CHAPTER 18 Refraction And Lenses
CHAPTERRefraction and Lenses18Practice Problems18.1 Refraction of Lightpages 485–492page 4871. A laser beam in air is incident upon ethanolat an angle of incidence of 37.0 . What isthe angle of refraction?n1 sin !1 ! n2 sin !2n sin !n211!2 ! sin"1! !!"! sin"1! !! "(1.00)(sin 37.0 )1.36! 26.3 2. Light in air is incident upon a piece ofcrown glass at an angle of incidence of45.0 . What is the angle of refraction?n1 sin !1 ! n2 sin !2n sin !n2Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.11!2 ! sin"1! !!"! sin"1! !! "(1.00)(sin 45.0 )1.52! 27.7 3. Light passes from air into water at 30.0 tothe normal. Find the angle of refraction.n1 sin !1 ! n2 sin !2!2 !n1 sin !1sin"1 !!!n2"! sin"1! !! "(1.00)(sin 30.0 )1.33! 22.1 5. A block of unknown material is submergedin water. Light in the water is incident onthe block at an angle of incidence of 31 .The angle of refraction of the light in theblock is 27 . What is the index of refractionof the material of the block?n1 sin !1 ! n2 sin !2n sin !sin !211n2 ! !!(1.33)(sin 31 )! !!sin 27 ! 1.5Section Review18.1 Refraction of Lightpages 485–492page 4926. Index of Refraction You notice that whena light ray enters a certain liquid fromwater, it is bent toward the normal, butwhen it enters the same liquid from crownglass, it is bent away from the normal. Whatcan you conclude about the liquid’s indexof refraction?nwater # nliquid # ncrown glass, therefore,nliquid must be between 1.33 and 1.52.7. Index of Refraction A ray of light has anangle of incidence of 30.0 on a blockof unknown material and an angle ofrefraction of 20.0 . What is the index ofrefraction of the material?n1 sin !1 ! n2 sin !24. Light is incident upon a diamond facet at45.0 . What is the angle of refraction?n sin !sin !211n2 ! !!n1 sin !1 ! n2 sin !2(1.00)(sin 30.0 )! !!n1 sin !1!2 ! sin"1 !!n2! 1.46!"sin 20.0 ! sin"1! !! " ! 17.0 (1.00)(sin 45.0 )2.42Physics: Principles and ProblemsSolutions Manual377
Chapter 18 continued8. Speed of Light Could an index ofrefraction ever be less than 1? What wouldthis imply about the speed of light in thatmedium?No, it would mean the speed of light inthe medium is faster than it is in avacuum.9. Speed of Light What is the speed of lightin chloroform (n " 1.51)?cn! !vcvchloroform ! !!nchloroform83.00 10 m/s! !!1.51! 1.99 108 m/s10. Total Internal Reflection If you were touse quartz and crown glass to make anoptical fiber, which would you use for thecladding layer? Why?crown glass because it has a lowerindex of refraction and would producetotal internal reflectionn1 sin !1 ! n2 sin !2n1 sin !1!2 ! sin"1 !!n2!"! sin"1! !! "(1.33)(sin 57.5 )1.50! 48.4 12. Critical Angle Is there a critical angle forlight traveling from glass to water? Fromwater to glass?Yes, because nglass % nwater. No.13. Dispersion Why can you see the image ofthe Sun just above the horizon when theSun itself has already set?because of bending of light rays in theatmosphere; refraction378Solutions ManualIn the east, because the Sun sets in thewest and sunlight must shine frombehind you in order for you to see arainbow.Practice Problems18.2 Convex and ConcaveLensespages 493–499page 49615. A 2.25-cm-tall object is 8.5 cm to the left ofa convex lens of 5.5-cm focal length. Findthe image position and height.111! ! ! & !dodifd fdo " fodi ! !(8.5 cm)(5.5 cm)! !!!8.5 cm " 5.5 cm! 15.6 cm, or 16 cmhho"ddom ! !i ! !i"d hdoi ohi ! !"(15.6 cm)(2.25 cm)! !!!8.5 cm! "4.1 cm16. An object near a convex lens produces a1.8-cm-tall real image that is 10.4 cm fromthe lens and inverted. If the focal lengthof the lens is 6.8 cm, what are the objectposition and height?111! ! ! & !dodifdfdi " fido ! !(10.4 cm)(6.8 cm)! !!!10.4 cm " 6.8 cm! 2.0 101 cmPhysics: Principles and ProblemsCopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.11. Angle of Refraction A beam of lightpasses from water into polyethylene withn " 1.50. If !i " 57.5 , what is the angle ofrefraction in the polyethylene?14. Critical Thinking In what direction canyou see a rainbow on a rainy late afternoon? Explain.
Chapter 18 continuedd fdo " f"ddohhoodi ! !m ! !i ! !i(25 cm)(5.0 cm)! !!!"d hdio iho ! !25 cm " 5.0 cm! 6.2 cm"(19.6 cm)("1.8 cm)! !!!10.4 cm! 3.4 cm17. An object is placed to the left of a convexlens with a 25-mm focal length so that itsimage is the same size as the object. Whatare the image and object positions?"(6.2 cm)(2.0 cm)! !!!25 cmpage 49720. A newspaper is held 6.0 cm from a convexlens of 20.0-cm focal length. Find the imageposition of the newsprint image.with do ! di because"ddom ! !i and m ! "1Therefore,111! ! ! & !fdido12! ! !fdid fdo " foSo di ! !di ! 2f! 2(25 mm)(6.0 cm)(20.0 cm)! !!!6.0 cm " 20.0 cm! 5.0 101 mm! "8.6 cmdo ! di ! 5.0 101 mmCopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc."d hdoi ohi ! !! "0.50 cm (inverted image)111! ! ! & !fdido18. Use a scale ray diagram to find the imageposition of an object that is 30 cm to theleft of a convex lens with a 10-cm focallength.di ! 15 cmO1"ddohhom ! !i ! !i111! ! ! & !fdidoRay 1di ! 15 cmRay 2Horizontal scale:1 block ! 1 cm21. A magnifying glass has a focal length of12.0 cm. A coin, 2.0 cm in diameter, isplaced 3.4 cm from the lens. Locate theimage of the coin. What is the diameter ofthe image?FFI119. Calculate the image position and height ofa 2.0-cm-tall object located 25 cm from aconvex lens with a focal length of 5.0 cm.What is the orientation of the image?d fdo " fodi ! !(3.4 cm)(12.0 cm)! !!!3.4 cm " 12.0 cm! "4.7 cm"hodi"(2.0 cm)("4.7 cm)! !!!hi ! !do3.4 cm! 2.8 cm111! ! ! & !fdodiPhysics: Principles and ProblemsSolutions Manual379
Chapter 18 continued22. A convex lens with a focal length of22.0 cm is used to view a 15.0-cm-longpencil located 10.0 cm away. Find theheight and orientation of the image.111! ! ! & !fdodiThe location should be about 15 cm onthe same side of the lens ("15 cm) andthe image should be upright and about1.5 cm tall.Section Reviewd fdo " fodi ! !18.2 Convex and ConcaveLensespages 493–499(10.0 cm)(22.0 cm)! !!!10.0 cm " 22.0 cm! "18.3 cmpage 49925. Magnification Magnifying glasses normally are used to produce images that are largerthan the related objects, but they also canproduce images that are smaller than therelated objects. Explain.h"dm ! !i ! !ihodo"d hdoi ohi ! !"("18.3 cm)(15.0 cm)! !!!10.0 cm! 27.5 cm (upright image)23. A stamp collector wants to magnify a stampby 4.0 when the stamp is 3.5 cm from thelens. What focal length is needed for thelens?"ddom ! !i! "14 cm26. Image Position and Height A 3.0-cm-tallobject is located 2.0 cm from a convex lenshaving a focal length of 6.0 cm. Draw a raydiagram to determine the location and sizeof the image. Use the thin lens equationand the magnification equation to verifyyour answer.111! ! ! & !fdidoI1O1dodi(3.5 cm)("14 cm)f! !! !!!do & diF3.5 cm & ("14 cm)! 4.7 cm24. A magnifier with a focal length of 30 cmis used to view a 1-cm-tall object. Use raytracing to determine the location andsize of the image when the magnifier ispositioned 10 cm from the object.d fdo " fodi ! !2.0 cm " 6.0 cmO1hi ! 1.5 cmdi ! "15 cm380111! ! !& !fdodi(2.0 cm)(6.0 cm)! !!!I1Fhi ! 4.5 cmdi ! "3.0 cmFHorizontal scale:2 blocks ! 1.0 cmVertical scale:1 block ! 1.0 cmSolutions ManualFHorizontal scale:1 block ! 2 cmVertical scale:3 blocks ! 1 cm! "3.0 cmhho"ddom # !i ! !iPhysics: Principles and ProblemsCopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.di ! "mdo ! "(4.0)(3.5 cm)If the object is located farther thantwice the focal length from the lens, thesize of the image is smaller than thesize of the object.
Chapter 18 continued"d hdoi ohi ! !Water"("3.0 cm)(3.0 cm)! !!!2.0 cm! 4.5 cmLight raysAir27. Types of Lenses The cross sections of fourdifferent thin lenses are shown in Figure18-16.Water Figure 18-17The light rays will diverge.Water Figure 18-16a. Which of these lenses, if any, areconvex, or converging, lenses?Lenses a and c are converging.Light raysn ! 1.3n ! 1.0n ! 1.3b. Which of these lenses, if any, areconcave, or diverging, lenses?Lenses b and d are diverging.Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.28. Chromatic Aberration All simple lenseshave chromatic aberration. Explain, then,why you do not see this effect when youlook through a microscope.All precision optical instruments usea combination of lenses, called anachromatic lens, to minimize chromaticaberration.29. Chromatic Aberration You shine whitelight through a convex lens onto a screenand adjust the distance of the screen fromthe lens to focus the red light. Which direction should you move the screen to focusthe blue light?closer to the lens30. Critical Thinking An air lens constructedof two watch glasses is placed in a tank ofwater. Copy Figure 18-17 and draw theeffect of this lens on parallel light raysincident on the lens.Physics: Principles and ProblemsWaterSection Review18.3 Applications of Lensespages 500–503page 50331. Refraction Explain why the cornea is theprimary focusing element in the eye.The difference in index of refractionbetween the air and the cornea isgreater than any other difference thatlight rays encounter when travelingtoward the retina.32. Lens Types Which type of lens, convex orconcave, should a nearsighted person use?Which type should a farsighted person use?A nearsighted person should use a concave lens. A farsighted person shoulduse a convex lens.Solutions Manual381
Chapter 18 continued33. Focal Length Suppose your camera isfocused on a person who is 2 m away. Younow want to focus it on a tree that is fartheraway. Should you move the lens closer tothe film or farther away?Closer; real images are always fartherfrom the lens than the focal point. Thefarther away the object is, the closer theimage is to the focal point.Chapter AssessmentConcept Mappingpage 50837. Complete the following concept map usingthe following terms: inverted, larger, smaller,virtual.Lenses34. Image Why is the image that you observein a refracting telescope inverted?convexAfter the light rays pass through theobjective lens, they cross, forming animage that is inverted. The eyepiecemaintains this orientation when it usesthis image as its object.35. Prisms What are three benefits of havingprisms in binoculars?The prisms extend the light’s path lengthto make the binoculars more compact,invert light rays so that the viewer seesan upright image, and increase separation between objective lenses to improvethe three-dimensional view.You are using the light that strikes onlya small area of the object. A brighterlamp could be rsmallerunchangedsizelargerMastering Conceptspage 50838. How does the angle of incidence comparewith the angle of refraction when a light raypasses from air into glass at a nonzeroangle? (18.1)The angle of incidence is larger thanthe angle of refraction, because air hasa smaller index of refraction.39. How does the angle of incidence comparewith the angle of refraction when a light rayleaves glass and enters air at a nonzeroangle? (18.1)The angle of incidence is smaller thanthe angle of refraction, because glasshas a larger index of refraction.40. Regarding refraction, what is the criticalangle? (18.1)The term critical angle refers to the incident angle that causes the refracted rayto lie right along the boundary of thesubstance when a ray is passing from aregion of higher index of refraction to aregion of lower index of refraction. If theincident angle exceeds the criticalangle, total internal reflection will occur.382Solutions ManualPhysics: Principles and ProblemsCopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.36. Critical Thinking When you use thehighest magnification on a microscope,the image is much darker than it is at lowermagnifications. What are some possiblereasons for the darker image? What couldyou do to obtain a brighter image?smallerconcave
Chapter 18 continued41. Although the light coming from the Sun isrefracted while passing through Earth’satmosphere, the light is not separated intoits spectrum. What does this indicateabout the speeds of different colors of lighttraveling through air? (18.1)The speeds of the different colors oflight traveling through air are the same.42. Explain why the Moon looks red during alunar eclipse. (18.1)During a lunar eclipse, Earth blocks theSun’s rays from the Moon. However,sunlight refracting off Earth’s atmosphere is directed inward toward theMoon. Because blue wavelengths oflight are dispersed more, red wavelengths of light reflect off the Moontoward Earth.43. How do the shapes of convex and concavelenses differ? (18.2)Convex lenses are thicker at the centerthan at the edges. Concave lenses arethinner in the middle than at the edges.Another lens is included in the opticssystem of the projector to invert theimage again. As a result, the image isupright compared to the original object.47. Describe why precision optical instrumentsuse achromatic lenses. (18.2)All lenses have chromatic aberration,which means different wavelengths oflight are bent at slightly different anglesnear their edges. An achromatic lens isa combination of two or more lenseswith different indices of refraction thatreduce this effect.48. Describe how the eye focuses light. (18.3)Light entering the eye is primarilyfocused by the cornea. Fine focusingoccurs when muscles change the shapeof the lens, allowing the eye to focus oneither near or far objects.49. What is the condition in which the focallength of the eye is too short to focus lighton the retina? (18.3)Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.nearsightedness44. Locate and describe the physical propertiesof the image produced by a convex lenswhen an object is placed some distancebeyond 2F. (18.2)It is a real image that is locatedbetween F and 2F, and that is invertedand smaller compared to the object.45. What factor, other than the curvature of thesurfaces of a lens, determines the locationof the focal point of the lens? (18.2)The index of refraction of the materialfrom which the lens is made also determines the focus.46. To project an image from a movie projectoronto a screen, the film is placed betweenF and 2F of a converging lens. This arrangement produces an image that is inverted.Why does the filmed scene appear to beupright when the film is viewed? (18.2)Physics: Principles and Problems50. What type of image is produced by theobjective lens in a refracting telescope?(18.3)real image, inverted51. The prisms in binoculars increase the distance between the objective lenses. Why isthis useful? (18.3)It improves the three-dimensional view.52. What is the purpose of a camera’s reflexmirror? (18.3)The reflex mirror diverts the image ontoa prism so that it can be viewed beforetaking a photograph. When the shutterrelease button is pressed, the reflexmirror moves out of the way so that thelens focuses the image onto the film orother photodetector.Solutions Manual383
Chapter 18 continuedApplying Conceptspages 508—50953. Which substance, A or B, in Figure 18-24has a larger index of refraction? Explain.A B!c, glass/air ! sin"1! ! "1.001.52! 41.1 Air and glass have the smaller criticalangle of 41.1 . The critical angle for airand water is 48.8 .58. Cracked Windshield If you crack thewindshield of your car, you will see a silveryline along the crack. The glass has separatedat the crack, and there is air in the crack.The silvery line indicates that light is reflecting off the crack. Draw a ray diagram toexplain why this occurs. What phenomenondoes this illustrate?Figure 18-24From outsideThe angle in substance A is smaller, soit has the larger index of refraction.54. A light ray strikes the boundary betweentwo transparent media. What is the angle ofincidence for which there is no refraction?55. How does the speed of light change as theindex of refraction increases?As the index of refraction of a materialincreases, the speed of light in thatmaterial decreases.56. How does the size of the critical anglechange as the index of refraction increases?The critical angle decreases as theindex of refraction increases.57. Which pair of media, air and water or airand glass, has the smaller critical angle?n2!c ! sin"1! !n "!1 # !cnglass!1 # !cnglassTo the driver’s eyesThis illustrates light reflected at angleslarger than the critical angle, or totalinternal reflection.59. Legendary Mirage According to legend,Eric the Red sailed from Iceland and discovered Greenland after he had seen the islandin a mirage. Describe how the mirage mighthave occurred.Even though Greenland is below thehorizon, it is visible as a mirage due tothe refraction of light.1!c, water/air ! sin"1! ! "1.001.33! 48.8 384Solutions ManualPhysics: Principles and ProblemsCopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.An angle of incidence of 0 allows thelight to go through unchanged. Or if theangle of incidence is greater than thecritical angle there is total internalreflection.Crackn ! 1.0
Chapter 18 continuedThe magnification is much less in waterthan in air. The difference in the indicesof refraction for water and glass ismuch less than the difference for airand glass.MirageCold,densea irmarW ira64. Why is there chromatic aberration for lightthat goes through a lens but not for lightthat reflects from a mirror?GreenlandIceland60. A prism bends violet light more than itbends red light. Explain.Violet light travels slower in a prismthan red light does.61. Rainbows Why would you never see a rainbow in the southern sky if you were in thenorthern hemisphere? In which directionshould you look to see rainbows if you arein the southern hemisphere?Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.You can see a rainbow only when theSun’s rays come from behind you at anangle not greater than 42 with the horizon. When you are facing south in thenorthern hemisphere, the Sun is neverbehind you at an angle of 42 or less.62. Suppose that Figure 18-14 is redrawn witha lens of the same focal length but a largerdiameter. Explain why the location of theimage does not change. Would the imagebe affected in any way?The location of the image depends onthe focal length of the lens and the distance of the object from the lens.Therefore, the location of the imagedoesn’t change.63. A swimmer uses a magnifying glass toobserve a small object on the bottom of aswimming pool. She discovers that the magnifying glass does not magnify the objectvery well. Explain why the magnifying glassis not functioning as it would in air.Physics: Principles and ProblemsChromatic aberration for lenses is due tothe dispersion of light (different wavelengths of light have different speeds inthe lens and refract with slightly different angles). Mirrors reflect, and reflection is independent of wavelength.65. When subjected to bright sunlight, the pupilsof your eyes are smaller than when they aresubjected to dimmer light. Explain why youreyes can focus better in bright light.Eyes can focus better in bright lightbecause rays that are refracted intolarger angles are cut off by the iris.Therefore, all rays converge at anarrow angle, so there is less sphericalaberration.66. Binoculars The objective lenses in binoculars form real images that are uprightcompared to their objects. Where are theimages located relative to the eyepiecelenses?Each side of the binoculars is like arefracting telescope. Therefore, theobjective lens image must be betweenthe eyepiece lens and its focal point tomagnify the image.Mastering Problems18.1 Refraction of Lightpages 509—510Level 167. A ray of light travels from air into a liquid,as shown in Figure 18-25. The ray is incident upon the liquid at an angle of 30.0 .The angle of refraction is 22.0 .Solutions Manual385
Chapter 18 continuedb. At what angle does the beam enter thewater?30 ng sin !g ! nw sin !wAirng sin !g!w ! si
Chapter 18 continued. 22. A convex lens with a focal length of 22.0 cm is used to view a 15.0-cm-long pencil located 10.0 cm away. Find the height and orientation of the image.! ! & d i! !! !!!! "18.3 cm m! ! h i! ! If the object is located farther than! 27.5 cm (upright image) 23. A stamp collector wants to magnify a stamp by 4.0 when the stamp is 3.5 cm from the lens. What focal length is .
Part One: Heir of Ash Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 Chapter 24 Chapter 25 Chapter 26 Chapter 27 Chapter 28 Chapter 29 Chapter 30 .
TO KILL A MOCKINGBIRD. Contents Dedication Epigraph Part One Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Part Two Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18. Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 Chapter 24 Chapter 25 Chapter 26
index of refraction, the ray will bend away from the normal (angle of incidence angle of refraction). If the second medium has a higher index of refraction, the ray will bend towards the normal (angle of incidence angle of refraction). From the diagrams, we can therefore tell that n A n i, n B n i, and n C n i
DEDICATION PART ONE Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 PART TWO Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 .
refraction has a shorter focal length than an identically shaped lens with a low index of refraction. A lens surrounded by air (w hich has a low index of refraction) has lower focal length than the same lens immersed in water (which has a high index of refrac-tion). There are two types of lenses: convergent and divergent. A convergent lens makes
Reducing the Number of Lenses with Aspheres Example photographic zoom lens Equivalent performance 9 lenses reduced to 6 lenses Overall length reduced Ref: H. Zügge 436 nm 588 nm 656 nm y p x p ' y ' x axis field 22 y p x p ' y ' x y p x p ' y ' x axis field 22 y p x p ' y ' x A 1 A 3 A 2 a) all spherical, 9 lenses b) 3 aspheres, 6 lenses .
The Formation of Images by Lenses RAY DIAGRAMS. Here are some useful rays in determining the nature of the images formed by converging and diverging lens. Since lenses pass light through them (unlike mirr
Experiment 4: Refraction and Interference with Microwaves 1 Experiment 4: Refraction and Interference with Microwaves Introduction Many phenomena whose study comes under the heading of "physical optics" arise from certain integral relationships between the wavelength of the radiation and dimensions of the experimental apparatus.
