1cc. In Solved Problem 32.1, we neglected the size of the light bulb
and treated it as a point source. What happens if the light bulb is too
large to make this assumption, for example, if it is larger than the
baseball?a) The shadow of the ball will not be sharp but will be fuzzy
around the edge.b) No shadow will be formed.c) Multiple shadows will be
formed.d) It is impossible to make a general statement about this
situation. Get solution
1mcq. Legend says that Archimedes set the Roman fleet on fire as it was invading Syracuse. Archimedes created a huge ________ mirror and used it to focus the Sun’s rays on the Roman vessels.a) planeb) parabolic divergingc) parabolic converging Get solution
2cc. An observer (represented by the eye in the figure) is looking at a light bulb reflected in a plane mirror. To the observer, where does the image of the light bulb appear to be?... Get solution
2mcq. Which of the following interface combinations has the smallest critical angle?a) light traveling from ice to diamondb) light traveling from quartz to Lucitec) light traveling from diamond to glassd) light traveling from Lucite to diamonde) light traveling from Lucite to quartz Get solution
3cc. The mirror equation tells us thata) moving an object farther from a converging mirror means that the image will be formed farther from the mirror.b) moving an object farther from a converging mirror means that the image will be formed closer to the mirror.c) either of the above could occur, depending on the focal length of the mirror. Get solution
3mcq. For specular reflection of a light ray, the angle of incidencea) must be equal to the angle of reflection.b) is always less than the angle of reflection.c) is always greater than the angle of reflection.d) is equal to 90°—the angle of reflection.e) may be greater than, less than, or equal to the angle of reflection. Get solution
4cc. Moving the object in Example 32.2 10% closer to the mirror would produce an image that wasa) closer to the mirror and larger than before.b) closer to the mirror and smaller than before.c) farther from the mirror and larger than before.d) farther from the mirror and smaller than before.e) It is not possible to predict the image’s characteristics.Exampl e 32.2 I mage Formed by a Converging Mirror...... Get solution
4mcq. Standing by a pool filled with water, under what condition will you see a reflection of the scenery on the opposite side through total internal reflection of the light from the scenery?a) Your eyes are level with the water.b) You observe the pool at an angle of 41.8°.c) There is no condition under which this can occur.d) You observe the pool at an angle of 48.2°. Get solution
5cc. Suppose you have a liquid-mirror telescope with focal length f1, and you want to double this focal length. What adjustment do you have to make to the rotational angular velocity of the liquid?a) reduce it by a factor of 0.5b) reduce it by a factor of 0.707c) keep it the samed) increase it by a factor of 0.707e) increase it by a factor of 2 Get solution
6cc. Using flat mirrors to focus the Sun’s rays at the top of a tower, as is done by the power plant shown in Figure 32.35, is only possible becausea) the Sun is essentially infinitely far away, so its rays are parallel when they strike the mirrors.b) the orientations of the flat mirrors are continuously and individually adjusted by computerized controls.c) the mirrors are located in a parabolic bowl.d) the Sun is directly overhead in Spain for several hours each day.e) the Earth is a sphere with a very large radius of curvature.Figure 32.35 The world’s first commercial tower solar farm, an 11-MW installation in Sanlúcar la Mayor, Spain.... Get solution
6mcq. What is the magnification for a plane mirror?a) +1b) –1c) greater than +1d) not defined for a plane mirror Get solution
7cc. If the same fish swimming at the same depth is seen by a different observer whose line of sight is at an angle larger than that given in Example 32.3, then, to that observer, the fish’s apparent depth will bea) larger than that calculated in Example 32.3.b) the same as that calculated in Example 32.3.c) smaller than that calculated in Example 32.3.Example 32.3 A pparent Depth...... Get solution
7mcq. A small object is placed in front of a converging mirror with radius R = 7.50 cm so that the image distance equals the object distance. How far is this object from the mirror?a) 2.50 cmb) 5.00 cmc) 7.50 cmd) 10.0 cme) 15.0 cm Get solution
8cc. In Solved Problem 32.2, the sheet of transparent material was surrounded by air. If the sheet were surrounded by water instead, what would happen to the displacement of the light ray with the same angle of incidence? (Assume that the index of refraction of the transparent material is still larger than that of water.)a) It would be larger.b) It would be the same.c) It would be smaller. Get solution
8mcq. Sunlight strikes a piece of glass at an angle of incidence of θi = 33.4°. What is the difference between the angle of refraction of a red light ray (λ = 660.0 nm) and that of a violet light ray (λ = 410.0 nm)? The glass’s index of refraction is n = 1.520 for red light and n = 1.538 for violet light.a) 0.03°b) 0.12°c) 0.19°d) 0.26°e) 0.82° Get solution
9cc. At the boundary between water and air, the critical angle for total internal reflection in the water is 48°. What does a diver in a swimming pool see when looking from under the water toward the surface at an angle greater than 48°?a) the sky above the poolb) the reflection of the floor of the poolc) a superposition of the sky and the reflection of the floord) nothing, because no light can reach the eyes of a diver looking toward the surface at this angle Get solution
9mcq. The image of yourself that you see in a bathroom mirror isa) left-right inverted.b) front-to-back inverted.c) bottom-to-top inverted.d) not inverted. Get solution
10mcq. Where do you have to place an object in front of a concave mirror with focal length f for the image to be the same size as the object?a) at do = 0.5fb) at do = fc) at do = 2fd) at do = 2.5fe) none of the above Get solution
11mcq. You are looking down into a swimming pool at an angle of 20° relative to the vertical, and you see a coin at the bottom of the pool. This coin appears to you to be ata) a lesser depth than it really is.b) the same depth as it really is.c) a greater depth than it really is. Get solution
12mcq. You are looking straight down into a swimming pool, that is, at an angle of 0° relative to the vertical, and you see a coin at the bottom of the pool. This coin appears to you to be ata) a lesser depth than it really is.b) the same depth as it really is.c) a greater depth than it really is. Get solution
13cq. The figure shows the difference between the refractive index profile of a step index fiber and the refractive index profile of a graded index fiber. Applying geometric optics principles, comment on the path followed by a light ray entering each of the optic fibers.... Get solution
15cq. A concave spherical mirror is used to create an image of an object 5.00 cm tall that is located at position x = 0 cm, which is 20.0 cm from point C, the center of curvature of the mirror, as shown in the figure. The magnitude of the radius of curvature of the mirror is 10.0 cm. Without changing the mirror, how can you reduce the spherical aberration produced by it? Are there any disadvantages to your approach to reducing the spherical aberration?... Get solution
14cq. A slab of Plexiglas 2.00 cm thick with index of refraction 1.51 is placed over a physics textbook. The slab has parallel sides. The text is at height y = 0. Consider two rays of light, A and B, that originate at the letter “t” in the text under the Plexiglas and travel toward an observer who is above the Plexiglas, looking down. Draw> on the figure the apparent y-position of the letter under the Plexiglas as seen by the observer. (Hint: From where in the Plexiglas do the two rays appear to originate for the observer?) You can easily do this experiment yourself. If you do not have a block of glass or Plexiglas, you can try placing a flat-bottomed drinking glass over the text.... Get solution
16cq. If you look at an object at the bottom of a pool, the pool looks less deep than it actually is.a) From what you have learned, calculate how deep a pool seems to be if it is actually 4 feet deep and you look directly down on it. The index of refraction of water is 1.33.b) Would the pool look more or less deep than it actually is if you looked at it from an angle other than vertical? Answer this qualitatively, without using an equation. Get solution
19cq. A physics student is eying a steel drum, the top part of which has the approximate shape of a concave spherical surface. The surface is sufficiently polished that the student can just make out the reflection of her finger when she places it above the drum. As she slowly moves her finger toward the surface and then away from it, you ask her what she is doing. She replies that she is estimating the radius of curvature of the drum. How can she do that? Get solution
17cq. Why does refraction occur? That is, what is the physical reason a wave moves with a different velocity when it passes from one medium into another? Get solution
18cq. Many optical fibers have minimum specified bending radii. Why? Get solution
20cq. State whether the following is true or false and explain your answer: The wavelength of He-Ne laser light in water is less than its wavelength in air. (The index of refraction of water is 1.33.) Get solution
22cq. A 45°-45°-90° triangular prism can be used to reverse a light beam: The light enters perpendicular to the hypotenuse of the prism, reflects off each leg, and emerges perpendicular to the hypotenuse again. The surfaces of the prism are not silvered. If the prism is made of glass with index of refraction nglass = 1.520 and is surrounded by air, the light beam will be reflected with a minimum loss of intensity (there are reflection losses as the light enters and leaves the prism).a) Will this work if the prism is under water, which has the index of refraction nH2O =1.333?b) Such prisms are used, in preference to mirrors, to bend the optical path in quality binoculars. Why? Get solution
21cq. Among the instruments Apollo astronauts left on the Moon were reflectors for bouncing laser beams back to Earth. These made it possible to measure the distance from the Earth to the Moon with unprecedented precision (uncertainties of a few centimeters in 384,000 km), for the study of both celestial mechanics and Earth’s plate tectonics. The reflectors consist not of ordinary mirrors, but of arrays of corner cubes, each constructed of three square plane mirrors fixed perpendicular to each other, as adjacent faces of a cube. Why? Explain the functioning and advantages of this design. Get solution
25cq. Holding a spoon in front of your face, convex side toward you, estimate the location of the image and its magnification. Get solution
23cq. An object is imaged by a converging spherical mirror as shown in the figure. Suppose a black cloth is put between the object and the mirror so that it covers everything above the optic axis. How will the image be affected?... Get solution
24cq. You are under water in a pond and look up through the smooth surface of the water at the Sun in the sky. Is the Sun in fact higher in the sky than it appears to you, or is it lower? Get solution
28. A periscope consists of two flat mirrors and is used for viewing objects when an obstacle impedes direct viewing. Suppose Curious George is looking through a periscope, in which the two flat mirrors are separated by a distance L = 0.400 m, at the Man in the Yellow Hat, whose hat is at do = 3.00 m from the upper mirror. What is the distance D of the final image of the yellow hat from the lower mirror? Get solution
27. A person sits 1.00 m in front of a plane mirror. What is the location of the image? Get solution
26cq. A solar furnace uses a large parabolic mirror (such mirrors can be several stories high) to focus the light of the Sun to heat a target. A large solar furnace can melt metals. Is it possible to attain temperatures exceeding 6000 K (the temperature of the photosphere of the Sun) in a solar furnace? If so, how? If not, why not? Get solution
29. A person stands at a point P relative to two plane mirrors oriented at 90.0°, as shown in the figure. How far away from each other do the person’s images appear to be?... Get solution
30. Even the best mirrors absorb or transmit some of the light incident on them. The highest-quality mirrors might reflect 99.997% of the incident light. Suppose a cubical “room,” 3.00 m on an edge, were constructed with such mirrors for the walls, floor, and ceiling. How slowly would such a room get dark? Estimate the time required for the intensity of light in such a room to fall to 1.00% of its initial value after the only light source in the room was switched off. Get solution
31. The radius of curvature of a convex mirror is –25.0 cm. What is its focal length? Get solution
32. A concave spherical mirror is used to create an image of an object 5.00 cm tall that is located at position x = 0 cm, which is 20.0 cm from point C, the center of curvature of the mirror, as shown in the figure. The magnitude of the radius of curvature of the mirror is 10.0 cm. Calculate the position xi where the image is formed. Use the coordinate system given in the drawing. What is the height hi of the image? Is the image upright (pointing up) or inverted (pointing down)? Is it real or virtual?... Get solution
34. A 5.00-cm-tall object is placed 30.0 cm away from a convex mirror with a focal length of –10.0 cm. Determine the size, orientation, and position of the image. Get solution
33. Convex mirrors are often used as sideview mirrors on cars. Many such mirrors display the warning “Objects in mirror are closer than they appear.” Assume that a convex sideview mirror has a radius of curvature of 14.0 m and that a car is 11.0 m behind the mirror. For a flat mirror, the image distance would be 11.0 m, and the magnification would be 1. Find the image distance and the magnification for this convex mirror. Get solution
35. The magnification of a convex mirror is 0.60× for an object 2.0 m from the mirror. What is the focal length of this mirror? Get solution
36. An object is located at a distance of 100. cm from a concave mirror of focal length 20.0 cm. Another concave mirror of focal length 5.00 cm is located 20.0 cm in front of the first concave mirror. The reflecting sides of the two mirrors face each other. What is the location of the final image formed by the two mirrors and the total magnification produced by them in combination? Get solution
37. The shape of an elliptical mirror is described by the curve ... with semimajor axis a and semiminor axis b. The foci of this ellipse are at the points (c,0) and (–c,0), with c = (a2 – b2)1/2. Show that any light ray in the xy-plane that passes through one focus is reflected through the other. “Whispering galleries” make use of this phenomenon for reflecting sound waves. Get solution
38. What is the speed of light in crown glass, whose index of refraction is 1.52? Get solution
39. An optical fiber with an index of refraction of 1.50 is used to transport light of wavelength 400. nm. What is the critical angle for transporting light through this fiber without loss? If the fiber is immersed in water? In oil? Get solution
40. A helium-neon laser produces light of wavelength λvac = 632.8 nmin vacuum. If this light passes into water, with index of refraction n = 1.333, what will each of the following characteristics be?a) speedb) frequencyc) wavelengthd) color Get solution
41. A light ray is incident from water, whose index of refraction is 1.33, on a plate of glass whose index of refraction is 1.73. What angle of incidence will result in fully polarized reflected light? Get solution
42. Suppose you are standing at the bottom of a swimming pool whose surface is perfectly calm. Looking up, you see a circular window to the “outer world.” If your eyes are approximately 2.00 m beneath the surface, what is the diameter of this circular window? Get solution
43. A ray of light of a particular wavelength is incident on an equilateral triangular prism whose index of refraction for light of this wavelength is 1.23. The ray is parallel to the base of the prism as it approaches and enters the prism at the midpoint of one of the sides, as shown in the figure. What is the direction of the ray when it emerges from the prism?... Get solution
44. A collimated laser beam strikes the left side (A) of a glass block at an angle of 20.0° with respect to the horizontal, as shown in the figure. The block has an index of refraction of 1.55 and is surrounded by air, with an index of refraction of 1.00. The left side of the glass block is vertical (90.0° from horizontal) while the right side (B) is at an angle of 60.0° from the horizontal. Determine the angle θBT with respect to the horizontal at which the light exits surface B.... Get solution
45. In a step index fiber, the index of refraction undergoes a discontinuity (jump) at the core-cladding boundary, as shown in the figure. Infrared light with wavelength 1550 nm propagates through such a fiber by total internal reflection at the corecladding boundary. The index of refraction of the core for the infrared light is ncore = 1.48. If the maximum angle, αmax, at which light can enter the fiber with no light lost into the cladding is αmax = 14.033°, calculate the percent difference between the index of refraction of the core and the index of refraction of the cladding....... Get solution
46. Refer to Figure 32.51 and prove that the arc of the primary rainbow represents the 42° angle from the direction of the sunlight.Figure 32.51 The paths taken by parallel light rays in a spherical drop of water.... Get solution
47. Use Fermat’s Principle to derive the law of reflection. Get solution
48. Fermat’s Principle, from which geometric optics can be derived, states that light travels by a path that minimizes the time of travel between points. Consider a light beam that travels a horizontal distance D and a vertical distance h, through two large flat slabs of material that have a vertical interface between them. One slab has a thickness D/2 and an index of refraction n1, and the other has a thickness D/2 and an index of refraction n2. Write the equation relating the indices of refraction and the angles from the horizontal that the light beam makes at the interface (θ1 and θ2) which minimize the time for this travel. Get solution
49. Suppose your height is 2.00 m and you are standing 50.0 cm in front of a plane mirror.a) What is the image distance?b) What is the image height?c) I s the image inverted or upright?d) Is the image real or virtual? Get solution
50. A light ray of wavelength 700. nm traveling in air (n1 = 1.00) is incident on a boundary with a liquid (n2 = 1.63).a) What is the frequency of the refracted ray?b) What is the speed of the refracted ray?c) What is the wavelength of the refracted ray? Get solution
51. You have a spherical mirror with a radius of curvature of +20.0 cm (so it is concave facing you). You are looking at an object whose image size you want to double so you can see it better. At what locations could you put the object? Where will the images be for these object locations, and will they be real or virtual? Get solution
52. You are submerged in a swimming pool. What is the maximum angle at which you can see light coming from above the pool surface? That is, what is the angle for total internal reflection from water into air? Get solution
53. Light hits the surface of water at an incident angle of 30.0° with respect to the normal to the surface. What is the angle between the reflected ray and the refracted ray? Get solution
54. A spherical metallic Christmas tree ornament has a diameter of 8.00 cm. If Saint Nicholas is by the fireplace, 1.56 m away, where will he see his reflection in the ornament? Is the image real or virtual? Get solution
55. One of the factors that cause a diamond to sparkle is its relatively small critical angle. Compare the critical angle for diamond in air with that for diamond in water. Get solution
56. What kind of image, virtual or real, is formed by a converging mirror when the object is placed a distance away from the mirror that isa) beyond the center of curvature of the mirror,b) between the center of curvature and half of the distance to the center of curvature, andc) closer than half of the distance to the center of curvature? Get solution
57. At what angle θ shown in the figure must a beam of light enter the water for the reflected beam to make an angle of 40.0° with respect to the normal of the water’s surface?... Get solution
59. How deep does a point in the middle of a 3.00-m-deep pool appear to be to a person standing beside the pool at a position 2.00 m horizontally from the point? Take the index of refraction for the liquid in the pool to be 1.30 and that for air to be 1.00. Get solution
60. What is the smallest incident angle θ i at which the light beam shown in the figure ill undergo total internal reflection in the prism, if the index of refraction of the prism for light of this wavelength is 1.500?... Get solution
62. Refer to Example 32.3 and use the numbers provided there. Further, assume that your eyes are at a height of 1.70 m above the water.a) Calculate the time it takes for light to travel on the path from the fish to your eyes.b) Calculate the time light would take on a straight-line path from the fish to your eyes.c) Calculate the time light would take on a path from the fish vertically upward to the water surface and then straight to your eyes.d) Calculate the time light would take on the straight-line path from the apparent location of the fish to your eyes.e) What can you say about Fermat’s Principle from the results of parts (a) through (d)?Example 32.3 A pparent Depth...... Get solution
63. If you want to construct a liquid mirror of focal length 2.50 m, with what angular velocity do you have to rotate your liquid? Get solution
64. One proposal for a space-based telescope is to put a large rotating liquid mirror on the Moon. Suppose you want to use a liquid mirror that is 100.0 m in diameter and has a focal length of 347.5 m. The gravitational acceleration on the Moon is 1.62 m/s2.a) What angular velocity does your mirror have?b) What is the linear speed of a point on the perimeter of the mirror?c) How high above the center is the perimeter of the mirror? Get solution
65. The origin of a coordinate system is placed at the center of curvature of a spherical mirror with radius of curvature R = 58.1 cm (see the figure). An object is placed at xo = 19.7 cm. What is the x-coordinate of the image?... Get solution
66. The origin of a coordinate system is placed at the center of curvature of a spherical mirror with radius of curvature R = 59.3 cm (see the figure). An object is placed at xo = 39.5 cm. What is the mirror’s magnification? Get solution
67. The origin of a coordinate system is placed at the center of a spherical mirror with radius of curvature R (see the figure). An object is placed at xo = 10.1 cm. The image is formed at x = –7.405 cm. What is the value of R? Get solution
68. The origin of a coordinate system is placed at the center of curvature of a spherical mirror with radius of curvature R (see the figure). An object is placed at xo = 10.3 cm. The image is formed at x = –7.548 cm. What is the focal length of the mirror? Get solution
69. A layer of methyl alcohol, with index of refraction 1.329, rests on a block of ice, with index of refraction 1.310. A ray of light passes through the methyl alcohol at an angle of φ1 = 61.07° relative to the alcohol-ice boundary. What is the angle φ2 relative to the boundary at which the ray passes through the ice?... Get solution
70. A layer of a transparent material rests on a block of fused quartz, whose index of refraction is 1.460. A ray of light passes through the unknown material at an angle of φ1 = 63.65° relative to the boundary between the materials and is refracted at an angle of φ2 =70.26° relative to the boundary. What is the index of refraction of the unknown material? Get solution
71. A layer of carbon dioxide, with index of refraction 1.00045, rests on a block of ice, with index of refraction 1.310. A ray of light passes through the carbon dioxide at an angle of φ 1 relative to the boundary between the materials and then passes through the ice at an angle of φ 2 = 72.06° relative to the boundary. What is the value of φ1? Get solution
72. A layer of water, with index of refraction 1.333, rests on a block of an unknown transparent material. A ray of light passes through the water at an angle of φ1 = 68.77° relative to the boundary between the materials and then passes through the unknown material at an angle of φ2 = 72.98° relative to the boundary. What is the speed of light in the unknown material? Get solution
1mcq. Legend says that Archimedes set the Roman fleet on fire as it was invading Syracuse. Archimedes created a huge ________ mirror and used it to focus the Sun’s rays on the Roman vessels.a) planeb) parabolic divergingc) parabolic converging Get solution
2cc. An observer (represented by the eye in the figure) is looking at a light bulb reflected in a plane mirror. To the observer, where does the image of the light bulb appear to be?... Get solution
2mcq. Which of the following interface combinations has the smallest critical angle?a) light traveling from ice to diamondb) light traveling from quartz to Lucitec) light traveling from diamond to glassd) light traveling from Lucite to diamonde) light traveling from Lucite to quartz Get solution
3cc. The mirror equation tells us thata) moving an object farther from a converging mirror means that the image will be formed farther from the mirror.b) moving an object farther from a converging mirror means that the image will be formed closer to the mirror.c) either of the above could occur, depending on the focal length of the mirror. Get solution
3mcq. For specular reflection of a light ray, the angle of incidencea) must be equal to the angle of reflection.b) is always less than the angle of reflection.c) is always greater than the angle of reflection.d) is equal to 90°—the angle of reflection.e) may be greater than, less than, or equal to the angle of reflection. Get solution
4cc. Moving the object in Example 32.2 10% closer to the mirror would produce an image that wasa) closer to the mirror and larger than before.b) closer to the mirror and smaller than before.c) farther from the mirror and larger than before.d) farther from the mirror and smaller than before.e) It is not possible to predict the image’s characteristics.Exampl e 32.2 I mage Formed by a Converging Mirror...... Get solution
4mcq. Standing by a pool filled with water, under what condition will you see a reflection of the scenery on the opposite side through total internal reflection of the light from the scenery?a) Your eyes are level with the water.b) You observe the pool at an angle of 41.8°.c) There is no condition under which this can occur.d) You observe the pool at an angle of 48.2°. Get solution
5cc. Suppose you have a liquid-mirror telescope with focal length f1, and you want to double this focal length. What adjustment do you have to make to the rotational angular velocity of the liquid?a) reduce it by a factor of 0.5b) reduce it by a factor of 0.707c) keep it the samed) increase it by a factor of 0.707e) increase it by a factor of 2 Get solution
6cc. Using flat mirrors to focus the Sun’s rays at the top of a tower, as is done by the power plant shown in Figure 32.35, is only possible becausea) the Sun is essentially infinitely far away, so its rays are parallel when they strike the mirrors.b) the orientations of the flat mirrors are continuously and individually adjusted by computerized controls.c) the mirrors are located in a parabolic bowl.d) the Sun is directly overhead in Spain for several hours each day.e) the Earth is a sphere with a very large radius of curvature.Figure 32.35 The world’s first commercial tower solar farm, an 11-MW installation in Sanlúcar la Mayor, Spain.... Get solution
6mcq. What is the magnification for a plane mirror?a) +1b) –1c) greater than +1d) not defined for a plane mirror Get solution
7cc. If the same fish swimming at the same depth is seen by a different observer whose line of sight is at an angle larger than that given in Example 32.3, then, to that observer, the fish’s apparent depth will bea) larger than that calculated in Example 32.3.b) the same as that calculated in Example 32.3.c) smaller than that calculated in Example 32.3.Example 32.3 A pparent Depth...... Get solution
7mcq. A small object is placed in front of a converging mirror with radius R = 7.50 cm so that the image distance equals the object distance. How far is this object from the mirror?a) 2.50 cmb) 5.00 cmc) 7.50 cmd) 10.0 cme) 15.0 cm Get solution
8cc. In Solved Problem 32.2, the sheet of transparent material was surrounded by air. If the sheet were surrounded by water instead, what would happen to the displacement of the light ray with the same angle of incidence? (Assume that the index of refraction of the transparent material is still larger than that of water.)a) It would be larger.b) It would be the same.c) It would be smaller. Get solution
8mcq. Sunlight strikes a piece of glass at an angle of incidence of θi = 33.4°. What is the difference between the angle of refraction of a red light ray (λ = 660.0 nm) and that of a violet light ray (λ = 410.0 nm)? The glass’s index of refraction is n = 1.520 for red light and n = 1.538 for violet light.a) 0.03°b) 0.12°c) 0.19°d) 0.26°e) 0.82° Get solution
9cc. At the boundary between water and air, the critical angle for total internal reflection in the water is 48°. What does a diver in a swimming pool see when looking from under the water toward the surface at an angle greater than 48°?a) the sky above the poolb) the reflection of the floor of the poolc) a superposition of the sky and the reflection of the floord) nothing, because no light can reach the eyes of a diver looking toward the surface at this angle Get solution
9mcq. The image of yourself that you see in a bathroom mirror isa) left-right inverted.b) front-to-back inverted.c) bottom-to-top inverted.d) not inverted. Get solution
10mcq. Where do you have to place an object in front of a concave mirror with focal length f for the image to be the same size as the object?a) at do = 0.5fb) at do = fc) at do = 2fd) at do = 2.5fe) none of the above Get solution
11mcq. You are looking down into a swimming pool at an angle of 20° relative to the vertical, and you see a coin at the bottom of the pool. This coin appears to you to be ata) a lesser depth than it really is.b) the same depth as it really is.c) a greater depth than it really is. Get solution
12mcq. You are looking straight down into a swimming pool, that is, at an angle of 0° relative to the vertical, and you see a coin at the bottom of the pool. This coin appears to you to be ata) a lesser depth than it really is.b) the same depth as it really is.c) a greater depth than it really is. Get solution
13cq. The figure shows the difference between the refractive index profile of a step index fiber and the refractive index profile of a graded index fiber. Applying geometric optics principles, comment on the path followed by a light ray entering each of the optic fibers.... Get solution
15cq. A concave spherical mirror is used to create an image of an object 5.00 cm tall that is located at position x = 0 cm, which is 20.0 cm from point C, the center of curvature of the mirror, as shown in the figure. The magnitude of the radius of curvature of the mirror is 10.0 cm. Without changing the mirror, how can you reduce the spherical aberration produced by it? Are there any disadvantages to your approach to reducing the spherical aberration?... Get solution
14cq. A slab of Plexiglas 2.00 cm thick with index of refraction 1.51 is placed over a physics textbook. The slab has parallel sides. The text is at height y = 0. Consider two rays of light, A and B, that originate at the letter “t” in the text under the Plexiglas and travel toward an observer who is above the Plexiglas, looking down. Draw> on the figure the apparent y-position of the letter under the Plexiglas as seen by the observer. (Hint: From where in the Plexiglas do the two rays appear to originate for the observer?) You can easily do this experiment yourself. If you do not have a block of glass or Plexiglas, you can try placing a flat-bottomed drinking glass over the text.... Get solution
16cq. If you look at an object at the bottom of a pool, the pool looks less deep than it actually is.a) From what you have learned, calculate how deep a pool seems to be if it is actually 4 feet deep and you look directly down on it. The index of refraction of water is 1.33.b) Would the pool look more or less deep than it actually is if you looked at it from an angle other than vertical? Answer this qualitatively, without using an equation. Get solution
19cq. A physics student is eying a steel drum, the top part of which has the approximate shape of a concave spherical surface. The surface is sufficiently polished that the student can just make out the reflection of her finger when she places it above the drum. As she slowly moves her finger toward the surface and then away from it, you ask her what she is doing. She replies that she is estimating the radius of curvature of the drum. How can she do that? Get solution
17cq. Why does refraction occur? That is, what is the physical reason a wave moves with a different velocity when it passes from one medium into another? Get solution
18cq. Many optical fibers have minimum specified bending radii. Why? Get solution
20cq. State whether the following is true or false and explain your answer: The wavelength of He-Ne laser light in water is less than its wavelength in air. (The index of refraction of water is 1.33.) Get solution
22cq. A 45°-45°-90° triangular prism can be used to reverse a light beam: The light enters perpendicular to the hypotenuse of the prism, reflects off each leg, and emerges perpendicular to the hypotenuse again. The surfaces of the prism are not silvered. If the prism is made of glass with index of refraction nglass = 1.520 and is surrounded by air, the light beam will be reflected with a minimum loss of intensity (there are reflection losses as the light enters and leaves the prism).a) Will this work if the prism is under water, which has the index of refraction nH2O =1.333?b) Such prisms are used, in preference to mirrors, to bend the optical path in quality binoculars. Why? Get solution
21cq. Among the instruments Apollo astronauts left on the Moon were reflectors for bouncing laser beams back to Earth. These made it possible to measure the distance from the Earth to the Moon with unprecedented precision (uncertainties of a few centimeters in 384,000 km), for the study of both celestial mechanics and Earth’s plate tectonics. The reflectors consist not of ordinary mirrors, but of arrays of corner cubes, each constructed of three square plane mirrors fixed perpendicular to each other, as adjacent faces of a cube. Why? Explain the functioning and advantages of this design. Get solution
25cq. Holding a spoon in front of your face, convex side toward you, estimate the location of the image and its magnification. Get solution
23cq. An object is imaged by a converging spherical mirror as shown in the figure. Suppose a black cloth is put between the object and the mirror so that it covers everything above the optic axis. How will the image be affected?... Get solution
24cq. You are under water in a pond and look up through the smooth surface of the water at the Sun in the sky. Is the Sun in fact higher in the sky than it appears to you, or is it lower? Get solution
28. A periscope consists of two flat mirrors and is used for viewing objects when an obstacle impedes direct viewing. Suppose Curious George is looking through a periscope, in which the two flat mirrors are separated by a distance L = 0.400 m, at the Man in the Yellow Hat, whose hat is at do = 3.00 m from the upper mirror. What is the distance D of the final image of the yellow hat from the lower mirror? Get solution
27. A person sits 1.00 m in front of a plane mirror. What is the location of the image? Get solution
26cq. A solar furnace uses a large parabolic mirror (such mirrors can be several stories high) to focus the light of the Sun to heat a target. A large solar furnace can melt metals. Is it possible to attain temperatures exceeding 6000 K (the temperature of the photosphere of the Sun) in a solar furnace? If so, how? If not, why not? Get solution
29. A person stands at a point P relative to two plane mirrors oriented at 90.0°, as shown in the figure. How far away from each other do the person’s images appear to be?... Get solution
30. Even the best mirrors absorb or transmit some of the light incident on them. The highest-quality mirrors might reflect 99.997% of the incident light. Suppose a cubical “room,” 3.00 m on an edge, were constructed with such mirrors for the walls, floor, and ceiling. How slowly would such a room get dark? Estimate the time required for the intensity of light in such a room to fall to 1.00% of its initial value after the only light source in the room was switched off. Get solution
31. The radius of curvature of a convex mirror is –25.0 cm. What is its focal length? Get solution
32. A concave spherical mirror is used to create an image of an object 5.00 cm tall that is located at position x = 0 cm, which is 20.0 cm from point C, the center of curvature of the mirror, as shown in the figure. The magnitude of the radius of curvature of the mirror is 10.0 cm. Calculate the position xi where the image is formed. Use the coordinate system given in the drawing. What is the height hi of the image? Is the image upright (pointing up) or inverted (pointing down)? Is it real or virtual?... Get solution
34. A 5.00-cm-tall object is placed 30.0 cm away from a convex mirror with a focal length of –10.0 cm. Determine the size, orientation, and position of the image. Get solution
33. Convex mirrors are often used as sideview mirrors on cars. Many such mirrors display the warning “Objects in mirror are closer than they appear.” Assume that a convex sideview mirror has a radius of curvature of 14.0 m and that a car is 11.0 m behind the mirror. For a flat mirror, the image distance would be 11.0 m, and the magnification would be 1. Find the image distance and the magnification for this convex mirror. Get solution
35. The magnification of a convex mirror is 0.60× for an object 2.0 m from the mirror. What is the focal length of this mirror? Get solution
36. An object is located at a distance of 100. cm from a concave mirror of focal length 20.0 cm. Another concave mirror of focal length 5.00 cm is located 20.0 cm in front of the first concave mirror. The reflecting sides of the two mirrors face each other. What is the location of the final image formed by the two mirrors and the total magnification produced by them in combination? Get solution
37. The shape of an elliptical mirror is described by the curve ... with semimajor axis a and semiminor axis b. The foci of this ellipse are at the points (c,0) and (–c,0), with c = (a2 – b2)1/2. Show that any light ray in the xy-plane that passes through one focus is reflected through the other. “Whispering galleries” make use of this phenomenon for reflecting sound waves. Get solution
38. What is the speed of light in crown glass, whose index of refraction is 1.52? Get solution
39. An optical fiber with an index of refraction of 1.50 is used to transport light of wavelength 400. nm. What is the critical angle for transporting light through this fiber without loss? If the fiber is immersed in water? In oil? Get solution
40. A helium-neon laser produces light of wavelength λvac = 632.8 nmin vacuum. If this light passes into water, with index of refraction n = 1.333, what will each of the following characteristics be?a) speedb) frequencyc) wavelengthd) color Get solution
41. A light ray is incident from water, whose index of refraction is 1.33, on a plate of glass whose index of refraction is 1.73. What angle of incidence will result in fully polarized reflected light? Get solution
42. Suppose you are standing at the bottom of a swimming pool whose surface is perfectly calm. Looking up, you see a circular window to the “outer world.” If your eyes are approximately 2.00 m beneath the surface, what is the diameter of this circular window? Get solution
43. A ray of light of a particular wavelength is incident on an equilateral triangular prism whose index of refraction for light of this wavelength is 1.23. The ray is parallel to the base of the prism as it approaches and enters the prism at the midpoint of one of the sides, as shown in the figure. What is the direction of the ray when it emerges from the prism?... Get solution
44. A collimated laser beam strikes the left side (A) of a glass block at an angle of 20.0° with respect to the horizontal, as shown in the figure. The block has an index of refraction of 1.55 and is surrounded by air, with an index of refraction of 1.00. The left side of the glass block is vertical (90.0° from horizontal) while the right side (B) is at an angle of 60.0° from the horizontal. Determine the angle θBT with respect to the horizontal at which the light exits surface B.... Get solution
45. In a step index fiber, the index of refraction undergoes a discontinuity (jump) at the core-cladding boundary, as shown in the figure. Infrared light with wavelength 1550 nm propagates through such a fiber by total internal reflection at the corecladding boundary. The index of refraction of the core for the infrared light is ncore = 1.48. If the maximum angle, αmax, at which light can enter the fiber with no light lost into the cladding is αmax = 14.033°, calculate the percent difference between the index of refraction of the core and the index of refraction of the cladding....... Get solution
46. Refer to Figure 32.51 and prove that the arc of the primary rainbow represents the 42° angle from the direction of the sunlight.Figure 32.51 The paths taken by parallel light rays in a spherical drop of water.... Get solution
47. Use Fermat’s Principle to derive the law of reflection. Get solution
48. Fermat’s Principle, from which geometric optics can be derived, states that light travels by a path that minimizes the time of travel between points. Consider a light beam that travels a horizontal distance D and a vertical distance h, through two large flat slabs of material that have a vertical interface between them. One slab has a thickness D/2 and an index of refraction n1, and the other has a thickness D/2 and an index of refraction n2. Write the equation relating the indices of refraction and the angles from the horizontal that the light beam makes at the interface (θ1 and θ2) which minimize the time for this travel. Get solution
49. Suppose your height is 2.00 m and you are standing 50.0 cm in front of a plane mirror.a) What is the image distance?b) What is the image height?c) I s the image inverted or upright?d) Is the image real or virtual? Get solution
50. A light ray of wavelength 700. nm traveling in air (n1 = 1.00) is incident on a boundary with a liquid (n2 = 1.63).a) What is the frequency of the refracted ray?b) What is the speed of the refracted ray?c) What is the wavelength of the refracted ray? Get solution
51. You have a spherical mirror with a radius of curvature of +20.0 cm (so it is concave facing you). You are looking at an object whose image size you want to double so you can see it better. At what locations could you put the object? Where will the images be for these object locations, and will they be real or virtual? Get solution
52. You are submerged in a swimming pool. What is the maximum angle at which you can see light coming from above the pool surface? That is, what is the angle for total internal reflection from water into air? Get solution
53. Light hits the surface of water at an incident angle of 30.0° with respect to the normal to the surface. What is the angle between the reflected ray and the refracted ray? Get solution
54. A spherical metallic Christmas tree ornament has a diameter of 8.00 cm. If Saint Nicholas is by the fireplace, 1.56 m away, where will he see his reflection in the ornament? Is the image real or virtual? Get solution
55. One of the factors that cause a diamond to sparkle is its relatively small critical angle. Compare the critical angle for diamond in air with that for diamond in water. Get solution
56. What kind of image, virtual or real, is formed by a converging mirror when the object is placed a distance away from the mirror that isa) beyond the center of curvature of the mirror,b) between the center of curvature and half of the distance to the center of curvature, andc) closer than half of the distance to the center of curvature? Get solution
57. At what angle θ shown in the figure must a beam of light enter the water for the reflected beam to make an angle of 40.0° with respect to the normal of the water’s surface?... Get solution
59. How deep does a point in the middle of a 3.00-m-deep pool appear to be to a person standing beside the pool at a position 2.00 m horizontally from the point? Take the index of refraction for the liquid in the pool to be 1.30 and that for air to be 1.00. Get solution
60. What is the smallest incident angle θ i at which the light beam shown in the figure ill undergo total internal reflection in the prism, if the index of refraction of the prism for light of this wavelength is 1.500?... Get solution
62. Refer to Example 32.3 and use the numbers provided there. Further, assume that your eyes are at a height of 1.70 m above the water.a) Calculate the time it takes for light to travel on the path from the fish to your eyes.b) Calculate the time light would take on a straight-line path from the fish to your eyes.c) Calculate the time light would take on a path from the fish vertically upward to the water surface and then straight to your eyes.d) Calculate the time light would take on the straight-line path from the apparent location of the fish to your eyes.e) What can you say about Fermat’s Principle from the results of parts (a) through (d)?Example 32.3 A pparent Depth...... Get solution
63. If you want to construct a liquid mirror of focal length 2.50 m, with what angular velocity do you have to rotate your liquid? Get solution
64. One proposal for a space-based telescope is to put a large rotating liquid mirror on the Moon. Suppose you want to use a liquid mirror that is 100.0 m in diameter and has a focal length of 347.5 m. The gravitational acceleration on the Moon is 1.62 m/s2.a) What angular velocity does your mirror have?b) What is the linear speed of a point on the perimeter of the mirror?c) How high above the center is the perimeter of the mirror? Get solution
65. The origin of a coordinate system is placed at the center of curvature of a spherical mirror with radius of curvature R = 58.1 cm (see the figure). An object is placed at xo = 19.7 cm. What is the x-coordinate of the image?... Get solution
66. The origin of a coordinate system is placed at the center of curvature of a spherical mirror with radius of curvature R = 59.3 cm (see the figure). An object is placed at xo = 39.5 cm. What is the mirror’s magnification? Get solution
67. The origin of a coordinate system is placed at the center of a spherical mirror with radius of curvature R (see the figure). An object is placed at xo = 10.1 cm. The image is formed at x = –7.405 cm. What is the value of R? Get solution
68. The origin of a coordinate system is placed at the center of curvature of a spherical mirror with radius of curvature R (see the figure). An object is placed at xo = 10.3 cm. The image is formed at x = –7.548 cm. What is the focal length of the mirror? Get solution
69. A layer of methyl alcohol, with index of refraction 1.329, rests on a block of ice, with index of refraction 1.310. A ray of light passes through the methyl alcohol at an angle of φ1 = 61.07° relative to the alcohol-ice boundary. What is the angle φ2 relative to the boundary at which the ray passes through the ice?... Get solution
70. A layer of a transparent material rests on a block of fused quartz, whose index of refraction is 1.460. A ray of light passes through the unknown material at an angle of φ1 = 63.65° relative to the boundary between the materials and is refracted at an angle of φ2 =70.26° relative to the boundary. What is the index of refraction of the unknown material? Get solution
71. A layer of carbon dioxide, with index of refraction 1.00045, rests on a block of ice, with index of refraction 1.310. A ray of light passes through the carbon dioxide at an angle of φ 1 relative to the boundary between the materials and then passes through the ice at an angle of φ 2 = 72.06° relative to the boundary. What is the value of φ1? Get solution
72. A layer of water, with index of refraction 1.333, rests on a block of an unknown transparent material. A ray of light passes through the water at an angle of φ1 = 68.77° relative to the boundary between the materials and then passes through the unknown material at an angle of φ2 = 72.98° relative to the boundary. What is the speed of light in the unknown material? Get solution
