課程名稱︰普通物理甲下 課程性質︰系上必修 課程教師︰張寶棣 開課學院：電資 開課系所︰資工 考試日期（年月日）︰2008/06/20 考試時限（分鐘）： 130分鐘 10:20 ~ 12:30 (最後大家都寫到快13:00) 是否需發放獎勵金：是，謝謝 （如未明確表示，則不予發放） 試題 : 1. Astronomers observe the chromosphere of the Sun with a filter that passes the red hydrogen spectral line of wave length 656.3 nm, called the H-alpha line. The fliter consists of a transparent dielectric of thickness d held between two partially aluminized glass plates. The filter is held at a constant temperature. (a) Find the minimum value of d that produce maximum transmission of perpendicular H-alpha light, if the dielectric has an index of refraction of 1.378. (b) What if? If the temperature of the filter increases above the normal value, what happened to the transmitted wavelength? (Its index of reflection does not change significantly.) (c) The dielectric will also pass what near visible wavelength? One of the glass plate is colored red to absorb this light? (15%) 2. Monochromatic light is incident on a sheet that has four long narrow parallel equally spased slits a distance d apart. (a) Show that the positions of the interference minima on a screen a large distance L away fronm the sheet that has the four equally spaced slits (spacing d, with d >> L) are given approximately by Ym = mλL/4d, where m = 1,2,3,5,6,7,9,10,..., that is, m is not a multiple of 4. (b) For a screen distance of 2.00 m, a light wavelength of 600 nm, and a source spacing of 0.1 mm, calculate the width of the principle interference maxima (the distance between the successive minimum) for four sources. Compare the width with that for two sources with the same spacing. (10%) 3. (a) How many bright fringes appear between the first diffraction-envelope minimum to either side of the central maximum in a double slit pattern if λ=550 nm, d = 0.150 mm, and a = 30μm? (b) What is the ratio of the intensity of the third bright fringe to the intensity of the central fringe? (10%) 4. Narrow, parallel, glowing gas-filled tubes in a variety of colors form block letters to spell out the name of a night club. Adjacent tubes are all 2.80 cm apare. The tubes forming one letter are filled with neon and radiate predominantly red light with a wavelength of 640 nm. For another letter, the tubes wmit predominantly voiolet light at 440 nm. The pupil of a dark-adapted viewer's eye is 5.20 mm in diameter. If she is in a certain range distance away, the reviewer can resolve the separate tubes of one color but nor the other. Which color is easier to resolve? Please explain. The viewer's distance must in what range for her to resolve the tubes of only one color? (10%) 5. If you double the wicth of a single slot, the intensity of the light passing through th slit is doubled. Please show that the intensity at the center of the screen increase by a factor of 4. Explain why this does not violate the conservation of energy. (8%) 6. A couple of astronauts left Earth in July 1st, 2010 by taking a spaceship with speed of 0.95c. The female astronaut realized that she was pregnant after she took off. After 10 months in her time, she gave birth to a baby boy. The male astronaut then immediately sent out a request with a speed of light to people in Earth to request a birth certificate. When did people on Earth receive his request? What's the birthday of the baby boy in Earth time? (Neglect the spaceship acceleration) (10%) 7. A particle moves with speed 0.800c in the +x'' direction along the x'' axis of frame S'', which moves with the same speed and in the same direction along the x' axis relative to frame S'. Frame S' moves with the same speed and in the same direction along the x axis relative to frame S. (a) Find the speed of the particle relative to frame S'. (b) Find the speed of the particle relative to frame S. (7%) 8. A red light flashes at position xR = 3.00 m and time tR = 1.00 x 10^-9 s, and a blue light flashes at xB = 5.00 m and tB = 9.00 x 10^-9 s, all measured in the S reference frame. Reference frame S' has its origin at the same point as S at t = t' = 0.; frame S' moves uniformly to the right. Both flashes are observed to occur at the same place in S'. (a) Find the relative speed between S ans S'. (b) At what time does the red flash occurs in the S' frame? (15%) 9. Let's use the Lorentz diagram to illustrate the pole vaulter puzzle. Assume that a pole vaulter holds a pole with rest length 4 m. He runs through a barn which has rest width 4 m between the first door and second door. (a) Draw a Lorentz diagram with A-frame as the pole vaulter and B-frame as the barn. Draw the world lines of the front and back of the pole. And the draw the world lines of the front and back doors. (b) Show that in each frame, ine will "see" that the length/width of the movine object is shorter. (c) Denote the world line intersection of the front pole and the first door as E0, which is the point that the front pole enters the first door. Do likewise for the other two intersections as the front pole leaves the second door (E1) and the back pole enters the first door (E2) to its projections at tA and tB axis. Show that when the front pole leaves the second door the pole vaulter "sees" that the back pole is still outside the first door but the barn people "thinks" that the back pole is inside the barn. Explain why this is not a puzzle. (15%) 相對論部分相對簡單，這次考卷上完全沒有圖 --

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