Quantum Physics

Answers to Quick Quizzes, Odd-Numbered Conceptual Questions and Problems A.257. 19.5° above the horizontal9. (a) 1.52 (b) 417 nm (c) 4.74 10 14 Hz(d) 1.98 10 8 m/s11. (a) 584 nm (b) 1.1213. 111°15. (a) 1.559 10 8 m/s (b) 329.1 nm (c) 4.738 10 14 Hz17. five times from the right-hand mirror and six times fromthe left19. 0.388 cm21. 30.4°, 22.3°23. 6.39 ns25. tan 1 (n g )27. 3.39 m29. red 48.22°, blue 47.79°31. (a) 1i 30°, 1r 19°, 2i 41°, 2r 77°(b) First surface: reflection 30°;second surface: reflection 41°33. (a) 31.3° (b) 44.2° (c) 49.8°35. (a) 33.4° (b) 53.4°37. (a) 40.8° (b) 60.6°39. 1.000 0841. (a) 10.7° (b) air (c) Sound falling on the wall frommost directions is 100% reflected.43. 27.5°45. 22.0°47. (a) 53.1° (b) 38.7°49. (a) 38.5° (b) 1.4453. 24.7°55. 1.9359.61. (a) 1.20 (b) 3.40 ns sin 1 √n 2 1 sin cosChapter 23QUICK QUIZZES1. At C.2. (c)3. (a) False (b) False (c) True4. (b)5. An infinite number6. (a) False (b) True (c) FalseCONCEPTUAL QUESTIONS1. You will not be able to focus your eyes on both the pictureand your image at the same time. To focus on the picture,you must adjust your eyes so that an object several centimetersaway (the picture) is in focus. Thus, you are focusingon the mirror surface. But, your image in the mirroris as far behind the mirror as you are in front of it.Thus, you must focus your eyes beyond the mirror, twiceas far away as the picture to bring the image into focus.3. A single flat mirror forms a virtual image of an object dueto two factors. First, the light rays from the object are necessarilydiverging from the object, and second, the lack ofcurvature of the flat mirror cannot convert diverging raysto converging rays. If another optical element is first usedto cause light rays to converge, then the flat mirror can beplaced in the region in which the converging rays arepresent, and it will change the direction of the rays so thatthe real image is formed at a different location. For example,if a real image is formed by a convex lens, and the flatmirror is placed between the lens and the image position,the image formed by the mirror will be real.5. The ultrasonic range finder sends out a sound wave andmeasures the time for the echo to return. Using this information,the camera calculates the distance to the subjectand sets the camera lens. When the camera is facing amirror, the ultrasonic signal reflects from the mirror surfaceand the camera adjusts its focus so that the mirrorsurface is at the correct focusing distance from the camera.But your image in the mirror is twice this distancefrom the camera, so it is blurry.7. Light rays diverge from the position of a virtual imagejust as they do from an actual object. Thus, a virtual imagecan be as easily photographed as any object can. Ofcourse, the camera would have to be placed near theaxis of the lens or mirror in order to intercept the lightrays.9. We consider the two trees to be two separate objects. Thefar tree is an object that is farther from the lens than thenear tree. Thus, the image of the far tree will be closer tothe lens than the image of the near tree. The screen mustbe moved closer to the lens to put the far tree in focus.11. If a converging lens is placed in a liquid having an index ofrefraction larger than that of the lens material, the directionof refractions at the lens surfaces will be reversed, andthe lens will diverge light. A mirror depends only on reflectionwhich is independent of the surrounding material, soa converging mirror will be converging in any liquid.13. This is a possible scenario. When light crosses a boundarybetween air and ice, it will refract in the same manner asit does when crossing a boundary of the same shape betweenair and glass. Thus, a converging lens may be madefrom ice as well as glass. However, ice is such a strong absorberof infrared radiation that it is unlikely you will beable to start a fire with a small ice lens.15. The focal length for a mirror is determined by the law ofreflection from the mirror surface. The law of reflectionis independent of the material of which the mirror ismade and of the surrounding medium. Thus, the focallength depends only on the radius of curvature and noton the material. The focal length of a lens depends onthe indices of refraction of the lens material andsurrounding medium. Thus, the focal length of a lensdepends on the lens material.17. (a) all signs are positive (b) f and p are positive, q isnegative19. (c) the image becomes fuzzy and disappearsPROBLEMS1. on the order of 10 9 s younger3. 10.0 ft, 30.0 ft, 40.0 ft5. 0.268 m behind the mirror; virtual, upright, anddiminished; M 0.026 87. (a) 13.3 cm in front of mirror, real, inverted, M 0.333(b) 20.0 cm in front of mirror, real, inverted, M 1.00(c) No image is formed. Parallel rays leave the mirror.9. Behind the worshipper, 3.33 m from the deepest point inthe niche.11. 5.00 cm13. 1.0 m15. 8.05 cm17. 20.0 cm19. (a) concave with focal length f 0.83 m(b) Object must be 1.0 m in front of the mirror.21. 38.2 cm below the upper surface of the ice