Problems

Note to Instructors: Most of the homework problems in this chapter are available for assignment via an online homework management program such as WileyPLUS or WebAssign, and those marked with the icon are presented in a guided tutorial format that provides enhanced interactivity. See Preface for additional details.
Unless specified otherwise, use the values given in Table 26.1 for the refractive indices.
ssm Solution is in the Student Solutions Manual.
This icon represents a biomedical application.
Section 26.1 The Index of Refraction

| 1 | ssm What is the speed of light in benzene?

| 2 | Light travels at a speed of in a certain substance. What substance from Table 26-1 could this be? For the speed of light in a vacuum use , and support your answer with a calculation.

| 3 | ssm www A plate glass window (n = 1.5) has a thickness of . How long does it take light to pass perpendicularly through the plate?

| 4 | The refractive indices of materials A and B have a ratio of . The speed of light in material A is . What is the speed of light in material B?

| 5 | The frequency of a light wave is the same when the light travels in ethyl alcohol as it is when it travels in carbon disulfide. Find the ratio of the wavelength of the light in ethyl alcohol to that in carbon disulfide.

| 6 | Light has a wavelength of 340.0 nm and a frequency of when traveling through a certain substance. What substance from Table 26-1 could this be? Support your answer with calculations.

* | 7 | Interactive Solution 26.7 at offers one model for problems like this one. In a certain time, light travels 6.20 km in a vacuum. During the same time, light travels only 3.40 km in a liquid. What is the refractive index of the liquid?

* | 8 | A flat sheet of ice has a thickness of 2.0 cm. It is on top of a flat sheet of crystalline quartz that has a thickness of 1.1 cm. Light strikes the ice perpendicularly and travels through it and then through the quartz. In the time it takes the light to travel through the two sheets, how far (in centimeters) would it have traveled in a vacuum?
Section 26.2 Snell’s Law and the Refraction of Light

| 9 | ssm A light ray in air is incident on a water surface at a 43° angle of incidence. Find (a) the angle of reflection and (b) the angle of refraction.

| 10 | A ray of light impinges from air onto a block of ice (n = 1.309) at a 60.0° angle of incidence. Assuming that this angle remains the same, find the difference water in the angles of refraction when the ice turns to water (n = 1.333).

| 11 | A spotlight on a boat is 2.5 m above the water, and the light strikes the water at a point that is 8.0 m horizontally displaced from the spotlight (see the drawing). The depth of the water is 4.0 m. Determine the distance d, which locates the point where the light strikes the bottom.

| 12 | Amber (n = 1.546) is a transparent brown-yellow fossil resin. An insect, trapped and preserved within the amber, appears to be 2.5 cm beneath the surface when viewed directly from above. How far below the surface is the insect actually located?

| 13 | ssm A beam of light is traveling in air and strikes a material. The angles of incidence and refraction are 63.0° and 47.0°, respectively. Obtain the speed of light in the material.

| 14 | A scuba diver, submerged under water, looks up and sees sunlight at an angle of 28.0° from the vertical. At what angle, measured from the vertical, does this sunlight strike the surface of the water?

| 15 | Light in a vacuum is incident on a transparent glass slab. The angle of incidence is 35.0°. The slab is then immersed in a pool of liquid. When the angle of incidence for the light striking the slab is 20.3°, the angle of refraction for the light entering the slab is the same as when the slab was in a vacuum. What is the index of refraction of the liquid?

* | 16 | A silver medallion is sealed within a transparent block of plastic. An observer in air, viewing the medallion from directly above, sees the medallion at an apparent depth of 1.6 cm beneath the top surface of the block. How far below the top surface would the medallion appear if the observer (not wearing goggles) and the block were under water?

* | 17 | Refer to Figure 26-4b and assume the observer is nearly above the submerged object. For this situation, derive the expression for the apparent depth: , Equation 26.3. (Hint: Use Snell’s law of refraction and the fact that the angles of incidence and refraction are small, so .)

* | 18 | The drawing shows a rectangular block of glass (n = 1.52) surrounded by liquid carbon disulfide (n = 1.63). A ray of light is incident on the glass at point A with a 30.0° angle of incidence. At what angle of refraction does the ray leave the glass at point B?

* | 19 | ssm www In Figure 26-6, suppose that the angle of incidence is , the thickness of the glass pane is 6.00 mm, and the refractive index of the glass is n2 = 1.52. Find the amount (in mm) by which the emergent ray is displaced relative to the incident ray.

* | 20 | Review Conceptual Example 4 as background for this problem. A man in a boat is looking straight down at a fish in the water directly beneath him. The fish is looking straight up at the man. They are equidistant from the air–water interface. To the man, the fish ap pears to be 2.0 m beneath his eyes. To the fish, how far above its eyes does the man appear to be?

** | 21 | ssm A small logo is embedded in a thick block of crown glass (n = 1.52), 3.20 cm beneath the top surface of the glass. The block is put under water, so there is 1.50 cm of water above the top surface of the block. The logo is viewed from directly above by an observer in air. How far beneath the top surface of the water does the logo appear to be?

** | 22 | A beaker has a height of 30.0 cm. The lower half of the beaker is filled with water, and the upper half is filled with oil (n = 1.48). To a person looking down into the beaker from above, what is the apparent depth of the bottom? Section 26.3 Total Internal Reflection

| 23 | ssm One method of determining the refractive index of a trans parent solid is to measure the critical angle when the solid is in air. If is found to be 40.5°, what is the index of refraction of the solid?

| 24 | A point source of light is submerged 2.2 m below the surface of a lake and emits rays in all directions. On the surface of the lake, directly above the source, the area illuminated is a circle. What is the maximum radius that this circle could have?

| 25 | Interactive Solution 26.25 at provides one model for solving problems such as this. A glass block (n = 1.56) is immersed in a liquid. A ray of light within the glass hits a glass–liquid surface at a 75.0° angle of incidence. Some of the light enters the liquid. What is the smallest possible refractive index for the liquid?

| 26 | What is the critical angle for light emerging from carbon disulfide into air?

| 27 | Concept Simulation 26.1 at illustrates the concepts that are pertinent to this problem. A ray of light is traveling in glass and strikes a glass–liquid interface. The angle of incidence is 58.0°, and the index of refraction of glass is n = 1.50. (a) What must be the index of refraction of the liquid such that the direction of the light entering the liquid is not changed? (b) What is the largest index of refraction that the liquid can have, such that none of the light is transmitted into the liquid and all of it is reflected back into the glass?

* | 28 | The drawing shows a ray of light traveling from point A to point B, a distance of 4.60 m in a material that has an index of refraction n1. At point B, the light encounters a different substance whose index of refraction is n2 = 1.63. The light strikes the interface at the critical angle of . How much time does it take for the light to travel from A to B?

* | 29 | A layer of liquid B floats on liquid A. A ray of light begins in liquid A and undergoes total internal reflection at the interface between the liquids when the angle of incidence exceeds 36.5°. When liquid B is replaced with liquid C, total internal reflection occurs for angles of incidence greater than 47.0°. Find the ratio nB/nC of the refractive indices of liquids B and C.

* | 30 | Multiple-Concept Example 7 and Interactive LearningWare 26.1 at provide helpful background for this problem. The drawing shows a crystalline quartz slab with a rectangular cross section. A ray of light strikes the slab at an incident angle of , enters the quartz, and travels to point P. This slab is surrounded by a fluid with a refractive index n. What is the maximum value of n such that total internal reflection occurs at point P?

Section 26.4 Polarization and the Reflection and Refraction of Light

| 31 | ssm Light is reflected from a glass coffee table. When the angle of incidence is 56.7°, the reflected light is completely polarized parallel to the surface of the glass. What is the index of refraction of the glass?

| 32 | For light that originates within a liquid and strikes the liquid–air interface, the critical angle is 39°. What is Brewster’s angle for this light?

| 33 | Sunlight strikes a diamond surface. At what angle of incidence is the reflected light completely polarized?

| 34 | Light is incident from air onto the surface of a liquid. The angle of incidence is 53.0°, and the angle of refraction is 34.0°. At what angle of incidence would the reflected light be 100% polarized?

| 35 | ssm www When light strikes the surface between two materials from above, the Brewster angle is 65.0°. What is the Brewster angle when the light encounters the same surface from below?

* | 36 | When red light in a vacuum is incident at the Brewster angle on a certain type of glass, the angle of refraction is 29.9°. What are (a) the Brewster angle and (b) the index of refraction of the glass?

* | 37 | In Section 26.4 it is mentioned that the reflected and refracted rays are perpendicular to each other when light strikes the surface at the Brewster angle. This is equivalent to saying that the angle of reflection plus the angle of refraction is 90°. Using Snell’s law and Brewster’s law, prove that the angle of reflection plus the angle of refraction is 90°.
Section 26.5 The Dispersion of Light: Prisms and Rainbows

| 38 | A ray of sunlight is passing from diamond into crown glass; the angle of incidence is 35.00°. The indices of refraction for the blue and red components of the ray are: blue (ndiamond = 2.444, ncrown glass = 1.531), and red (ndiamond = 2.410, ncrown glass = 1.520). Determine the angle between the refracted blue and red rays in the crown glass.

| 39 | Red light (n = 1.520) and violet light (n = 1.538) traveling in air are incident on a slab of crown glass. Both colors enter the glass at the same angle of refraction. The red light has an angle of incidence of 30.00°. What is the angle of incidence of the violet light?

| 40 | Violet light and red light travel through air and strike a block of plastic at the same angle of incidence. The angle of refraction is 30.400° for the violet light and 31.200° for the red light. The index of refraction for violet light in plastic is greater than that for red light by 0.0400. Delaying any rounding off of calculations until the very end, find the index of refraction for violet light in plastic.

| 41 | ssm A beam of sunlight encounters a plate of crown glass at a 45.00° angle of incidence. Using the data in Table 26-2, find the angle between the violet ray and the red ray in the glass.

* | 42 | Refer to Conceptual Example 8 as background material for this problem. The drawing shows a horizontal beam of light that is incident on a prism made from ice. The base of the prism is also horizontal. The prism (n = 1.31) is surrounded by oil whose index of refraction is 1.48. Determine the angle that the exiting light makes with the normal to the right face of the prism.

* | 43 | ssm This problem relates to Figure 26-18, which illustrates the dispersion of light by a prism. The prism is made from glass, and its cross section is an equilateral triangle. The indices of refraction for the red and violet light are 1.662 and 1.698, respectively. The angle of incidence for both the red and violet light is 60.0°. Find the angles of refraction at which the red and violet rays emerge into the air from the prism.
Section 26.6 Lenses,
Section 26.7 The Formation of Images by Lenses,
Section 26.8 The Thin-Lens Equation and the Magnification Equation
(Note: When drawing ray diagrams, be sure that the object height ho is much smaller than the focal length f of the lens or mirror.)

| 44 | A diverging lens has a focal length of −32 cm. An object is placed 19 cm in front of this lens. Calculate (a) the image distance and (b) the magnification. Is the image (c) real or virtual, (d) upright or inverted, and (e) enlarged or reduced in size?

| 45 | ssm A macroscopic (or macro) lens for a camera is usually a converging lens of normal focal length built into a lens barrel that can be adjusted to provide the additional lens-to-film distance needed when focusing at very close range. Suppose that a macro lens (f = 50.0 mm) has a maximum lens-to-film distance of 275 mm. How close can the object be located in front of the lens?

| 46 | A converging lens (f = 12.0 cm) is held 8.00 cm in front of a newspaper, the print size of which has a height of 2.00 mm. Find (a) the image distance (in cm) and (b) the height (in mm) of the magnified print.

| 47 | A tourist takes a picture of a mountain 14 km away using a camera that has a lens with a focal length of 50 mm. She then takes a second picture when she is only 5.0 km away. What is the ratio of the height of the mountain’s image on the film for the second picture to its height on the film for the first picture?

| 48 | Concept Simulation 26.3 at reviews the concepts that play a role in this problem. A converging lens has a focal length of 88.00 cm. An object 13.0 cm tall is located 155.0 cm in front of this lens. (a) What is the image distance? (b) Is the image real or virtual? (c) What is the image height? Be sure to include the proper algebraic sign.

| 49 | A diverging lens has a focal length of −25 cm. (a) Find the image distance when an object is placed 38 cm from the lens. (b) Is the image real or virtual?

| 50 | To focus a camera on objects at different distances, the converging lens is moved toward or away from the film, so a sharp im age always falls on the film. A camera with a telephoto lens (f = 200.0 mm) is to be focused on an object located first at a distance of 3.5 m and then at 50.0 m. Over what distance must the lens be movable?

| 51 | Consult Interactive Solution 26.51 at to review the concepts on which this problem depends. A camera is supplied with two interchangeable lenses, whose focal lengths are 35.0 and 150.0 mm. A woman whose height is 1.60 m stands 9.00 m in front of the camera. What is the height (including sign) of her image on the film, as produced by (a) the 35.0-mm lens and (b) the 150.0-mm lens?

* | 52 | Concept Simulation 26.4 at provides the option of exploring the ray diagram that applies to this problem. The distance between an object and its image formed by a diverging lens is 49.0 cm. The focal length of the lens is −233.0 cm. Find (a) the image distance and (b) the object distance.

* | 53 | ssm www The moon’s diameter is , and its mean distance from the earth is . The moon is being photographed by a camera whose lens has a focal length of 50.0 mm. (a) Find the diameter of the moon’s image on the slide film. (b) When the slide is projected onto a screen that is 15.0 m from the lens of the projector (f = 110.0 mm), what is the diameter of the moon’s image on the screen?

* | 54 | When a converging lens is used in a camera (as in Figure 26-26b), the film must be placed at a distance of 0.210 m from the lens to record an image of an object that is 4.00 m from the lens. The same lens is then used in a projector (see Figure 26-27b), with the screen 0.500 m from the lens. How far from the projector lens should the film be placed?

* | 55 | ssm An object is 18 cm in front of a diverging lens that has a focal length of −12 cm. How far in front of the lens should the object be placed so that the size of its image is reduced by a factor of 2.0?

* | 56 | An object is placed in front of a converging lens in such a position that the lens (f = 12.0 cm) creates a real image located 21.0 cm from the lens. Then, with the object remaining in place, the lens is replaced with another converging lens (f = 16.0 cm). A new, real image is formed. What is the image distance of this new image?

* | 57 | A converging lens (f = 25.0 cm) is used to project an image of an object onto a screen. The object and the screen are 125 cm apart, and between them the lens can be placed at either of two locations. Find the two object distances.

** | 58 | An object is 20.0 cm from a converging lens, and the image falls on a screen. When the object is moved 4.00 cm closer to the lens, the screen must be moved 2.70 cm farther away from the lens to register a sharp image. Determine the focal length of the lens.
Section 26.9 Lenses in Combination

| 59 | Two identical diverging lenses are separated by 16 cm. The focal length of each lens is −8.0 cm. An object is located 4.0 cm to the left of the lens that is on the left. Determine the final image distance relative to the lens on the right.

| 60 | Two converging lenses are separated by 24.00 cm. The focal length of each lens is 12.00 cm. An object is placed 36.00 cm to the left of the lens that is on the left. Determine the final image distance relative to the lens on the right.

| 61 | A converging lens (f1 = 24.0 cm) is located 56.0 cm to the left of a diverging lens (f2 = −28.0 cm). An object is placed to the left of the converging lens, and the final image produced by the two-lens combination lies 20.7 cm to the left of the diverging lens. How far is the object from the converging lens?

| 62 | Interactive LearningWare 26.2 at offers a review of the concepts that play roles in this problem. A diverging lens (f = −10.0 cm) is located 20.0 cm to the left of a converging lens (f = 30.0 cm). A 3.00-cm-tall object stands to the left of the diverging lens, exactly at its focal point. (a) Determine the distance of the final image relative to the converging lens. (b) What is the height of the final image (including the proper algebraic sign)?

| 63 | ssm A converging lens (f = 12.0 cm) is located 30.0 cm to the left of a diverging lens (f = −6.00 cm). A postage stamp is placed 36.0 cm to the left of the converging lens. (a) Locate the final image of the stamp relative to the diverging lens. (b) Find the overall magnification, (c) Is the final image real or virtual? With respect to the original object, is the final image (d) upright or inverted, and is it (e) larger or smaller?

* | 64 | A coin is located 20.0 cm to the left of a converging lens (f = 16.0 cm). A second, identical lens is placed to the right of the first lens, such that the image formed by the combination has the same size and orientation as the original coin. Find the separation between the lenses.

* | 65 | ssm An object is placed 20.0 cm to the left of a diverging lens (f = −8.00 cm). A concave mirror (f = 12.0 cm) is placed 30.0 cm to the right of the lens. (a) Find the final image distance, mea sured relative to the mirror. (b) Is the final image real or virtual? (c) Is the final image upright or inverted with respect to the original object?

** | 66 | Two converging lenses (f1 = 9.00 cm and f2 = 6.00 cm) are separated by 18.0 cm. The lens on the left has the longer focal length. An object stands 12.0 cm to the left of the left-hand lens in the combination. (a) Locate the final image relative to the lens on the right. (b) Obtain the overall magnification. (c) Is the final image real or virtual? With respect to the original object, is the final image (d) upright or inverted and is it (e) larger or smaller?
Section 26.10 The Human Eye

| 67 | Interactive Solution 26.67 at illustrates one approach to solving problems such as this one. A farsighted person has a near point that is 67.0 cm from her eyes. She wears eyeglasses that are designed to enable her to read a newspaper held at a distance of 25.0 cm from her eyes. Find the focal length of the eyeglasses, assuming that they are worn (a) 2.2 cm from the eyes and (b) 3.3 cm from the eyes.

| 68 | A student is reading a lecture written on a blackboard. Contact lenses in her eyes have a refractive power of 57.50 diopters; the lens-to-retina distance is 1.750 cm. (a) How far (in meters) is the blackboard from her eyes? (b) If the writing on the blackboard is 5.00 cm high, what is the size of the image on her retina?

| 69 | ssm A person has far points of 5.0 m from the right eye and 6.5 m from the left eye. Write a prescription for the refractive power of each corrective contact lens.

| 70 | Your friend has a near point of 138 cm, and she wears contact lenses that have a focal length of 35.1 cm. How close can she hold a magazine and still read it clearly?

| 71 | ssm An optometrist prescribes contact lenses that have a focal length of 55.0 cm. (a) Are the lenses converging or diverging, and (b) is the person who wears them nearsighted or farsighted? (c) Where is the unaided near point of the person located, if the lenses are designed so that objects no closer than 35.0 cm can be seen clearly?

| 72 | A farsighted woman breaks her current eyeglasses and is using an old pair whose refractive power is 1.660 diopters. Since these eyeglasses do not completely correct her vision, she must hold a newspaper 42.00 cm from her eyes in order to read it. She wears the eyeglasses 2.00 cm from her eyes. How far is her near point from her eyes?

* | 73 | A nearsighted person wears contacts to correct for a far point that is only 3.62 m from his eyes. The near point of his unaided eyes is 25.0 cm from his eyes. If he does not remove the lenses when reading, how close can he hold a book and see it clearly?

** | 74 | The contacts worn by a farsighted person allow her to see objects clearly that are as close as 25.0 cm, even though her uncorrected near point is 79.0 cm from her eyes. When she is looking at a poster, the contacts form an image of the poster at a distance of 217 cm from her eyes. (a) How far away is the poster actually located? (b) If the poster is 0.350 m tall, how tall is the image formed by the contacts?

** | 75 | Bill is farsighted and has a near point located 125 cm from his eyes. Anne is also farsighted, but her near point is 75.0 cm from her eyes. Both have glasses that correct their vision to a normal near point (25.0 cm from the eyes), and both wear the glasses 2.0 cm from the eyes. Relative to the eyes, what is the closest object that can be seen clearly (a) by Anne when she wears Bill’s glasses and (b) by Bill when he wears Anne’s glasses?
Section 26.11 Angular Magnification and the Magnifying Glass

| 76 | A jeweler whose near point is 72 cm from his eye uses a magni fying glass as in Figure 26-40b to examine a watch. The watch is held 4.0 cm from the magnifying glass. Find the angular magnification of the magnifying glass.

| 77 | ssm A quarter (diameter = 2.4 cm) is held at arm’s length (70.0 cm). The sun has a diameter of and is from the earth. What is the ratio of the angular size of the quarter to that of the sun?

| 78 | An engraver uses a magnifying glass (f = 9.50 cm) to examine some work, as in Figure 26-40b. The image he sees is located 25.0 cm from his eye, which is his near point. (a) What is the distance between the work and the magnifying glass? (b) What is the angular magnification of the magnifying glass?

| 79 | An object has an angular size of 0.0150 rad when placed at the near point (21.0 cm) of an eye. When the eye views this object using a magnifying glass, the largest possible angular size of the image is 0.0380 rad. What is the focal length of the magnifying glass?

| 80 | A spectator, seated in the left field stands, is watching a baseball player 1.9 m tall who is 75 m away. On a TV screen, located 3.0 m from a person watching the game at home, the same player has a 0.12-m image. Find the angular size of the player as seen by (a) the spectator watching the game live and (b) the TV viewer. (c) To whom does the player appear to be larger?

* | 81 | ssm A person using a magnifying glass as in Figure 26-40b observes that for clear vision its maximum angular magnification is 1.25 times as large as its minimum angular magnification. Assuming that the person has a near point located 25 cm from her eye, what is the focal length of the magnifying glass?

** | 82 | A farsighted person can read printing as close as 25.0 cm when she wears contacts that have a focal length of 45.4 cm. One day, however, she forgets her contacts and uses a magnifying glass, as in Figure 26-40b. It has a maximum angular magnification of 7.50 for a young person with a normal near point of 25.0 cm. What is the maximum angular magnification that the magnifying glass can provide for her?
Section 26.12 The Compound Microscope

| 83 | ssm A compound microscope has a barrel whose length is 16.0 cm and an eyepiece whose focal length is 1.4 cm. The viewer has a near point located 25 cm from his eyes. What focal length must the objective have so that the angular magnification of the microscope will be −320?

| 84 | An anatomist is viewing heart muscle cells with a microscope that has two selectable objectives with refracting powers of 100 and 300 diopters. When she uses the 100-diopter objective, the image of a cell subtends an angle of rad with the eye. What angle is subtended when she uses the 300-diopter objective?

| 85 | An insect subtends an angle of only rad at the unaided eye when placed at the near point. What is the angular size (magnitude only) when the insect is viewed through a microscope whose angular magnification has a magnitude of 160?

| 86 | A microscope for viewing blood cells has an objective with a focal length of 0.50 cm and an eyepiece with a focal length of 2.5 cm. The distance between the objective and eyepiece is 14.0 cm. If a blood cell subtends an angle of rad when viewed with the naked eye at a near point of 25.0 cm, what angle (magnitude only) does it subtend when viewed through the microscope?

* | 87 | In a compound microscope, the focal length of the objective is 3.50 cm and that of the eyepiece is 6.50 cm. The distance between the lenses is 26.0 cm. (a) What is the angular magnification of the microscope if the person using it has a near point of 35.0 cm? (b) If, as usual, the first image lies just inside the focal point of the eyepiece (see Figure 26-33), how far is the object from the objective? (c) What is the magnification (not the angular magnification) of the objective?

* | 88 | In a compound microscope, the objective has a focal length of 0.60 cm, while the eyepiece has a focal length of 2.0 cm. The separation between the objective and the eyepiece is L = 12.0 cm. An other microscope that has the same angular magnification can be constructed by interchanging the two lenses, provided that the distance between the lenses is adjusted to a value . Find .
Section 26.13 The Telescope

| 89 | Mars subtends an angle of rad at the unaided eye. An astronomical telescope has an eyepiece with a focal length of 0.032 m. When Mars is viewed using this telescope, it subtends an angle of rad. Find the focal length of the telescope’s objective lens.

| 90 | An astronomical telescope for hobbyists has an angular magnification of −155. The eyepiece has a focal length of 5.00 mm. (a) Determine the focal length of the objective. (b) About how long is the telescope?

| 91 | ssm An astronomical telescope has an angular magnification of −184 and uses an objective with a focal length of 48.0 cm. What is the focal length of the eyepiece?

| 92 | An astronomical telescope has an angular magnification of −132. Its objective has a refractive power of 1.50 diopters. What is the refractive power of its eyepiece?

| 93 | ssm An amateur astronomer decides to build a telescope from a discarded pair of eyeglasses. One of the lenses has a refractive power of 11 diopters, and the other has a refractive power of 1.3 diopters. (a) Which lens should be the objective? (b) How far apart should the lenses be separated? (c) What is the angular magnification of the telescope?

* | 94 | A refracting telescope has an angular magnification of −83.00. The length of the barrel is 1.500 m. What are the focal lengths of (a) the objective and (b) the eyepiece?

* | 95 | The telescope at Yerkes Observatory in Wisconsin has an objective whose focal length is 19.4 m. Its eyepiece has a focal length of 10.0 cm. (a) What is the angular magnification of the telescope? (b) If the telescope is used to look at a lunar crater whose diameter is 1500 m, what is the size of the first image, assuming the surface of the moon is from the surface of the earth? (c) How close does the crater appear to be when seen through the telescope?

** | 96 | An astronomical telescope is being used to examine a relatively close object that is only 114.00 m away from the objective of the telescope. The objective and eyepiece have focal lengths of 1.500 and 0.070 m, respectively. Noting that the expression is no longer applicable because the object is so close, use the thin-lens and magnification equations to find the angular magnification of this telescope. (Hint: See Figure 26-42 and note that the focal points Fo and Fe are so close together that the distance between them may be ignored.)

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