Interference and Diffraction

Transcription

1 CHAPTER 9 Interference and Diffraction Copyright Glencoe/McGra-Hill, a division of The McGra-Hill Companies, Inc. Practice Problems 9. Interference pages page 59. Violet light falls on to slits separated by m. A first-order bright band appears 3.2 mm from the central bright band on a screen m from the slits. What is? x d 48 nm 2. Yello-orange light from a sodium lamp of avelength 596 nm is aimed at to slits that are separated by m. What is the distance from the central band to the first-order yello band if the screen is m from the slits? x d m 8.8 mm 3. In a double-slit experiment, physics students use a laser ith nm. A student places the screen.000 m from the slits and finds the first-order bright band 65.5 mm from the central line. What is the slit separation? x d d x ( m)( m) m ( m)( m) m ( m)(.000 m) m m 9.66 m 4. Yello-orange light ith a avelength of 596 nm passes through to slits that are separated by m and makes an interference pattern on a screen. If the distance from the central line to the first-order yello band is m, ho far is the screen from the slits? x d x d m page In the situation in Example Problem 2, hat ould be the thinnest film that ould create a reflected red ( 635 nm) band? 2t m 2 n oil For the thinnest film, m 0. t 4 ( m)( m) m noil 635 nm ( 4)(. 45) 09 nm 6. A glass lens has a nonreflective coating placed on it. If a film of magnesium fluoride, n.38, is placed on the glass, n.52, ho thick should the layer be to keep yello-green light from being reflected? Because n film n air,there is a phase inversion on the first reflection. Because n glass n film,there is a phase inversion on the second reflection. For destructive interference to keep yello-green from being reflected: 2t m 2 nfilm Physics: Principles and Problems Solutions Manual 399

2 For the thinnest film, m 0. t nm ( 4)(. 38) 0 nm 7. A silicon solar cell has a nonreflective coating placed on it. If a film of sodium monoxide, n.45, is placed on the silicon, n 3.5, ho thick should the layer be to keep yello-green light ( 555 nm) from being reflected? Because n film n air,there is a phase inversion on the first reflection. Because n silicon n film,there is a phase inversion on the second reflection. For destructive interference to keep yello-green from being reflected: For the thinnest film, m 0. t 4 nfilm 2t m 2 nfilm nfilm 555 nm ( 4)(. 45) 95.7 nm 8. You can observe thin-film interference by dipping a bubble and into some bubble solution and holding the and in the air. What is the thickness of the thinnest soap film at hich you ould see a black stripe if the light illuminating the film has a avelength of 52 nm? Use n.33. Because n film n air,there is a phase change on the first reflection. Because n air n film,there is no phase change on the second reflection. For destructive interference to get a black stripe m 2t n film For the thinnest film, m. t 2n film 96 nm 9. What is the thinnest soap film (n.33) for hich light of avelength 52 nm ill constructively interfere ith itself? For constructive interference 2t m 2 nfilm For the thinnest film, m 0. t 4 52 nm ( 4)(. 33) 97.9 nm Section Revie 9. Interference pages page Film Thickness ucien is bloing bubbles and holds the bubble and up so that a soap film is suspended vertically in the air. What is the second thinnest idth of the soap film at hich he could expect to see a bright stripe if the light illuminating the film has a avelength of 575 nm? Assume the soap solution has an index of refraction of.33. There is one phase inversion, so constructive interference ill be hen 2t m 2 nfilm For the second thinnest thickness, m. t nm (2)(.33) nfilm nfilm (3)(575 nm) (4)(.33) 324 nm Copyright Glencoe/McGra-Hill, a division of The McGra-Hill Companies, Inc. 400 Solutions Manual Physics: Principles and Problems

3 . Bright and Dark Patterns To very narro slits are cut close to each other in a large piece of cardboard. They are illuminated by monochromatic red light. A sheet of hite paper is placed far from the slits, and a pattern of bright and dark bands is seen on the paper. Describe ho a ave behaves hen it encounters a slit, and explain hy some regions are bright hile others are dark. When a ave encounters a slit, the ave bends. ight is diffracted by the slits. ight from one slit interferes ith light from the other. If interference is constructive, there is a bright band; if destructive, the region is dark. 2. Interference Patterns Sketch the pattern described in problem. Repeats and fades Red Red Red Repeats and fades reflection. For constructive interference to reflect yello-green light: 2t m 2 nfilm For the thinnest film, m 0. t nm b. Unfortunately, a film this thin cannot be manufactured. What is the nextthinnest film that ill produce the same effect? For the next thinnest film, m. t 3 4 color nfilm 555 nm (4)(.83) color nfilm (3)(555 nm) (4)(.83) 227 nm Copyright Glencoe/McGra-Hill, a division of The McGra-Hill Companies, Inc. 3. Interference Patterns Sketch hat happens to the pattern in problem hen the red light is replaced by blue light. Repeats and fades Blue Red Blue Red Blue Blue Red Blue The light bands become more closely spaced. 4. Film Thickness A plastic reflecting film (n.83) is placed on an auto glass indo (n.52). a. What is the thinnest film that ill reflect yello-green light? Because n film n air,there is a phase change on the first reflection. Because n glass n film,there is not a phase change on the second Repeats and fades 5. Critical Thinking The equation for avelength from a double-slit experiment uses the simplification that is small so that sin tan. Up to hat angle is this a good approximation hen your data has to significant figures? Would the maximum angle for a valid approximation increase or decrease as you increase the precision of your angle measurement? sin tan to to significant digits up to 9.9. An increase in the precision of the measurement reduces this angle to Practice Problems 9.2 Diffraction pages page Monochromatic green light of avelength 546 nm falls on a single slit ith a idth of mm. The slit is located 75 cm from a screen. Ho ide ill the central bright band be? Physics: Principles and Problems Solutions Manual 40

4 x min x min 4.3 mm 7. Yello light ith a avelength of 589 nm passes through a slit of idth 0.0 mm and makes a pattern on a screen. If the idth of the central bright band is m, ho far is it from the slits to the screen? m 8. ight from a He-Ne laser ( nm) falls on a slit of unknon idth. A pattern is formed on a screen.5 m aay, on hich the central bright band is 5 mm ide. Ho ide is the slit? 2 2 2x m 97 m 9. Yello light falls on a single slit mm ide. On a screen that is 60.0 cm aay, the central bright band is 24.0 mm ide. What is the avelength of the light? 2 () 2 ( ) 2 ( m)(0.75 m) m ( m)( m) (2)( m) (2)( m)(.5 m) 50 3 m ( m)( m) (2)( m) nm 20. White light falls on a single slit that is mm ide. A screen is placed.00 m aay. A student first puts a blue-violet filter ( 44 nm) over the slit, then a red filter ( 622 nm). The student measures the idth of the central bright band. a. Which filter produced the ider band? Red, because central peak idth is proportional to avelength. b. Calculate the idth of the central bright band for each of the to filters. 2 For blue, For red, 8 mm 25 mm page White light shines through a grating onto a screen. Describe the pattern that is produced. A full spectrum of color is seen. Because of the variety of avelengths, dark fringes of one avelength ould be filled by bright fringes of another color. 22. If blue light of avelength 434 nm shines on a diffraction grating and the spacing of the resulting lines on a screen that is.05 m aay is 0.55 m, hat is the spacing beteen the slits in the grating? d sin d here tan sin x sin tan x m sin tan m m 2( m)(.00 m) m 2( m)(.00 m) m Copyright Glencoe/McGra-Hill, a division of The McGra-Hill Companies, Inc. 402 Solutions Manual Physics: Principles and Problems

5 Copyright Glencoe/McGra-Hill, a division of The McGra-Hill Companies, Inc. Chapter 9 continued 23. A diffraction grating ith slits separated by m is illuminated by violet light ith a avelength of 42 nm. If the screen is 80.0 cm from the grating, hat is the separation of the lines in the diffraction pattern? d sin sin d tan x x tan tan sin d (0.800 m)tan sin m m m 24. Blue light shines on the DVD in Example Problem 3. If the dots produced on a all that is 0.65 m aay are separated by 58.0 cm, hat is the avelength of the light? d sin d sin tan x ( m)sin tan 0.58 m 0.65 m 490 nm 25. ight of avelength 632 nm passes through a diffraction grating and creates a pattern on a screen that is 0.55 m aay. If the first bright band is 5.6 cm from the central bright band, ho many slits per centimeter does the grating have? d sin There is one slit per distance d, so d gives slits per centimeter. d sin m.05 6 m sin tan m m cm slit slits/cm cm sin tan x Section Revie 9.2 Diffraction pages page Distance Beteen First-Order Dark Bands Monochromatic green light of avelength 546 nm falls on a single slit of idth mm. The slit is located 68.0 cm from a screen. What is the separation of the first dark bands on each side of the central bright band? 2x min 2 (2)( m)( m) m 9.3 mm 27. Diffraction Patterns Many narro slits are close to each other and equally spaced in a large piece of cardboard. They are illuminated by monochromatic red light. A sheet of hite paper is placed far from the slits, and a pattern of bright and dark bands is visible on the paper. Sketch the pattern that ould be seen on the screen. Pattern repeats Bright red lines Pattern repeats Band spacing is exactly the same as in the pattern produced by the to slits, but no light bands are much thinner and separated by ider dark bands. 28. ine Spacing You shine a red laser light through one diffraction grating and form a pattern of red dots on a screen. Then you substitute a second diffraction grating for the first one, forming a different pattern. The dots produced by the first grating are spread out more than those produced by the second. Which grating has more lines Physics: Principles and Problems Solutions Manual 403

6 per millimeter? x d,so the greater the dot spacings, x, the narroer the slit spacing,d, and thus more lines per millimeter. 29. Rayleigh Criterion The brightest star in the inter sky in the northern hemisphere is Sirius. In reality, Sirius is a system of to stars that orbit each other. If the Hubble Space Telescope (diameter 2.4 m) is pointed at the Sirius system, hich is 8.44 light-years from Earth, hat is the minimum separation there ould need to be beteen the stars in order for the telescope to be able to resolve them? Assume that the average light coming from the stars has a avelength of 550 nm. x obj.22 obj D.22( m)( m) 2.4 m m 30. Critical Thinking You are shon a spectrometer, but do not kno hether it produces its spectrum ith a prism or a grating. By looking at a hite-light spectrum, ho could you tell? Determine if the violet or the red end of the spectrum makes the largest angle ith the direction of the beam of incident hite light. A prism bends the violet end of the spectrum the most, hereas a grating diffracts red avelengths the most. Chapter Assessment Concept Mapping page Monochromatic light of avelength illuminates to slits in a Young s double-slit experiment setup that are separated by a distance, d. A pattern is projected onto a screen a distance,, aay from the slits. Complete the folloing concept map using,, and d to indicate ho you could vary them to produce the indicated change in the spacing beteen adjacent bright bands, x. increase to increase x, decrease x d increase to decrease x, decrease d d Mastering Concepts page Why is it important that monochromatic light as used to make the interference pattern in Young s interference experiment? (9.) When monochromatic light is used, you get a sharp interference pattern; if you use hite light, you get sets of colored bands. 33. Explain hy the position of the central bright band of a double-slit interference pattern cannot be used to determine the avelength of the light aves. (9.) All avelengths produce the line in the same place. 34. Describe ho you could use light of a knon ave-length to find the distance beteen to slits. (9.) et the light fall on the double slit, and let the interference pattern fall on a sheet of paper. Measure the spacings beteen the bright bands, x, and use the equation d. x 35. Describe in your on ords hat happens in thin-film interference hen a dark band is produced by light shining on a soap film suspended in air. Make sure you include in your explanation ho the avelength of the light and thickness of the film are related. (9.) Copyright Glencoe/McGra-Hill, a division of The McGra-Hill Companies, Inc. 404 Solutions Manual Physics: Principles and Problems

7 Copyright Glencoe/McGra-Hill, a division of The McGra-Hill Companies, Inc. Chapter 9 continued When the light strikes the front of the film, some reflects off this surface and some passes through the film and reflects off the back surface of the film. When light reflects off a medium ith a higher index of refraction, it undergoes a phase shift of one-half avelength; this happens to the light that initially reflects. In order for a dark band to be produced, the to light rays must be one-half avelength out of phase. If the thickness of the film is such that the ray reflecting off the back surface goes through a hole number of cycles hile passing through the film, the light rays arriving at your eye ill be out of phase and destructively interfere. Remember that the avelength is altered by the index of refraction of the film, so that the thickness of the film must equal a multiple of half a avelength of the light, divided by the film s index of refraction. 36. White light shines through a diffraction grating. Are the resulting red lines spaced more closely or farther apart than the resulting violet lines? Why? (9.2) The spacing is directly proportional to the avelength, and because red light has a longer avelength than violet, the red lines ill be spaced farther apart than the violet lines. 37. Why do diffraction gratings have large numbers of slits? Why are these slits so close together? (9.2) The large number of grooves in diffraction gratings increases the intensity of the diffraction patterns. The grooves are close together, producing sharper images of light. 38. Why ould a telescope ith a small diameter not be able to resolve the images of to closely spaced stars? (9.2) Small apertures have large diffraction patterns that limit resolution. 39. For a given diffraction grating, hich color of visible light produces a bright line closest to the central bright band? (9.2) violet light, the color ith the smallest avelength Applying Concepts page For each of the folloing examples, indicate hether the color is produced by thin-film interference, refraction, or the presence of pigments. a. soap bubbles interference b. rose petals pigments c. oil films interference d. a rainbo refraction 4. Ho can you tell hether a pattern is produced by a single slit or a double slit? A double-slit interference pattern consists of equally spaced lines of almost equal brightness. A single-slit diffraction pattern has a bright, broad central band and dimmer side bands. 42. Describe the changes in a single-slit diffraction pattern as the idth of the slit is decreased. The bands get ider and dimmer. 43. Science Fair At a science fair, one exhibition is a very large soap film that has a fairly consistent idth. It is illuminated by a light ith a avelength of 432 nm, and nearly the entire surface appears to be a lovely shade of purple. What ould you see in the folloing situations? a. the film thickness as doubled complete destructive interference b. the film thickness as increased by half a avelength of the illuminating light complete constructive interference Physics: Principles and Problems Solutions Manual 405

8 c. the film thickness as decreased by one quarter of a avelength of the illuminating light complete destructive interference 44. What are the differences in the characteristics of the diffraction patterns formed by diffraction gratings containing 0 4 lines/cm and 0 5 lines/cm? The lines in the diffraction pattern are narroer for the 0 5 lines/cm grating. 45. aser Pointer Challenge You have to laser pointers, a red one and a green one. Your friends Mark and Carlos disagree about hich has the longer avelength. Mark insists that red light has a longer avelength, hile Carlos is sure that green has the longer avelength. You have a diffraction grating handy. Describe hat demonstration you ould do ith this equipment and ho you ould explain the results to Carlos and Mark to settle their disagreement. Shine each laser pointer through the grating onto a nearby all. The color ith the longer avelength ill produce dots ith a greater spacing on the all because the spacing is directly proportional to the avelength. (Mark is correct; red light has a longer avelength than green light.) 46. Optical Microscope Why is blue light used for illumination in an optical microscope? ess diffraction results from the short avelength of blue light. Mastering Problems 9. Interference pages evel 47. ight falls on a pair of slits 9.0 m apart and 80.0 cm from a screen, as shon in Figure 9-7. The first-order bright band is.90 cm from the central bright band. What is the avelength of the light? 9.0 m Figure 9-7 (Not to scale) x d 45 nm 48. Oil Slick After a short spring shoer, Tom and Ann take their dog for a alk and notice a thin film of oil (n.45) on a puddle of ater, producing different colors. What is the minimum thickness of a place here the oil creates constructive interference for light ith a avelength of 545 nm? There is one phase inversion, so constructive interference ill be hen For the minimum thickness, m 0. t nm evel ight of avelength 542 nm falls on a double slit. First-order bright bands appear 4.00 cm from the central bright band. The screen is.20 m from the slits. Ho far apart are the slits? x d d x Double slit ( m)( m) m 2t m 2 nfilm nfilm 545 nm (4)(.45) ( m)(.20 m) m 6.3 m 80.0 cm Screen 50. Insulation Film Winter is approaching and Alejandro is helping to cover the indos Copyright Glencoe/McGra-Hill, a division of The McGra-Hill Companies, Inc. 406 Solutions Manual Physics: Principles and Problems

9 Copyright Glencoe/McGra-Hill, a division of The McGra-Hill Companies, Inc. Chapter 9 continued in his home ith thin sheets of clear plastic (n.8) to keep the drafts out. After the plastic is taped up around the indos such that there is air beteen the plastic and the glass panes, the plastic is heated ith a hair dryer to shrink-rap the indo. The thickness of the plastic is altered during this process. Alejandro notices a place on the plastic here there is a blue stripe of color. He realizes that this is created by thin-film interference. What are three possible thicknesses of the portion of the plastic here the blue stripe is produced if the avelength of the light is nm? There is one phase inversion, so constructive interference ill be hen 2t m 2 nfilm Three possible thicknesses occur at m 0,, and 2. t 4 for m nm t 3 4 for m 82 nm t for m nfilm nm (4)(.8) nfilm (3)( nm) (4)(.8) nfilm (5)( nm) (4)(.8) 304 nm evel 3 5. Samir shines a red laser pointer through three different double-slit setups. In setup A, the slits are separated by 0.50 mm and the screen is 0.60 m aay from the slits. In setup B, the slits are separated by 0.75 mm and the screen is 0.80 m aay. Setup C has the slits separated by 0.50 mm and the screen a distance of 0.80 m aay. Rank the three setups according to the separation beteen the central bright band and the first-order bright band, from least to most separation. Specifically indicate any ties. x d x d Because is the same for each setup, x calculate to compare the setups. x d Setup A: Setup B: Setup C: x C x B x A 9.2 Diffraction page 537 evel 52. Monochromatic light passes through a single slit ith a idth of 0.00 cm and falls on a screen 00 cm aay, as shon in Figure 9-8. If the idth of the central band is.20 cm, hat is the avelength of the light? 0.00 cm Single slit 2 x 0.60 m m 0.80 m m 0.80 m m 00 cm Screen Figure 9-8 (Not to scale) Physics: Principles and Problems Solutions Manual 407

10 (0.60 cm)(0.00 cm) 00 cm 600 nm 53. A good diffraction grating has lines per cm. What is the distance beteen to lines in the grating? d cm evel ight ith a avelength of cm passes through a single slit and falls on a screen 00 cm aay. If the slit is 0.05 cm ide, hat is the distance from the center of the pattern to the first dark band? 2 is the idth of the bright band, so to get the distance from the center to the first dark band, divide by 2. x lines/cm ( cm)(00 m) 0.05 cm 0.3 cm 55. Hubble Space Telescope Suppose the Hubble Space Telescope, 2.4 m in diameter, is in orbit.00 5 m above Earth and is turned to vie Earth, as shon in Figure 9-9. If you ignore the effect of the atmosphere, ho large an object can the telescope resolve? Use m. x obj obj x obj.2 2 D m 2.6 cm evel Monochromatic light ith a avelength of 425 nm passes through a single slit and falls on a screen 75 cm aay. If the central bright band is 0.60 cm ide, hat is the idth of the slit? 2 x x 2 ( ) 0.30 cm.0 2 cm 57. Kaleidoscope Jennifer is playing ith a kaleidoscope from hich the mirrors have been removed. The eyehole at the end is 7.0 mm in diameter. If she can just distinguish to bluish-purple specks on the other end of the kaleidoscope separated by 40 m, hat is the length of the kaleidoscope? Use 650 nm and assume that the resolution is diffraction limited through the eyehole. x obj obj 2 2x ( cm)(75 cm) 0.30 cm.22 obj D (.22)(5.0 7 m)(.00 5 m) 2.4 m.22 obj D x obj D.22 (400 6 m)( m) (.22)( m) 0.4 m Copyright Glencoe/McGra-Hill, a division of The McGra-Hill Companies, Inc. Figure Solutions Manual Physics: Principles and Problems

11 Copyright Glencoe/McGra-Hill, a division of The McGra-Hill Companies, Inc. Chapter 9 continued 58. Spectroscope A spectroscope uses a grating ith 2,000 lines/cm. Find the angles at hich red light, 632 nm, and blue light, 42 nm, have first-order bright lines. d 2,000 lines/cm d sin sin d For red light, sin cm cm 49.3 For blue light, sin cm cm 30.3 Mixed Revie page cm evel 59. Record Marie uses an old 33 rpm record 3 as a diffraction grating. She shines a laser, nm, on the record, as shon in Figure On a screen 4.0 m from the record, a series of red dots 2 mm apart are visible. 2 mm 2 mm Screen Figure 9-20 (Not to scale) a. Ho many ridges are there in a centimeter along the radius of the record? d sin d sin 4.0 m sin tan x aser Record m sin tan m.20 4 m.20 2 cm 83 ridges/cm b. Marie checks her results by noting that the ridges represent a song that lasts 4.0 minutes and takes up 6 mm on the record. Ho many ridges should there be in a centimeter? Number of ridges is (4.0 min)(33.3 rev/min) 34 ridges 3 4 ridges 84 ridges/cm.6 cm evel An anti-reflective coating, n.2, is applied to a lens. If the thickness of the coating is 25 nm, hat is (are) the color(s) of light for hich complete destructive interference ill occur? Hint: Assume the lens is made out of glass. Because n film n air,there is a phase inversion on the first reflection. Because n lens.52 n film,there is a phase inversion on the second reflection. For destructive interference: 2d m 2 nfilm d 2dn film m 2 (2)(25 nm)(.2) m 2 m For m 0 3 m.20 2 cm 2 ( nm) 2 ( nm) nm The light is reddish-orange. For other values of m, the avelength is shorter than that of light. Physics: Principles and Problems Solutions Manual 409

12 evel 3 6. Camera When a camera ith a 50-mm lens is set at f/8, its aperture has an opening 6.25 mm in diameter. a. For light ith 550 nm, hat is the resolution of the lens? The film is 50.0 mm from the lens..22 obj x obj D (.22)( mm)(50.0 mm) 6.25 mm mm b. The oner of a camera needs to decide hich film to buy for it. The expensive one, called fine-grained film, has 200 grains/mm. The less costly, coarsegrained film has only 50 grains/mm. If the oner ants a grain to be no smaller than the idth of the central bright spot calculated in part a, hich film should he purchase? Central bright band idth 2x mm The 200 grains/mm film has 200 mm beteen grains 50 3 mm, so this film ill ork. The 50 grains/mm has 50 mm beteen grains mm, so this film on t ork. Thinking Critically page Apply Concepts Yello light falls on a diffraction grating. On a screen behind the grating, you see three spots: one at zero degrees, here there is no diffraction, and one each at 30 and 30. You no add a blue light of equal intensity that is in the same direction as the yello light. What pattern of spots ill you no see on the screen? A green spot at 0, yello spots at 30 and 30, and to blue spots slightly closer in. 63. Apply Concepts Blue light of avelength passes through a single slit of idth. A diffraction pattern appears on a screen. If you no replace the blue light ith a green light of avelength.5, to hat idth should you change the slit to get the original pattern back? The angle of diffraction depends on the ratio of slit idth to avelength. Thus, you ould increase the idth to Analyze and Conclude At night, the pupil of a human eye has an aperture diameter of 8.0 mm. The diameter is smaller in daylight. An automobile s headlights are separated by.8 m. a. Based upon Rayleigh s criterion, ho far aay can the human eye distinguish the to headlights at night? Hint: Assume a avelength of 525 nm..22 obj x obj D xo b obj. 2 j D 2 ( m)(.80 m) (.22)( m) m 22 km b. Can you actually see a car s headlights at the distance calculated in part a? Does diffraction limit your eyes sensing ability? Hypothesize as to hat might be the limiting factors. No; a fe hundred meters, not several kilometers, is the limit. Diffraction doesn t limit the sensing ability of your eyes. More probable factors are the refractive effects of the atmosphere, like those that cause stars to tinkle, or the limitations of the retina and the optic area of the brain to separate to dim sources. Writing in Physics page Research and describe Thomas Young s contributions to physics. Evaluate the impact of his research on the scientific thought about the nature of light. Copyright Glencoe/McGra-Hill, a division of The McGra-Hill Companies, Inc. 40 Solutions Manual Physics: Principles and Problems

13 Student ansers ill vary. Ansers should include Young s to-slit experiment that alloed him to precisely measure the avelength of light. 66. Research and interpret the role of diffraction in medicine and astronomy. Describe at least to applications in each field. Student ansers ill vary. Ansers could include diffraction in telescopes and microscopes, as ell as spectroscopy. Cumulative Revie page Ho much ork must be done to push a 0.5-m 3 block of ood to the bottom of a 4-m-deep simming pool? The density of ood is 500 kg/m 3. (Chapter 3) The block ould float, but to submerge it ould require an extra force donard. W Fd a. What is the avelength of the sound in still air?.50 m b. If the speed of sound is 330 m/s, hat is the frequency of the source? v f v 330 m/s f 220 Hz.50 m c. What is the speed of the airplane? The plane moves forard 0.50 m for every.50 m that the sound ave travels, so the plane s speed is onethird the speed of sound, or 0 m/s. 70. A concave mirror has a 48.0-cm radius. A 2.0-cm-tall object is placed 2.0 cm from the mirror. Calculate the image position and image height. (Chapter 7) f 2 r 48.0 cm 2 Copyright Glencoe/McGra-Hill, a division of The McGra-Hill Companies, Inc. F F buoyancy F g F g Vg (500 kg/m 3 )(0.5 m 3 )(9.80 m/s 2 ) 2450 N F buoyancy Vg (000 kg/m 3 )(0.5 m 3 ) (9.80 m/s 2 ) 4900 N Work (4900 N 2450 N)(4 m) 0 kj 68. What are the avelengths of microaves in an oven if their frequency is 2.4 GHz? (Chapter 4) c f c m/s f Hz 0.2 m 69. Sound ave crests that are emitted by an airplane are.00 m apart in front of the plane, and 2.00 m apart behind the plane. (Chapter 5) 24.0 cm f do d i d i 24.0 cm hi m di h d o ih o h i d d d o f do f (2.0 cm)(24.0 cm) 2.0 cm 24.0 cm o 4.0 cm o (24.0 cm)(2.0 cm) 2.0 cm 7. The focal length of a convex lens is 2.0 cm. A 2.00-cm-tall candle is located 7.50 cm from the lens. Use the thin-lens equation to calculate the image position and image height. (Chapter 8) f do d i Physics: Principles and Problems Solutions Manual 4

14 d i.7 cm hi m h h i d o f do f (7.50 cm)(2.0 cm) 7.50 cm 2.0 cm o d i h o do d i do (.7 cm)(2.00 cm) 7.50 cm 3. cm Challenge Problem page 526 You have several unknon substances and ish to use a single-slit diffraction apparatus to determine hat each one is. You decide to place a sample of an unknon substance in the region beteen the slit and the screen and use the data that you obtain to determine the identity of each substance by calculating its index of refraction. Incoming light Unknon substance. Come up ith a general formula for the index of refraction of an unknon substance in terms of the avelength of the light, vacuum, the idth of the slit,, the distance from the slit to the screen,, and the distance beteen the central bright band and the first dark band, x. x Use () c and (3) n substance. v Combine (2) and (3).,(2) v substance f, n substance (4), because the frequency remains constant as the light crosses a boundary. Rerite () in terms of a substance in the space beteen the slits and the screen. x substance min (5) Combine (4) and (5) and solve for x. n substance x min 2. If the source you used had a avelength of 634 nm, the slit idth as 0.0 mm, the distance from the slit to the screen as.5 m, and you immersed the apparatus in ater (n substance.33), then hat ould you expect the idth of the center band to be? x x min vacuum nsubstance vacuum nsubstance d ( m)(.5 m) (.33)( m) m vacuum f substance f vacuum x min vacuum substance Copyright Glencoe/McGra-Hill, a division of The McGra-Hill Companies, Inc. 42 Solutions Manual Physics: Principles and Problems