedit is designed to provide clear vision of objects at innity. 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, nd 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

Suppose a exible, adaptive IOLhas 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 innity 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

Referring to Example 272 Suppose a persons eyeglasses have a focal length of , are 2.00 cm in front of the eyes, and allow the person to focus on distant objects. (a)Is this persons 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 length of ? Explain. (b) Find the far point for this person.

Referring to Example 272In Example 272, 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 , distant objects can be brought into focus. Suppose a second persons far point is 353 cm. (a) Is the magnitude of the focal length of the eyeglasses that allow this person to focus on distant objects greater than or less than ? Assume the glasses are 2.00 cm in front of the eyes. (b) Find the required focal length for the second persons eyeglasses.

Referring to Example 273 Suppose a persons 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 persons near point greater than or less than 57.0 cm, which is the near-point distance when the glasses have a refractive power of 2.53 diopters? Explain. (b) Find the near point for this person.

Referring to Example 273 Suppose a persons nearpoint 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 worn 2.00 cm in front of the eyes. (b) Find the required refractive power for this persons eyeglasses.