1cc. If you shift all parallel rays in Figure 33.3 a bit up from
their present location, the focal point willa) move a bit down from its
present location.b) move a bit up from its present location.c) remain
unchanged.d) move a bit right from its present location.e) move a bit
left from its present location.Figure 33.3 (a) Five parallel red light
rays hit a converging lens from the left and focused at a single
point.... Get solution
1mcq. For a microscope to work as intended, the separation between the objective lens and the eyepiece must be such that the intermediate image produced by the objective lens will occur at a distance (as measured from the optical center of the eyepiece)a) slightly larger than the focal length.b) slightly smaller than the focal length.c) equal to the focal length.d) The position of the intermediate image is irrelevant. Get solution
2cc. If you move the object in Figure 33.4 to the left of its present location, the image willa) move to the left and become larger.b) move to the left and become smaller.c) remain unchanged.d) move to the right and become larger.e) move to the right and become smaller.Figure 33.4 Real image produced by a converging lens for the case that the object distance is larger than the focal length.... Get solution
2mcq. Which one of the following is not a characteristic of a simple two-lens astronomical refracting telescope?a) The final image is virtual.b) The objective forms a virtual image.c) The final image is inverted. Get solution
3cc. If you cover the top half of the lens in Figure 33.4 with a material that does not allow light to pass through, thena) the top half of the image will vanish.b) the bottom half of the image will vanish.c) the entire image will vanish.d) the entire image will still be visible, but will be fainter.e) nothing will change.Figure 33.4 Real image produced by a converging lens for the case that the object distance is larger than the focal length.... Get solution
3mcq. A converging lens will be used as a magnifying glass. In order for this to work, the object must be placed at a distancea) do > f.b) do = f.c) do f.d) None of the above. Get solution
4mcq. An object is moved from a distance of 30 cm to a distance of 10 cm in front of a converging lens of focal length 20 cm. What happens to the image?a) Image goes from real and upright to real and inverted.b) Image goes from virtual and upright to real and inverted.c) Image goes from virtual and inverted to real and upright.d) Image goes from real and inverted to virtual and upright.e) None of the above. Get solution
5cc. If you have a converging lens with a focal length of 15.0 cm in air and then put this lens in water, its focal length will bea) smaller than 15.0 cm.b) still the same 15.0 cm.c) larger than 15.0 cm.d) either smaller or larger than 15.0 cm, depending on the index of refraction of the lens. Get solution
5mcq. What type of lens is a magnifying glass?a) convergingb) divergingc) sphericald) cylindricale) plain Get solution
6mcq. LASIK surgery uses a laser to modify thea) curvature of the retina.b) index of refraction of the aqueous humor.c) curvature of the lens.d) curvature of the cornea. Get solution
7cc. What is the focal length (in meters) of a magnifying glass that gives an angular magnification of 6?a) 0.010 mb) 0.021 mc) 0.035 md) 0.042 me) 0.055 m Get solution
7mcq. What is the focal length of a flat sheet of transparent glass?a) zerob) infinityc) thickness of the glassd) undefined Get solution
8mcq. Where is the image formed if an object is placed 25 cm from the eye of a nearsighted person. What kind of a corrective lens should the person wear?a) Behind the retina. Converging lenses.b) Behind the retina. Diverging lenses.c) In front of the retina. Converging lenses.d) In front of the retina. Diverging lenses. Get solution
9cc. A hyperopic (farsighted) person can read a newspaper at a distance of d = 125 cm, but no closer. What power lens should this person use for reading if they wish to hold the newspaper at a distance of 25 cm from their eyes?a) –3.5 diopterb) –1.25 diopterc) +0.50 diopterd) +2.5 dioptere) +3.2 diopter Get solution
9mcq. An object is placed on the left of a converging lens at a distance that is less than the focal length of the lens. The image produced will bea) real and inverted.b) virtual and upright.c) virtual and inverted.d) real and upright. Get solution
10cc. A microscope is intended to have a linear magnification whose magnitude is 330. If the objective lens has a power of 350 diopter and the eyepiece lens has a power of 10.0 diopter, how long must the microscope be? Assuming final image is produced at a distance of 25 cm.a) 37.7 cmb) 40.0 cmc) 51.3 cmd) 65.0 cme) 75.0 cm Get solution
10mcq. What would you expect to happen to the magnitude of the power of a lens when it is placed in water (n = 1.33)?a) It would increase.b) It would decrease.c) It would stay the same.d) It would depend if the lens was converging or diverging. Get solution
11cc. Suppose a reflecting telescope consists of a concave spherical mirror with a radius of curvature R = 17.0 m and an eyepiece lens of focal length fe = 29.0 cm. What is the magnitude of the magnification of this telescope?a) 29.3b) 45.0c) 58.6d) 66.1e) 78.9 Get solution
11mcq. An unknown lens forms an image of an object that is 24 cm away from the lens, inverted, and a factor of 4 larger in size than the object. Where is the object located?a) 6 cm from the lens on the same side of the lensb) 6 cm from the lens on the other side of the lensc) 96 cm from the lens on the same side of the lensd) 96 cm from the lens on the other side of the lense) No object could have formed this image. Get solution
12cc. Reflecting telescopes with large mirror diameters are better than those with smaller diameters. Why?a) Because they have a shorter focal length.b) Because they have a longer focal length.c) Because they have a greater magnification.d) Because they can collect more light. Get solution
12mcq. A single lens with two convex surfaces made of sapphire with index of refraction n = 1.77 has surfaces with radii of curvature R1 = 27.0 cm and R2 = –27.0 cm. What is the focal length of this lens in air?a) 17.5 cmb) 27.0 cmc) 30.7 cmd) 40.8 cme) 54.0 cm Get solution
13mcq. A single lens with two convex surfaces made of sapphire with index of refraction n = 1.77 has surfaces with radii of curvature R1 = 27.0 cm and R2 = –27.0 cm. What is the focal length of this lens in water (n = 1.33)?a) 17.5 cmb) 27.0 cmc) 30.7 cmd) 40.8 cme) 54.0 cm Get solution
14mcq. An object is placed 15.0 cm to the left of a converging lens with focal length f = 5.00 cm, as shown in the figure. Where is the image formed?a) 1.25 cm to the right of the lensb) 2.75 cm to the left of the lensc) 3.75 cm to the right of the lensd) 5.00 cm to the left of the lense) 7.50 cm to the right of the lens... Get solution
15mcq. The eyepiece for the Yerkes telescope has a focal length of approximately 10 cm. The Hubble Space Telescope can reach an effective angular magnification factor of 8000. What would the focal length of the objective lens at Yerkes need to be in order to reach the same factor of 8000?a) 8 mb) 80 mc) 0.125 md) 0.00125 me) 800 m Get solution
16mcq. Where is the image of the objective lens of a microscope located and what does it look like?a) real and uprightb) real and invertedc) virtual and uprightd) virtual and inverted Get solution
17mcq. A pea sits at the focal point of a converging lens, 3 cm to the left of that lens on the optical axis. A second identical lens is at a distance of 12 cm to the right from the first one. Where is the image of the pea located, and is it real or virtual?a) A virtual image 3 cm to the left of lens 2b) A real image 3 cm to the left of lens 2c) A virtual image 3 cm to the right of lens 2d) A real image 3 cm to the right of lens 2e) No image can be formed, because the 2 lenses are more than 2 focal lengths apart. Get solution
18cq. Several small drops of paint (less than 1 mm in diameter) splatter on a painter’s eyeglasses, which are approximately 2 cm in front of the painter’s eyes. Do the dots appear in what the painter sees? How do the dots affect what the painter sees? Get solution
19cq. When a diver with 20/20 vision removes her mask underwater, her vision becomes blurry. Why is this the case? Does the diver become nearsighted (eye lens focuses in front of retina) or farsighted (eye lens focuses behind retina)? As the index of refraction of the medium approaches that of the lens, where does the object get imaged? Typically, the index of refraction for water is 1.33, while the index of refraction for the lens in a human eye is 1.40. Get solution
20cq. In H.G. Wells’s classic story The Invisible Man, a man manages to change the index of refraction of his body to 1.0; thus, light would not bend as it enters his body (assuming he is in air and not swimming). If the index of refraction of his eyes were equal to one, would he be able to see? If so, how would things appear? Get solution
21cq. Astronomers sometimes place filters in the path of light as it passes through their telescopes and optical equipment. The filters allow only a single color to pass through. What are the advantages of this? What are the disadvantages? Get solution
22cq. Is it possible to start a fire by focusing the light of the Sun with ordinary eyeglasses? How, or why not? Get solution
23cq. Will the magnification produced by a simple magnifier increase, decrease, or stay the same when the object and the lens are both moved from air into water? Get solution
24cq. Is it possible to design a system that will form an image without lenses or mirrors? If so, how? and what drawbacks, if any, would it have? Get solution
25cq. A lens system widely used in machine vision for dimensional measurement is the so-called telecentric lens system. In its basic configuration, it consists of two thin lenses of focal lengths f1 and f2, respectively, placed a distance d = f1 + f2 apart, and a small circular aperture called a stop aperture placed at the common focal point between the two lenses. The purpose of such a system is to provide a magnification that is independent of the distance between the object and the lens system, within a specified range of distances that define the so-called depth of field of the system.a) Draw a ray diagram through the system.b) Determine the magnification of such a system.c) Determine the requirements that must be met by the two lenses in order for a telecentric system to be able to image with maximum resolution an object with a diameter of 50.0 mm on a so-called ½ -inch CCD camera head (detector dimensions are ~ 6.50 mm × 5.00 mm). Get solution
26cq. Lenses or lens systems for photography are rated by both focal length and “speed.” The “speed” of a lens is measured by its f-number or f-stop, the ratio of its focal length to its aperture diameter. For many commercially available lenses this number is approximately a power of ..., e.g., 1.4, 2.0, 2.8, 4.0, etc.; the lens is provided with a mechanical iris diaphragm that can be set to different apertures or f-stops. The smaller the f-number, the “faster” the lens. “Faster” lenses are more expensive, as a wide aperture requires a higherquality lens.a) Explain the connection between f-number, (i.e., aperture diameter) and “speed.”b) Look up the necessary data and calculate the f-numbers of (the primary mirrors of) the Keck 10-meter telescope, the Hubble Space Telescope, and the Arecibo radio telescope. Get solution
27cq. The f-number of a photographic system determines not just its speed but also its “depth of field,” the range of distances over which objects remain in acceptable focus. Low f-numbers correspond to small depth of field, high f-numbers to large depth of field. Explain this. Get solution
28cq. Mirrors for astronomical instruments are invariably first-surface mirrors: The reflective coating is applied on the surface exposed to the incoming light. Household mirrors, on the other hand, are second-surface mirrors: The coating is applied to the back of the glass or plastic material of the mirror. (You can tell the difference by bringing the tip of an object close to the surface of the mirror. Object and image will nearly touch with a first-surface mirror; a gap will remain between them with a second-surface mirror.) Explain the reasons for these design differences. Get solution
30cq. Using ray tracing in the diagram below, find the image of the object (upright arrow) in the following system having a diverging (double-concave) lens. Is the image real or virtual? Is the image height less than or greater than the object height?... Get solution
31cq. You have made a simple telescope from two convex lenses. The objective lens is the one of the two lenses that is closer to the object being observed. What kind of image is produced by the eyepiece lens if the eyepiece is closer to the objective lens than the image produced by the objective lens? Get solution
33cq. A physics student epoxies two converging lenses to the opposite ends of a 2.0 · 101-cm-long tube. One lens has a focal length of f1 = 6.0 cm and the other has a focal length of f2 = 3.0 cm. She wants to use this device as a microscope. Which end should she look through to obtain the highest magnification of an object? Get solution
34. An object of height h is placed at a distance do on the left side of a converging lens of focal length f ( f do).a) What must do be in order for the image to form at a distance 3f on the right side of the lens?b) What will be the magnification? Get solution
36. A biconvex ice lens is made so that the radius of curvature of the front surface is 15.0 cm and that for the back is 20.0 cm. Determine how far you would put dry twigs if you wish to start a fire with your ice lens. Get solution
37. As a high-power laser engineer you need to focus a 1.06-mm diameter laser beam to a 10.0-µm diameter spot 20.0 cm behind the lens. What focal length lens would you use? Get solution
38. A plastic cylinder of length 3.0 · 101 cm has its ends ground to convex (from the rod outward) spherical surfaces, each having radius of curvature 1.0 · 101 cm. A small object is placed 1.0 · 101 cm from the left end. How far will the image of the object lie from the right end, if the index of refraction of the plastic is 1.5? Get solution
39. The object (upright arrow) in the following system has a height of 2.5 cm and is placed 5.0 cm away from a converging (convex) lens with a focal length of 3.0 cm. What is the magnification of the image? Is the image upright or inverted? Confirm your answers by ray tracing.... Get solution
40. Demonstrate that the minimum distance possible between a real object and its real image through a thin convex lens is 4f, where f is the focal length of the lens. Get solution
41. An air-filled cavity bound by two spherical surfaces is created inside a glass block. The two spherical surfaces have radii of 30.0 cm and 20.0 cm, respectively, and the thickness of the cavity is 40.0 cm (see diagram below). A light-emitting diode (LED) is embedded inside the block a distance of 60.0 cm in front of the cavity. Given nglass = 1.50 and nair = 1.00, and using only paraxial light rays (i.e., in the paraxial approximation):a) Calculate the final position of the image of the LED through the air-filled cavity.b) Draw a ray diagram showing how the image is formed... Get solution
42. To study a tissue sample better, a pathologist holds a 5.00-cm focal length magnifying glass 3.00 cm from the sample. How much magnification can he get from the lens? Get solution
43. Suppose a magnifying glass has a focal length of 5.0 cm. Find the magnifying power of this glass when the object is placed at the near point. Get solution
44. What is the focal length of a magnifying glass if a 1.0-mm object appears to be 10. mm? Get solution
45. A person with a near-point distance of 24.0 cm finds that a magnifying glass gives an angular magnification that is 1.25 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? Get solution
46. A beam of parallel light, 1.00 mm in diameter passes through a lens with a focal length of 10.0 cm. Another lens, this one of focal length 20.0 cm, is located behind the first lens so that the light traveling out from it is again parallel.a) What is the distance between the two lenses?b) How wide is the outgoing beam? Get solution
47. How large does a 5.0-mm insect appear when viewed with a system of two identical lenses of focal length 5.0 cm separated by a distance 12.0 cm if the insect is 10.0 cm from the first lens? Is the image real or virtual? Inverted or upright? Get solution
48. Three converging lenses of focal length 5.0 cm are arranged with a spacing of 2.0·101 cm between them, and are used to image an insect 2.0·101 cm away.a) Where is the image?b) Is it real or virtual?c) Is it upright or inverted? Get solution
49. Two identical thin convex lenses, each of focal length f, are separated by a distance d = 2.5f. An object is placed in front of the first lens at a distance do,1 = 2f.a) Calculate the position of the final image of the object through the system of lenses.b) Calculate the total transverse magnification of the system.c) Draw the ray diagram for this system and show the final image.d) Describe the final image (real or virtual, erect or inverted, larger or smaller) in relation to the initial object.... Get solution
50. Two converging lenses with focal lengths 5.00 cm and 10.0 cm, respectively, are placed 30.0 cm apart. An object of height h = 5.00 cm is placed 10.0 cm to the left of the 5.00-cm lens. What will be the position and height of the final image produced by this lens system? Get solution
51. Two lenses are used to create an image for a source 10.0 cm tall that is located 30.0 cm to the left of the first lens, as shown in the figure. Lens L1 is a biconcave lens made of crown glass (index of refraction n = 1.55) and has a radius of curvature of 20.0 cm for both surface 1 and 2. Lens L2 is 40.0 cm to the right of the first lens L1. Lens L2 is a converging lens with a focal length of 30.0 cm. At what distance relative to the object does the image get formed? Determine this position by sketching rays and calculating algebraically.... Get solution
52. Sophisticated optical systems can be analyzed and designed with the aid of techniques from linear algebra. Light rays (or particle beams) are described at any point along the axis of the system by a two-component column vector containing y, the distance of the ray from the optic axis, and dy/dx, the slope of the ray. Components of the system are described by 2×2 matrices which incorporate their effects on the ray; combinations of components are described by products of these matrices.a) A thin lens does not alter the position of a ray, but increases (diverging) or decreases (converging) its slope an amount proportional to the distance of the ray from the axis. Construct the matrix for a thin lens of focal length f.b) A space between components does not alter the slope of a ray; the distance of the ray from the axis changes by the slope of the ray times the length of the space. Write the matrix for a space of length x.c) Write the matrix for the two-lens “zoom lens” system described in Section 33.3. Get solution
53. The typical length of a human eyeball is 2.50 cm.a) What is the effective focal length of the two-lens system made from a normal person’s cornea and lens when viewing objects far away?b) What is the effective focal length for viewing objects at the near point? Get solution
54. Using your answers from the previous question, and given that the cornea in a typical human eye has a fixed focal length of 2.33 cm, what range of focal lengths does the lens in a typical eye have? Get solution
55. Jane has a near point of 125 cm and wishes to read from a computer screen 40. cm from her eye.a) What is the object distance?b) What is the image distance?c) What is the focal length?d) What is the power of the corrective lens needed?e) Is the corrective lens diverging or converging? Get solution
56. Bill has a far point of 125 cm and wishes to see distant objects clearly.a) What is the object distance?b) What is the image distance?c) What is the focal length?d) What is the power of the corrective lens needed?e) Is the corrective lens diverging or converging? Get solution
57. A person wearing bifocal glasses is reading a newspaper a distance of 25 cm. The lower part of the lens is converging for reading and has a focal length of 70. cm. The upper part of the lens is diverging for seeing at distances far away and has a focal length of 50. cm. What are the uncorrected near and far points for the person? Get solution
58. The radius of curvature for the outer part of the cornea is 8.0 mm, the inner portion is relatively flat. If the index of refraction of the cornea and the aqueous humor is 1.34:a) Find the power of the cornea.b) If the combination of the lens and the cornea has a power of 50. diopter, find the power of the lens (assume the two are touching). Get solution
59. As objects are moved closer to the human eye, the ciliary muscle causes the lens at the front of the eye to become more curved, thereby decreasing the focal length of the lens. The shortest focal length fmin of this lens is typically 2.3 cm. What is the closest one can bring an object to a normal human eye (see left side of figure below) and still have the image of the object projected sharply on the retina, which is 2.5 cm behind the lens? Now consider a nearsighted human eye that has the same fmin but is stretched horizontally, with a retina that is 3.0 cm behind the lens (see right side of figure below). What is the closest one can bring an object to this nearsighted human eye and still have the image of the object projected sharply on the retina. Compare the maximum angular magnification produced by this nearsighted eye with that of the normal eye.... Get solution
60. A person is nearsighted (myopic). The power of his eyeglass lenses is –5.75 diopters, and he wears the lenses 1.00 cm in front of his corneas. What is the prescribed power of his contact lenses? Get solution
61. An amateur photographer attempts to build a custom zoom lens using a converging lens followed by a diverging lens. The two lenses are separated by a distance x = 50. mm as shown below. If the focal length of the first lens is 2.0 · 102 mm and the focal length of the second lens is –3.0 · 102 mm, what will the effective focal length of this compound lens be? What will feff be if the lens separation is changed to 1.0 · 102 mm?... Get solution
62. For a certain camera, the distance between the lens and the film is 10.0 cm. You observe that objects that are very far away appear properly focused. How far from the film would you have to move the lens in order to properly focus an object 100. cm away? Get solution
63. A camera has a lens with a focal length of 60. mm. Suppose you replace the normal lens with a zoom lens whose focal length can be varied from 35. mm to 250. mm and use the camera to photograph an object very far away. Compared to a 60.-mm lens, what magnification of the image would be achieved using the 240.-mm focal length? Get solution
64. A camera lens usually consists of a combination of two or more lenses to produce a good-quality image. Suppose a camera lens has two lenses—a diverging lens of focal length 10.0 cm and a converging lens of focal length 5.00 cm. The two lenses are held 7.00 cm apart. A flower of length 10.0 cm, to be pictured, is held upright at a distance 50.0 cm in front of the diverging lens; the converging lens is placed behind the diverging lens. What are the location, orientation, size, and the magnification of the final image? Get solution
65. A student finds a tube 20. cm long with a lens attached to one end. The attached lens has a focal length of 0.70 cm. The student wants to use the tube and lens to make a microscope with a magnification of 3.0 · 102×. What focal length lens should the student attach to the other end of the tube? Get solution
67. You have found in the lab an old microscope, which has lost its eyepiece. It still has its objective lens, and markings indicate that its focal length is 7.00 mm. You can put in a new eyepiece, which goes in 20.0 cm from the objective. You need a magnification of about 200. Assume you want the comfortable viewing distance for the final image to be 25.0 cm. You find in a drawer eyepieces marked 2.00-, 4.00-, and 8.00-cm focal length. Which is your best choice? Get solution
68. A microscope has a 2.00-cm focal length eyepiece and a 0.800-cm objective lens. For a relaxed normal eye, calculate the position of the object if the distance between the lenses is 16.2 cm. Get solution
70. A refracting telescope has the objective lens of focal length 10.0 m. Assume it is used with an eyepiece of focal length 2.00 cm. What is the magnification of this telescope? Get solution
71. What is the magnification of a telescope with fo = 1.00 · 102 cm and fe = 5.00 cm? Get solution
73. Galileo discovered the moons of Jupiter in the fall of 1609. He used a telescope of his own design that had an objective lens with a focal length of fo = 40.0 inches and an eyepiece lens with a focal length of fe = 2.00 inches. Calculate the magnifying power of Galileo’s telescope. Get solution
74. Two distant stars are separated by an angle of 35 arcseconds. If you have a refracting telescope whose objective lens focal length is 3.5 m, what focal length eyepiece do you need in order to observe the stars as though they were separated by 35 arcminutes? Get solution
75. A 180× astronomical telescope is adjusted for a relaxed eye when the two lenses are 1.30 m apart. What is the focal length of each lens? Get solution
77. Some reflecting telescope mirrors utilize a rotating tub of mercury to produce a large parabolic surface. If the tub is rotating on its axis with an angular frequency ω, show that the focal length of the resulting mirror is: f = g/2 ω2. Get solution
78. An object 4.0 cm high is projected onto a screen using a converging lens with a focal length of 35 cm. The image on the screen is 56 cm. Where are the lens and the object located relative to the screen? Get solution
80. Suppose the near point of your eye is 2.0 · 101 cm and the far point is infinity. If you put on –0.20 diopter spectacles, what will be the range over which you will be able to see objects distinctly? Get solution
81. A fish is swimming in an aquarium at an apparent depth d = 1.00 · 101 cm. At what depth should you grab in order to catch it? Get solution
83. An object is 6.0 cm from a thin lens along the axis of the lens. If the lens has a focal length of 9.0 cm, determine the image distance. Get solution
84. A thin spherical lens is fabricated from glass so that it bulges outward in the middle on both sides. The glass lens has been ground so that the surfaces are part of a sphere with a radius of 25.0 cm on one side and a radius of 30.0 cm on the other. What is the power of this lens in diopters? Get solution
85. A diverging lens is fabricated from glass such that one surface of the lens is convex and the other surface is concave. The glass lens has been ground so that the convex surface is part of a sphere with a radius of 45 cm and the concave surface is part of a sphere with a radius of 2.0 · 101 cm. What is the power of this lens in diopters? Get solution
86. A person who is farsighted can see clearly an object that is at least 2.5 m away. To be able to read a book 2.0 · 101 cm away, what kind of corrective glasses should he purchase? Get solution
88. A girl forgets to put on her glasses and . finds that she needs to hold a book 15 cm from her eyes in order to clearly see the print.a) If she were to hold the book 25 cm away, what type of corrective lens would she need to use to clearly see the print?b) What is the focal length of the lens? Get solution
89. The focal length of the lens of a camera is 38.0 mm. How far must the lens be moved to change focus from a person 30.0 m away to one that is 5.00 m away? Get solution
90. A telescope is advertised as providing a magnification of magnitude 41 using an eyepiece of focal length 4.0 · 101 mm. What is the focal length of the objective? Get solution
91. Determine the position and size of the final image formed by a system of elements consisting of an object 2.0 cm high located at x = 0 m, a converging lens with focal length 5.0 · 101 cm located at x = 3.0 · 101 cm and a plane mirror located at x = 7.0 · 101 cm. Get solution
93. You visit your eye doctor and discover that you require lenses having a diopter value of –8.4. Are you nearsighted or farsighted? With uncorrected vision, how far away from your eyes must you hold a book to read clearly? Get solution
94. Jack has a near point of 32 cm and uses a magnifier of 25 diopter.a) What is the magnification if the final image is at infinity?b) What is the magnification if the final image is at the near point? Get solution
96. A diverging lens with f = –30.0 cm is placed 15.0 cm behind a converging lens with f = 20.0 cm. Where will an object at infinity in front of the converging lens be focused? Get solution
97. An instructor wants to use a lens to project a real image of a light bulb onto a screen 1.71 m from the bulb. In order to get the image to be twice as large as the bulb, what focal length lens will be needed? Get solution
99. A converging lens of focal length f = 50.0 cm is placed 175 cm to the left. of a metallic sphere of radius R = 100. cm. An object of height h = 20.0 cm is placed 30.0 cm to the le. of the lens. What is the height of the image formed by the metallic sphere? Get solution
100. When performing optical spectroscopy (for example, photoluminescence or Raman spectroscopy), a laser beam is focused on the sample to be investigated by means of a lens having a focal distance f. Assume that the laser beam exits a pupil Do in diameter that is located at a distance do from the focusing lens. For the case when the image of the exit pupil forms on the sample, calculatea) at what distance di from the lens is the sample located.b) the diameter Di of the laser spot (image of the exit pupil) on the sample.c) the numerical results for: f = 10.0 cm, Do = 2.00 mm, do = 1.50 m. Get solution
101. For a person whose near point is 115 cm, so that he can read a computer monitor at 55 cm, what power of reading glasses should his optician prescribe, keeping the lens–eye distance of 2.0 cm for his spectacles? Get solution
103. A lens of a pair of eyeglasses with index of refraction 1.723 has a power of 4.29 D in air. What is the power of this lens if it is put in water with n = 1.333? Get solution
104. A lens of a pair of eyeglasses has a power of 5.55 D in air. The power of this same lens is 2.262 if it is put in water with n = 1.333. What is the index of refraction of this lens? Get solution
105. A lens of a pair of eyeglasses with index of refraction 1.735 has a power of 2.794 D in water, with n = 1.333. What is the power of this lens if it is put in air? Get solution
107. A telescope, consisting of two lenses, has an objective lens with refractive power 0.186 D and an eyepiece with focal length of 5.33 cm. What is the absolute value of the angular magnification of this telescope? Get solution
108. A telescope, consisting of two lenses, has an objective lens with focal length 646.7 cm and an eyepiece with focal length 5.41 cm. What is the absolute value of its angular magnification? Get solution
1mcq. For a microscope to work as intended, the separation between the objective lens and the eyepiece must be such that the intermediate image produced by the objective lens will occur at a distance (as measured from the optical center of the eyepiece)a) slightly larger than the focal length.b) slightly smaller than the focal length.c) equal to the focal length.d) The position of the intermediate image is irrelevant. Get solution
2cc. If you move the object in Figure 33.4 to the left of its present location, the image willa) move to the left and become larger.b) move to the left and become smaller.c) remain unchanged.d) move to the right and become larger.e) move to the right and become smaller.Figure 33.4 Real image produced by a converging lens for the case that the object distance is larger than the focal length.... Get solution
2mcq. Which one of the following is not a characteristic of a simple two-lens astronomical refracting telescope?a) The final image is virtual.b) The objective forms a virtual image.c) The final image is inverted. Get solution
3cc. If you cover the top half of the lens in Figure 33.4 with a material that does not allow light to pass through, thena) the top half of the image will vanish.b) the bottom half of the image will vanish.c) the entire image will vanish.d) the entire image will still be visible, but will be fainter.e) nothing will change.Figure 33.4 Real image produced by a converging lens for the case that the object distance is larger than the focal length.... Get solution
3mcq. A converging lens will be used as a magnifying glass. In order for this to work, the object must be placed at a distancea) do > f.b) do = f.c) do f.d) None of the above. Get solution
4mcq. An object is moved from a distance of 30 cm to a distance of 10 cm in front of a converging lens of focal length 20 cm. What happens to the image?a) Image goes from real and upright to real and inverted.b) Image goes from virtual and upright to real and inverted.c) Image goes from virtual and inverted to real and upright.d) Image goes from real and inverted to virtual and upright.e) None of the above. Get solution
5cc. If you have a converging lens with a focal length of 15.0 cm in air and then put this lens in water, its focal length will bea) smaller than 15.0 cm.b) still the same 15.0 cm.c) larger than 15.0 cm.d) either smaller or larger than 15.0 cm, depending on the index of refraction of the lens. Get solution
5mcq. What type of lens is a magnifying glass?a) convergingb) divergingc) sphericald) cylindricale) plain Get solution
6mcq. LASIK surgery uses a laser to modify thea) curvature of the retina.b) index of refraction of the aqueous humor.c) curvature of the lens.d) curvature of the cornea. Get solution
7cc. What is the focal length (in meters) of a magnifying glass that gives an angular magnification of 6?a) 0.010 mb) 0.021 mc) 0.035 md) 0.042 me) 0.055 m Get solution
7mcq. What is the focal length of a flat sheet of transparent glass?a) zerob) infinityc) thickness of the glassd) undefined Get solution
8mcq. Where is the image formed if an object is placed 25 cm from the eye of a nearsighted person. What kind of a corrective lens should the person wear?a) Behind the retina. Converging lenses.b) Behind the retina. Diverging lenses.c) In front of the retina. Converging lenses.d) In front of the retina. Diverging lenses. Get solution
9cc. A hyperopic (farsighted) person can read a newspaper at a distance of d = 125 cm, but no closer. What power lens should this person use for reading if they wish to hold the newspaper at a distance of 25 cm from their eyes?a) –3.5 diopterb) –1.25 diopterc) +0.50 diopterd) +2.5 dioptere) +3.2 diopter Get solution
9mcq. An object is placed on the left of a converging lens at a distance that is less than the focal length of the lens. The image produced will bea) real and inverted.b) virtual and upright.c) virtual and inverted.d) real and upright. Get solution
10cc. A microscope is intended to have a linear magnification whose magnitude is 330. If the objective lens has a power of 350 diopter and the eyepiece lens has a power of 10.0 diopter, how long must the microscope be? Assuming final image is produced at a distance of 25 cm.a) 37.7 cmb) 40.0 cmc) 51.3 cmd) 65.0 cme) 75.0 cm Get solution
10mcq. What would you expect to happen to the magnitude of the power of a lens when it is placed in water (n = 1.33)?a) It would increase.b) It would decrease.c) It would stay the same.d) It would depend if the lens was converging or diverging. Get solution
11cc. Suppose a reflecting telescope consists of a concave spherical mirror with a radius of curvature R = 17.0 m and an eyepiece lens of focal length fe = 29.0 cm. What is the magnitude of the magnification of this telescope?a) 29.3b) 45.0c) 58.6d) 66.1e) 78.9 Get solution
11mcq. An unknown lens forms an image of an object that is 24 cm away from the lens, inverted, and a factor of 4 larger in size than the object. Where is the object located?a) 6 cm from the lens on the same side of the lensb) 6 cm from the lens on the other side of the lensc) 96 cm from the lens on the same side of the lensd) 96 cm from the lens on the other side of the lense) No object could have formed this image. Get solution
12cc. Reflecting telescopes with large mirror diameters are better than those with smaller diameters. Why?a) Because they have a shorter focal length.b) Because they have a longer focal length.c) Because they have a greater magnification.d) Because they can collect more light. Get solution
12mcq. A single lens with two convex surfaces made of sapphire with index of refraction n = 1.77 has surfaces with radii of curvature R1 = 27.0 cm and R2 = –27.0 cm. What is the focal length of this lens in air?a) 17.5 cmb) 27.0 cmc) 30.7 cmd) 40.8 cme) 54.0 cm Get solution
13mcq. A single lens with two convex surfaces made of sapphire with index of refraction n = 1.77 has surfaces with radii of curvature R1 = 27.0 cm and R2 = –27.0 cm. What is the focal length of this lens in water (n = 1.33)?a) 17.5 cmb) 27.0 cmc) 30.7 cmd) 40.8 cme) 54.0 cm Get solution
14mcq. An object is placed 15.0 cm to the left of a converging lens with focal length f = 5.00 cm, as shown in the figure. Where is the image formed?a) 1.25 cm to the right of the lensb) 2.75 cm to the left of the lensc) 3.75 cm to the right of the lensd) 5.00 cm to the left of the lense) 7.50 cm to the right of the lens... Get solution
15mcq. The eyepiece for the Yerkes telescope has a focal length of approximately 10 cm. The Hubble Space Telescope can reach an effective angular magnification factor of 8000. What would the focal length of the objective lens at Yerkes need to be in order to reach the same factor of 8000?a) 8 mb) 80 mc) 0.125 md) 0.00125 me) 800 m Get solution
16mcq. Where is the image of the objective lens of a microscope located and what does it look like?a) real and uprightb) real and invertedc) virtual and uprightd) virtual and inverted Get solution
17mcq. A pea sits at the focal point of a converging lens, 3 cm to the left of that lens on the optical axis. A second identical lens is at a distance of 12 cm to the right from the first one. Where is the image of the pea located, and is it real or virtual?a) A virtual image 3 cm to the left of lens 2b) A real image 3 cm to the left of lens 2c) A virtual image 3 cm to the right of lens 2d) A real image 3 cm to the right of lens 2e) No image can be formed, because the 2 lenses are more than 2 focal lengths apart. Get solution
18cq. Several small drops of paint (less than 1 mm in diameter) splatter on a painter’s eyeglasses, which are approximately 2 cm in front of the painter’s eyes. Do the dots appear in what the painter sees? How do the dots affect what the painter sees? Get solution
19cq. When a diver with 20/20 vision removes her mask underwater, her vision becomes blurry. Why is this the case? Does the diver become nearsighted (eye lens focuses in front of retina) or farsighted (eye lens focuses behind retina)? As the index of refraction of the medium approaches that of the lens, where does the object get imaged? Typically, the index of refraction for water is 1.33, while the index of refraction for the lens in a human eye is 1.40. Get solution
20cq. In H.G. Wells’s classic story The Invisible Man, a man manages to change the index of refraction of his body to 1.0; thus, light would not bend as it enters his body (assuming he is in air and not swimming). If the index of refraction of his eyes were equal to one, would he be able to see? If so, how would things appear? Get solution
21cq. Astronomers sometimes place filters in the path of light as it passes through their telescopes and optical equipment. The filters allow only a single color to pass through. What are the advantages of this? What are the disadvantages? Get solution
22cq. Is it possible to start a fire by focusing the light of the Sun with ordinary eyeglasses? How, or why not? Get solution
23cq. Will the magnification produced by a simple magnifier increase, decrease, or stay the same when the object and the lens are both moved from air into water? Get solution
24cq. Is it possible to design a system that will form an image without lenses or mirrors? If so, how? and what drawbacks, if any, would it have? Get solution
25cq. A lens system widely used in machine vision for dimensional measurement is the so-called telecentric lens system. In its basic configuration, it consists of two thin lenses of focal lengths f1 and f2, respectively, placed a distance d = f1 + f2 apart, and a small circular aperture called a stop aperture placed at the common focal point between the two lenses. The purpose of such a system is to provide a magnification that is independent of the distance between the object and the lens system, within a specified range of distances that define the so-called depth of field of the system.a) Draw a ray diagram through the system.b) Determine the magnification of such a system.c) Determine the requirements that must be met by the two lenses in order for a telecentric system to be able to image with maximum resolution an object with a diameter of 50.0 mm on a so-called ½ -inch CCD camera head (detector dimensions are ~ 6.50 mm × 5.00 mm). Get solution
26cq. Lenses or lens systems for photography are rated by both focal length and “speed.” The “speed” of a lens is measured by its f-number or f-stop, the ratio of its focal length to its aperture diameter. For many commercially available lenses this number is approximately a power of ..., e.g., 1.4, 2.0, 2.8, 4.0, etc.; the lens is provided with a mechanical iris diaphragm that can be set to different apertures or f-stops. The smaller the f-number, the “faster” the lens. “Faster” lenses are more expensive, as a wide aperture requires a higherquality lens.a) Explain the connection between f-number, (i.e., aperture diameter) and “speed.”b) Look up the necessary data and calculate the f-numbers of (the primary mirrors of) the Keck 10-meter telescope, the Hubble Space Telescope, and the Arecibo radio telescope. Get solution
27cq. The f-number of a photographic system determines not just its speed but also its “depth of field,” the range of distances over which objects remain in acceptable focus. Low f-numbers correspond to small depth of field, high f-numbers to large depth of field. Explain this. Get solution
28cq. Mirrors for astronomical instruments are invariably first-surface mirrors: The reflective coating is applied on the surface exposed to the incoming light. Household mirrors, on the other hand, are second-surface mirrors: The coating is applied to the back of the glass or plastic material of the mirror. (You can tell the difference by bringing the tip of an object close to the surface of the mirror. Object and image will nearly touch with a first-surface mirror; a gap will remain between them with a second-surface mirror.) Explain the reasons for these design differences. Get solution
30cq. Using ray tracing in the diagram below, find the image of the object (upright arrow) in the following system having a diverging (double-concave) lens. Is the image real or virtual? Is the image height less than or greater than the object height?... Get solution
31cq. You have made a simple telescope from two convex lenses. The objective lens is the one of the two lenses that is closer to the object being observed. What kind of image is produced by the eyepiece lens if the eyepiece is closer to the objective lens than the image produced by the objective lens? Get solution
33cq. A physics student epoxies two converging lenses to the opposite ends of a 2.0 · 101-cm-long tube. One lens has a focal length of f1 = 6.0 cm and the other has a focal length of f2 = 3.0 cm. She wants to use this device as a microscope. Which end should she look through to obtain the highest magnification of an object? Get solution
34. An object of height h is placed at a distance do on the left side of a converging lens of focal length f ( f do).a) What must do be in order for the image to form at a distance 3f on the right side of the lens?b) What will be the magnification? Get solution
36. A biconvex ice lens is made so that the radius of curvature of the front surface is 15.0 cm and that for the back is 20.0 cm. Determine how far you would put dry twigs if you wish to start a fire with your ice lens. Get solution
37. As a high-power laser engineer you need to focus a 1.06-mm diameter laser beam to a 10.0-µm diameter spot 20.0 cm behind the lens. What focal length lens would you use? Get solution
38. A plastic cylinder of length 3.0 · 101 cm has its ends ground to convex (from the rod outward) spherical surfaces, each having radius of curvature 1.0 · 101 cm. A small object is placed 1.0 · 101 cm from the left end. How far will the image of the object lie from the right end, if the index of refraction of the plastic is 1.5? Get solution
39. The object (upright arrow) in the following system has a height of 2.5 cm and is placed 5.0 cm away from a converging (convex) lens with a focal length of 3.0 cm. What is the magnification of the image? Is the image upright or inverted? Confirm your answers by ray tracing.... Get solution
40. Demonstrate that the minimum distance possible between a real object and its real image through a thin convex lens is 4f, where f is the focal length of the lens. Get solution
41. An air-filled cavity bound by two spherical surfaces is created inside a glass block. The two spherical surfaces have radii of 30.0 cm and 20.0 cm, respectively, and the thickness of the cavity is 40.0 cm (see diagram below). A light-emitting diode (LED) is embedded inside the block a distance of 60.0 cm in front of the cavity. Given nglass = 1.50 and nair = 1.00, and using only paraxial light rays (i.e., in the paraxial approximation):a) Calculate the final position of the image of the LED through the air-filled cavity.b) Draw a ray diagram showing how the image is formed... Get solution
42. To study a tissue sample better, a pathologist holds a 5.00-cm focal length magnifying glass 3.00 cm from the sample. How much magnification can he get from the lens? Get solution
43. Suppose a magnifying glass has a focal length of 5.0 cm. Find the magnifying power of this glass when the object is placed at the near point. Get solution
44. What is the focal length of a magnifying glass if a 1.0-mm object appears to be 10. mm? Get solution
45. A person with a near-point distance of 24.0 cm finds that a magnifying glass gives an angular magnification that is 1.25 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? Get solution
46. A beam of parallel light, 1.00 mm in diameter passes through a lens with a focal length of 10.0 cm. Another lens, this one of focal length 20.0 cm, is located behind the first lens so that the light traveling out from it is again parallel.a) What is the distance between the two lenses?b) How wide is the outgoing beam? Get solution
47. How large does a 5.0-mm insect appear when viewed with a system of two identical lenses of focal length 5.0 cm separated by a distance 12.0 cm if the insect is 10.0 cm from the first lens? Is the image real or virtual? Inverted or upright? Get solution
48. Three converging lenses of focal length 5.0 cm are arranged with a spacing of 2.0·101 cm between them, and are used to image an insect 2.0·101 cm away.a) Where is the image?b) Is it real or virtual?c) Is it upright or inverted? Get solution
49. Two identical thin convex lenses, each of focal length f, are separated by a distance d = 2.5f. An object is placed in front of the first lens at a distance do,1 = 2f.a) Calculate the position of the final image of the object through the system of lenses.b) Calculate the total transverse magnification of the system.c) Draw the ray diagram for this system and show the final image.d) Describe the final image (real or virtual, erect or inverted, larger or smaller) in relation to the initial object.... Get solution
50. Two converging lenses with focal lengths 5.00 cm and 10.0 cm, respectively, are placed 30.0 cm apart. An object of height h = 5.00 cm is placed 10.0 cm to the left of the 5.00-cm lens. What will be the position and height of the final image produced by this lens system? Get solution
51. Two lenses are used to create an image for a source 10.0 cm tall that is located 30.0 cm to the left of the first lens, as shown in the figure. Lens L1 is a biconcave lens made of crown glass (index of refraction n = 1.55) and has a radius of curvature of 20.0 cm for both surface 1 and 2. Lens L2 is 40.0 cm to the right of the first lens L1. Lens L2 is a converging lens with a focal length of 30.0 cm. At what distance relative to the object does the image get formed? Determine this position by sketching rays and calculating algebraically.... Get solution
52. Sophisticated optical systems can be analyzed and designed with the aid of techniques from linear algebra. Light rays (or particle beams) are described at any point along the axis of the system by a two-component column vector containing y, the distance of the ray from the optic axis, and dy/dx, the slope of the ray. Components of the system are described by 2×2 matrices which incorporate their effects on the ray; combinations of components are described by products of these matrices.a) A thin lens does not alter the position of a ray, but increases (diverging) or decreases (converging) its slope an amount proportional to the distance of the ray from the axis. Construct the matrix for a thin lens of focal length f.b) A space between components does not alter the slope of a ray; the distance of the ray from the axis changes by the slope of the ray times the length of the space. Write the matrix for a space of length x.c) Write the matrix for the two-lens “zoom lens” system described in Section 33.3. Get solution
53. The typical length of a human eyeball is 2.50 cm.a) What is the effective focal length of the two-lens system made from a normal person’s cornea and lens when viewing objects far away?b) What is the effective focal length for viewing objects at the near point? Get solution
54. Using your answers from the previous question, and given that the cornea in a typical human eye has a fixed focal length of 2.33 cm, what range of focal lengths does the lens in a typical eye have? Get solution
55. Jane has a near point of 125 cm and wishes to read from a computer screen 40. cm from her eye.a) What is the object distance?b) What is the image distance?c) What is the focal length?d) What is the power of the corrective lens needed?e) Is the corrective lens diverging or converging? Get solution
56. Bill has a far point of 125 cm and wishes to see distant objects clearly.a) What is the object distance?b) What is the image distance?c) What is the focal length?d) What is the power of the corrective lens needed?e) Is the corrective lens diverging or converging? Get solution
57. A person wearing bifocal glasses is reading a newspaper a distance of 25 cm. The lower part of the lens is converging for reading and has a focal length of 70. cm. The upper part of the lens is diverging for seeing at distances far away and has a focal length of 50. cm. What are the uncorrected near and far points for the person? Get solution
58. The radius of curvature for the outer part of the cornea is 8.0 mm, the inner portion is relatively flat. If the index of refraction of the cornea and the aqueous humor is 1.34:a) Find the power of the cornea.b) If the combination of the lens and the cornea has a power of 50. diopter, find the power of the lens (assume the two are touching). Get solution
59. As objects are moved closer to the human eye, the ciliary muscle causes the lens at the front of the eye to become more curved, thereby decreasing the focal length of the lens. The shortest focal length fmin of this lens is typically 2.3 cm. What is the closest one can bring an object to a normal human eye (see left side of figure below) and still have the image of the object projected sharply on the retina, which is 2.5 cm behind the lens? Now consider a nearsighted human eye that has the same fmin but is stretched horizontally, with a retina that is 3.0 cm behind the lens (see right side of figure below). What is the closest one can bring an object to this nearsighted human eye and still have the image of the object projected sharply on the retina. Compare the maximum angular magnification produced by this nearsighted eye with that of the normal eye.... Get solution
60. A person is nearsighted (myopic). The power of his eyeglass lenses is –5.75 diopters, and he wears the lenses 1.00 cm in front of his corneas. What is the prescribed power of his contact lenses? Get solution
61. An amateur photographer attempts to build a custom zoom lens using a converging lens followed by a diverging lens. The two lenses are separated by a distance x = 50. mm as shown below. If the focal length of the first lens is 2.0 · 102 mm and the focal length of the second lens is –3.0 · 102 mm, what will the effective focal length of this compound lens be? What will feff be if the lens separation is changed to 1.0 · 102 mm?... Get solution
62. For a certain camera, the distance between the lens and the film is 10.0 cm. You observe that objects that are very far away appear properly focused. How far from the film would you have to move the lens in order to properly focus an object 100. cm away? Get solution
63. A camera has a lens with a focal length of 60. mm. Suppose you replace the normal lens with a zoom lens whose focal length can be varied from 35. mm to 250. mm and use the camera to photograph an object very far away. Compared to a 60.-mm lens, what magnification of the image would be achieved using the 240.-mm focal length? Get solution
64. A camera lens usually consists of a combination of two or more lenses to produce a good-quality image. Suppose a camera lens has two lenses—a diverging lens of focal length 10.0 cm and a converging lens of focal length 5.00 cm. The two lenses are held 7.00 cm apart. A flower of length 10.0 cm, to be pictured, is held upright at a distance 50.0 cm in front of the diverging lens; the converging lens is placed behind the diverging lens. What are the location, orientation, size, and the magnification of the final image? Get solution
65. A student finds a tube 20. cm long with a lens attached to one end. The attached lens has a focal length of 0.70 cm. The student wants to use the tube and lens to make a microscope with a magnification of 3.0 · 102×. What focal length lens should the student attach to the other end of the tube? Get solution
67. You have found in the lab an old microscope, which has lost its eyepiece. It still has its objective lens, and markings indicate that its focal length is 7.00 mm. You can put in a new eyepiece, which goes in 20.0 cm from the objective. You need a magnification of about 200. Assume you want the comfortable viewing distance for the final image to be 25.0 cm. You find in a drawer eyepieces marked 2.00-, 4.00-, and 8.00-cm focal length. Which is your best choice? Get solution
68. A microscope has a 2.00-cm focal length eyepiece and a 0.800-cm objective lens. For a relaxed normal eye, calculate the position of the object if the distance between the lenses is 16.2 cm. Get solution
70. A refracting telescope has the objective lens of focal length 10.0 m. Assume it is used with an eyepiece of focal length 2.00 cm. What is the magnification of this telescope? Get solution
71. What is the magnification of a telescope with fo = 1.00 · 102 cm and fe = 5.00 cm? Get solution
73. Galileo discovered the moons of Jupiter in the fall of 1609. He used a telescope of his own design that had an objective lens with a focal length of fo = 40.0 inches and an eyepiece lens with a focal length of fe = 2.00 inches. Calculate the magnifying power of Galileo’s telescope. Get solution
74. Two distant stars are separated by an angle of 35 arcseconds. If you have a refracting telescope whose objective lens focal length is 3.5 m, what focal length eyepiece do you need in order to observe the stars as though they were separated by 35 arcminutes? Get solution
75. A 180× astronomical telescope is adjusted for a relaxed eye when the two lenses are 1.30 m apart. What is the focal length of each lens? Get solution
77. Some reflecting telescope mirrors utilize a rotating tub of mercury to produce a large parabolic surface. If the tub is rotating on its axis with an angular frequency ω, show that the focal length of the resulting mirror is: f = g/2 ω2. Get solution
78. An object 4.0 cm high is projected onto a screen using a converging lens with a focal length of 35 cm. The image on the screen is 56 cm. Where are the lens and the object located relative to the screen? Get solution
80. Suppose the near point of your eye is 2.0 · 101 cm and the far point is infinity. If you put on –0.20 diopter spectacles, what will be the range over which you will be able to see objects distinctly? Get solution
81. A fish is swimming in an aquarium at an apparent depth d = 1.00 · 101 cm. At what depth should you grab in order to catch it? Get solution
83. An object is 6.0 cm from a thin lens along the axis of the lens. If the lens has a focal length of 9.0 cm, determine the image distance. Get solution
84. A thin spherical lens is fabricated from glass so that it bulges outward in the middle on both sides. The glass lens has been ground so that the surfaces are part of a sphere with a radius of 25.0 cm on one side and a radius of 30.0 cm on the other. What is the power of this lens in diopters? Get solution
85. A diverging lens is fabricated from glass such that one surface of the lens is convex and the other surface is concave. The glass lens has been ground so that the convex surface is part of a sphere with a radius of 45 cm and the concave surface is part of a sphere with a radius of 2.0 · 101 cm. What is the power of this lens in diopters? Get solution
86. A person who is farsighted can see clearly an object that is at least 2.5 m away. To be able to read a book 2.0 · 101 cm away, what kind of corrective glasses should he purchase? Get solution
88. A girl forgets to put on her glasses and . finds that she needs to hold a book 15 cm from her eyes in order to clearly see the print.a) If she were to hold the book 25 cm away, what type of corrective lens would she need to use to clearly see the print?b) What is the focal length of the lens? Get solution
89. The focal length of the lens of a camera is 38.0 mm. How far must the lens be moved to change focus from a person 30.0 m away to one that is 5.00 m away? Get solution
90. A telescope is advertised as providing a magnification of magnitude 41 using an eyepiece of focal length 4.0 · 101 mm. What is the focal length of the objective? Get solution
91. Determine the position and size of the final image formed by a system of elements consisting of an object 2.0 cm high located at x = 0 m, a converging lens with focal length 5.0 · 101 cm located at x = 3.0 · 101 cm and a plane mirror located at x = 7.0 · 101 cm. Get solution
93. You visit your eye doctor and discover that you require lenses having a diopter value of –8.4. Are you nearsighted or farsighted? With uncorrected vision, how far away from your eyes must you hold a book to read clearly? Get solution
94. Jack has a near point of 32 cm and uses a magnifier of 25 diopter.a) What is the magnification if the final image is at infinity?b) What is the magnification if the final image is at the near point? Get solution
96. A diverging lens with f = –30.0 cm is placed 15.0 cm behind a converging lens with f = 20.0 cm. Where will an object at infinity in front of the converging lens be focused? Get solution
97. An instructor wants to use a lens to project a real image of a light bulb onto a screen 1.71 m from the bulb. In order to get the image to be twice as large as the bulb, what focal length lens will be needed? Get solution
99. A converging lens of focal length f = 50.0 cm is placed 175 cm to the left. of a metallic sphere of radius R = 100. cm. An object of height h = 20.0 cm is placed 30.0 cm to the le. of the lens. What is the height of the image formed by the metallic sphere? Get solution
100. When performing optical spectroscopy (for example, photoluminescence or Raman spectroscopy), a laser beam is focused on the sample to be investigated by means of a lens having a focal distance f. Assume that the laser beam exits a pupil Do in diameter that is located at a distance do from the focusing lens. For the case when the image of the exit pupil forms on the sample, calculatea) at what distance di from the lens is the sample located.b) the diameter Di of the laser spot (image of the exit pupil) on the sample.c) the numerical results for: f = 10.0 cm, Do = 2.00 mm, do = 1.50 m. Get solution
101. For a person whose near point is 115 cm, so that he can read a computer monitor at 55 cm, what power of reading glasses should his optician prescribe, keeping the lens–eye distance of 2.0 cm for his spectacles? Get solution
103. A lens of a pair of eyeglasses with index of refraction 1.723 has a power of 4.29 D in air. What is the power of this lens if it is put in water with n = 1.333? Get solution
104. A lens of a pair of eyeglasses has a power of 5.55 D in air. The power of this same lens is 2.262 if it is put in water with n = 1.333. What is the index of refraction of this lens? Get solution
105. A lens of a pair of eyeglasses with index of refraction 1.735 has a power of 2.794 D in water, with n = 1.333. What is the power of this lens if it is put in air? Get solution
107. A telescope, consisting of two lenses, has an objective lens with refractive power 0.186 D and an eyepiece with focal length of 5.33 cm. What is the absolute value of the angular magnification of this telescope? Get solution
108. A telescope, consisting of two lenses, has an objective lens with focal length 646.7 cm and an eyepiece with focal length 5.41 cm. What is the absolute value of its angular magnification? Get solution
