Properties of Light Solutions Lecture Notes

26 Properties of Light Answers and Solutions Reading Check Questions 1. A changing magnetic field induces a changing electric field. 2. A changing electric field induces a changing magnetic field. 3. An electromagnetic wave is produced by vibrating electric and magnetic fields. 4. If the wave slowed, regeneration of waves would decrease, and lose energy. Therefore this doesnÕt occur. 5. If the wave sped up, there would be greater regeneration of waves and energy would increase. Therefore this doesnÕt occur. 6. Electric and magnetic fields contain and transport energy. 7. The principle difference between radio, light, and X-rays is frequency. 8. Light occupies about one millionth of 1% of the measured spectrum. 9. Red for lowest frequencies, violet for highest visible frequencies. 10. The frequencies of vibrating electrons are transferred to the waves, so the frequencies of both are the same. 11. Higher frequencies of light have shorter wavelengths. 12. The wavelength is 300,000 km long. 13. Outer space is filled with electromagnetic waves, for one thing. 14. Light encountering a transparent material causes atoms in the material to vibrate. 15. The resonant frequency of glass is in the ultraviolet region. 16. The energy of ultraviolet light becomes thermal energy. 17. The energy of visible light transmits through the glass and passes out the other side. 18. The energy of infrared light becomes thermal energy. 19. The frequencies match. 20. The average speed of light in glass is less than its speed in a vacuum. 21. The incident and emerging speed of light are the same. 22. Infrared waves cause whole atoms and molecules to vibrate. 23. Light is absorbed and turns to thermal energy. 24. Metals are shiny because their free electrons easily vibrate to incoming light. 25. Multiple reflections absorb light and the light emerging is weaker. 26. Umbra is the totally dark part of a shadow; a partial shadow is a penumbra. 27. All object in sunshine cast shadows, so yes, Earth and Moon always cast shadows. When the Sun or Moon passes within the otherÕs shadow, we have an eclipse. 28. Rods in the eye see brightness but not color; cones are sensitive to color. 29. Object on the periphery is best seen when moving. 30. The pupil widens with emotional interest. Think and Do 31. You may be surprised to find that the size of the Moon in the sky is that same whether low or high in the sky, even though a casual look finds it larger nearer the horizon. The explanation is physiological. 32. Open ended and interesting! Think and Solve 300, 000, 000 km 33. Speed = = 231,000 km/s. This value is 77% the modern value. 1300 s 34. Roundtripis30km,sofromd=ct,t=d/c=30km/300,000km/s=0.0001second. 35. 11 d d d 1.5«10 m 8 =500 s(whichequals8.3min). t v c 3 « 10 m Fromv = ,t = = = / s The time to cross the diameter of the EarthÕs orbit is twice this, or 1000 s, as estimated fairly closely by Roemer (question 33). 36. Earth-Moon distance is 3.8 « 108 m, so the round-trip distance is 7.6 « 108 m. As in the previous problem, t = v c 3 « 10 8 d = d = 8 7.6 «10 m =2.5 s. m/s 272 16 d d 4.2«10 m 8 8 =1.4«10 s. v c 3 « 10 m / s 37. Asinthepreviousproblem,t = = = Converting to years by dimensional analysis, 1.4 « 108 s « yr. 1 h 1 day 1 yr = 4.4 « « 38. 39. (a) Frequency = speed/wavelength = (3 « 108 m/s)/(0.03 m) = 1.0 « 1010 Hz = 10 GHz. (b) Distance = speed « time, so time = distance/speed = (10,000 m)/(3 « 108 m/s) = 3.3 « 10Ð5 s. (Note the importance of consistent SI units to get the right numerical answers.) 40.Light in water travels at 0.75c. l = for light in water. ff c for light in a vacuum (or air), and l = 0.75c The ratio of lwater to lair is therefore 0.75, the same for all frequencies. So the wavelength of light in water is 3/4 its value in air. Wavelength changes while frequency remains the same. In water, the wavelength of this orange light is (0.75)(600) = 450 nm. In Plexiglas, its wavelength is (0.67)(600) = 400 nm. Think and Explain 41. Yourfriendiscorrect.Alsoinaprofoundtone,yourfriendcouldsaythatsoundisth eonlythingwe hear! 42. Yourfriendisagaincorrect.Lightistheoscillationofelectricandmagneticfieldsth atcontinually regenerate each other. 43. The fundamental source of electromagnetic radiation isoscillating electric charges, which emit oscillating electric and magnetic fields. 44. Thewavelengthsofradiowavesarelongerthanthoseoflightwaves,whicharelon gerthanthe wavelengths of X-rays. 45. Ultraviolethasshorterwavelengthsthaninfrared.Correspondingly,ultravioletal sohasthehigher frequencies. 46. Usefilmoraphotosensitiveelementthatissensitivetotheinfraredpartofthespectrum,forthingsin the environment emit infrared waves, whether they are in darkness or in light. 47. Whatwavesinalightwavearetheelectricandmagneticfields.Theiroscillationfre quencyisthe frequency of the wave. 48. Frequency; a gamma ray has a higher frequency (and therefore more energy per photon) than an infrared ray. 3600 s 24 h 365 day The lines OAD and PBE are parallel, so the umbra, between D and E, has the same diameter as the ball. The triangles OAB and ODF are similar, with sides in the ratio of 2 to 1, so the distance DF is twice the distance AB. This means that the distances CD, DE, and EF are the same, so the penumbra, between C and F, has three times the diameter of the ball. 49. Speed is c, the speed of light. 50. Both travel at the same speed c. 51. Agree. They are both electromagnetic waves. 52. Agree, for a radio wave is an E&M wave while sound is a mechanical wave. 53. Agree. Electromagnetic wave are everywhere. 54. Both are much longer because their frequencies are much lower than the frequencies of visible light. 55. The faster wave has the longer wavelengthÑlight, in accord with the rule l = v/f. 56. Sound requires a physical medium in which to travel. Light does not. 57. Radio waves are electromagnetic waves and travel at the speed of light. (DonÕt confuse sound waves with radio waves!) 58. Radiowavesandlightarebothelectromagnetic,transverse,moveatthespeedof light,andare created and absorbed by oscillating charge. They differ in their frequency and wavelength and in the type of oscillating charge that creates and absorbs them. 59. The shorter wavelength corresponds to a higher frequency, so the frequency of the blue-green light from the argon laser has higher frequency than the red light from the helium-neon laser. 60. Theaveragespeedoflightwillbelesswhereitinteractswithabsorbingandreemittingparticlesof matter, such as in the atmosphere. The greater the number of interactions along the lightÕs path, the less the average speed. 61. Glass is opaque to frequencies of light that match its own natural frequencies. This is because the electrons in the absorbing medium are driven to oscillations of much larger amplitudes than occurs for nonresonant frequencies. These large amplitudes result in energy transfer to neighboring atoms and an increase in internal energy rather than a reemission of light. 62. Thegreaternumberofinteractionsperdistancetendstoslowthelightandresultis asmalleraverage speed. 63. Transparency or opaqueness is determined by the match between incident light frequencies and the resonant frequency of the material. A substance that is transparent to a range of light frequencies will be opaque to those frequencies that match its own resonant frequency. 64. Clouds are transparent to ultraviolet light, which is why clouds offer very little protection from sunburn. Glass, however, is opaque to ultraviolet light, and will therefore shield you from sunburn. 65. Thesunglasseswillbewarmerinsunlightthanregularreadingglassesbecauset hereadingglasses transmit most of the light energy that is incident upon them, whereas the sunglasses absorb more light energy, increasing their internal energy. 66. Anyshadowcastbyafarawayobjectsuchasahighflyingplaneisfilledinmainlybylighttaperingin from the Sun, which is not a point source. This tapering is responsible for the umbra and penumbra of solar eclipses (Figure 26.14). If the plane is low to the ground, however, the tapering of light around the airplane may be insufficient to fill in the shadow, part of which can be seen. This idea is shown in Figure 26.12. 67. Rods,notcones,willrespondtoweaklight,soyouwanttofocuslow- intensitylightonapartofthe retina that is composed of rods. That would be off to the side of the fovea. If youÕre looking at a dim star, look a bit off to the side of where you expect to see it. Then its image will fall on a part of your eye where rods may pick it up. 68. Thelightreflectedbyobjectsinthemoonlightismostoftentoodimtostimulatethec olor-perceiving cones in the eye. So we see these objects primarily with our rods, which explains their lack of color. 69. Weseenocolorattheperipheryofourvisionsimplybecausetherearenoconeslo catedonthe outermost regions of the retina. 70. Unlesslightreachinghereyeshasincreasedinintensity,hercontractingpupilsim plythatsheis displeased with what she sees, hears, tastes, smells, or how she feels. In short, she may be displeased with you! 71. Theblindspotislocatedonthesideofthefoveaawayfromyournose. 72. Wecannotinferthatpeoplewithlargepupilsaregenerallyhappierthanpeoplewit hsmallpupils.The size of a personÕs pupils has to do with the sensitivity of the retina to light intensity. Your pupils tend to become smaller with age as well. It is the change in pupil size that suggests oneÕs psychological disposition. 73. Inaccordwiththeinversesquarelaw,brightnessislessthan1/25thatseenfromEarth. 74. No,forthebrighteststarmaysimplybethecloseststar. 75. YouÕre seeing the galaxy as it ÒwasÓ when light left it, long, long ago. 76.You see your hand in the past! How much? To find out, simply divide the distance between your hands and your eyes by the speed of light. (At 30 cm, this is about a billionth of a second.) 77. From the Conversion Factors table on the inside back cover, note that 1 ft = 0.3048 m. So 20 feet is 20 « 0.3048 m = 6.096 m. So rounded off, in the metric system you could hope for 6/6 vision. Think and Discuss 78. Thetermsaremisleadinginthattheyimplythatultravioletandinfraredareformsof visiblelight.More correctly, they are forms of electromagnetic radiation. So in the sense used, ÒlightÓ is used to mean Òelectromagnetic radiation.Ó This usage stems from the fact that the ultraviolet and infrared regions of the spectrum are adjacent to visible light. The terms Òradio lightÓ and Òx-ray lightÓ are uncommon, for one likely reason, that radio x-ray parts of the spectrum are far removed from the visible part. 79. WecanseetheSunandstars. 80. Radio waves are electromagnetic waves, not to be confused with sound, which is a mechanical wave entirely different than any electromagnetic wave. Neither is visible. 81.The fact that the different parts of the electromagnetic spectrum emitted in the explosion are received simultaneously is evidence for the frequency independence of the speed of light. If wave speed depended on frequency, different frequencies would be received at different times. 82. Theinstantaneousspeedofthebulletafterpenetratingtheboardislessthanitsinc identspeed,but not so with light. The instantaneous speed of light before meeting the glass, while passing through it, and when emerging is a constant, c. The fundamental difference between a bullet fired through a board and light passing through glass is that the same bullet strikes and later emerges. Not so for light. The Òbullet of lightÓ (photon) that is incident upon glass is absorbed by its interaction with an atom or molecule. The atom or molecule in turn then emits, with some time delay, a new Òbullet of lightÓ in the same direction. This process cascades through the glass with the result being that the Òbullet of lightÓ emerging is not the same ÒbulletÓ that was first incident. In the space between the atoms in matter the instantaneous speed of light is c. Because of the time delay of the interactions, only its average speed is less than c. The light that emerges has speed c. 83. Walkingacrossaroomandpausingtogreetothersisanalogoustothetransmissi on-of-lightmodelin that there is a pause with each interaction. However, the same person that begins the walk ends the walk, whereas in light transmission there is a Òdeath-birthÓ sequence of events as light is absorbed and Ònew lightÓ is emitted in its place. The light to first strike the glass is not the same light that finally emerges. (Another analogy is a relay race, where the runner to begin the race is not the runner to cross the finish line.) 84. AsolareclipseisashadowoftheMoonthatreachesarelativelysmallpartoftheEar th,andonly those people in the shadow or partial shadow experience it. But a lunar eclipse is the EarthÕs shadow 275 upon the Moon, which is visible to all who can see the Moon. So everyone who can see the Sun wonÕt see its eclipse unless theyÕre in its shadow, but everyone who can see the Moon will see its eclipse where there is one. 85. Yes.Evidenceisalunareclipse,whentheMoonpassesintheEarthÕsshadow. 86. AlunareclipseoccurswhentheEarth,Sun,andMoonallfallonastraightline,witht heEarthbetween the Sun and the Moon. During perfect alignment the EarthÕs shadow falls on the Moon. Not-quite- perfect alignment gives Earth observers a full view of the Moon. Moonlight is brightest and the Moon is always fullest when the alignment is closest to perfectÑon the night of a lunar eclipse. At the time of a half moon, however, lines from Earth to Moon and from Earth to Sun are at right angles to each other. This is as non-aligned as the Earth, Moon, and Sun can be, with the Moon nowhere near the EarthÕs shadowÑno eclipse is possible. Similarly for the nonaligned times of a crescent moon. 87. During a partial eclipse where crescents of the Sun are cast, the Moon is partly in front of the Sun. 88. The solid angle from each opening in the leaves to the circles cast on Dean is the same solid angle between the leaves and the Sun. So just as 100 circles, each the size of the solar image, fit between Dean and the tree opening, 100 Suns would fit between the tree and its position from Earth, a distance of 150,000,000 km. 89. The Moon is farther away from its average distance from Earth, so is smaller in the sky. If it were closer, the Moon would appear bigger and the Sun would be entirely blocked when the Moon, Sun, and Earth align. 90. Noeclipseoccurredbecausenoshadowwascastonanyotherbody. 91. (a)MoonobserverswouldseetheEarthinthepathofthesunlightandseeasolarec lipse.(b)Moon observers would see a small shadow of the Moon slowly move across the full Earth. The shadow would consist of a dark spot (the umbra) surrounded by a not-as-dark circle (the penumbra). 92. Energyisspreadoutanddiluted,butnotÒlost.ÓWedistinguishbetweensomethin gbeingdilutedand something being annihilated. In accord with the inversesquare law, light intensity gets weaker with distance, but the total amount of light over a spherical surface is the same at all distances from the source. 276 93. Lightfromtheflashspreadsviatheinversesquarelawtothegroundbelow,andwhatlittlereturnsto the airplane spreads further. The passenger will find that the flash makes no difference at all. Taking pictures at great distances, whether from an airplane or the football stands, with the flash intentionally turned on is rather foolish. 94. Someairplanesbounceradarwavestoandfromthegroundbelow,measuringth eroundtriptimefor determining distance to the ground, much as a ship bounces sonic waves from the ocean floor to measure water depth. Far above the ground an altimeter is fine for determining the airplaneÕs height above sea level, but close to the ground the pilot wants to know the airplaneÕs distance from local ground.