课程名称︰普通物理学甲下 课程性质︰系必修 课程教师︰张宝棣 开课学院：电资学院 开课系所︰资讯系 考试日期（年月日）︰2008/06/20 考试时限（分钟）：140 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 1. Astronomers observe the chromosphere of the Sun with a filter that passes the red hydrogen spectral line of wave length 656.3nm, called the Hα line. The filter consists of a transparent dielectric of thickness d held between two partially aluminized glass plates. The filter is held a constant temperature. (a) Find the minimum value of d that produces maximum transmission of perpendicular Hα 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 visiable 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 spaced slits a distance d apart. (a) Show that the positions of the interference minima on a screen a large distance L away from the sheet that has the four equally spaced slits (spacing d, with d << λ) 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 2.00m, alight wavelength of 600nm, and a source spaacing of 0.1mm, 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 the either side of the central maximum in a double slit pattern if λ = 550nm, d = 0.150mm, and a = 30.0μm? (b) What is the ratioof 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 from block letters to spell out the name of a night club. Adjacent tubes are all 2.80cm apart. The tubes froming one letter are filled with neon and radiate predominantly red light with a wavelength of 640nm. For another letter, the tubes emit predominantly violet light at 440nm. The pupil of a dark-adapted viewer's eye is 5.20mm in diameter. If she is in a certain range distance away, the reviewer can resolve the separate tubes of one color but not the other. Which color is easier to resolve? Please explain. The viewers's distance must in what range for her to resolve the tubes of only one color? (10%) 5. If you double the width of a single slot, the intensity of the light passing through the slit is doubled. Please show that the intensity at the center of the screen increases by a factor of 4. Explain why this does not violate the conservation of energy. (8%) 6. A couple of astronauts left Earth on 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 on 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? (10%). (Neglect the spaceship acceleration). 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 = 3.00m and time tR = 1.00 * 10E-9s, and a blue light flashes at xB = 5.00m and tB = 9.00 * 10E-9s, all measured in 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 and S'. (b) Find the location of the two flashes in frame S'. (c) 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 4m. He runs through a barn which has rest width 4m 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 then draw the world lines of the front and back doors. (b) Show that in each frame, one will "see" that the length/width of the moving 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). Draw dashed lines from E1(E2) to its projections at tA and tB axes. 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%) --

※ 发信站: 批踢踢实业坊(ptt.cc) ◆ From: 140.112.242.66