PHYSICS 106 TEST #3 May 5, 2010

Transcription

1 NAME: PHYSICS 106 TEST #3 May 5, 010 ID NUMBER: LECTURE SECTION: [ ] A1 (8 am) [ ] B1/HP ( pm) [ ] C1 (6 pm) INSTRUCTIONS: 1. Do not turn over this cover sheet until instructed to do so.. No talking is allowed during this test. 3. Please include appropriate units with all numerical answers. 4. Show all steps in your solutions! If you need more space for calculations, use the back of the page preceding the question. For example, calculations for problem 3 should be done on the back of the page containing question. You must show correct work to receive full credit. Support your answers with brief written explanations and/or arguments based on equations. 5. Indicate clearly which part of your solution is the final answer for each part. 6. No notes, calculators, or books allowed! You should have only pencils and/or pens. A formula sheet is included on the last page of the test. Feel free to remove it carefully. 7. Please turn off and put away all electronic devices, including cell phones, pagers, personal stereos (including those with headphones), and calculators. 8. Optional - Please rank (circle the number provided at the bottom of each page) each problem from 1 (very similar to practice problems considered before the test), to (somewhat similar), to 3 (very different from previous problems) (see the example at the bottom of this page) Angle (θ) sin(θ) cos(θ) tanθ = sinθ cosθ This problem was: 1 very similar to practice problems somewhat similar 3 very different from practice problems 1

2 rank Problem 1: /10 Problem : /10 Problem 3: /10 Problem 4: /10 Problem 5: /10 Problem 6: /10 TOTAL: /60 This problem was: 1 very similar to practice problems somewhat similar 3 very different from practice problems

3 PROBLEM 1 10 points A particular beam of light, with an intensity of 800 W/m, is linearly polarized at an angle of +45 to the vertical. You have three polarizers, which have their transmission axes aligned as follows: Polarizer A - the transmission axis is at 0 to the vertical; Polarizer B - the transmission axis is at +15 to the vertical; Polarizer C - the transmission axis is at +45 to the vertical. You will select two of these polarizers, and have the light pass through one and then the other. [1 point] (a) If you want to maximize the intensity of the light emerging from the second polarizer, which two polarizers should you use, and in what order should the light pass through them? [ ] first through A, then B [ ] first through B, then A [ ] A and B, in either order [ ] first through A, then C [ ] first through C, then A [ ] A and C, in either order [ ] first through B, then C [ ] first through C, then B [ ] B and C, in either order [ points] (b) For the situation in (a), when you maximize the intensity of the light emerging from the second polarizer, what is that intensity? [1 point] (c) If, instead, you want to minimize the intensity of the light emerging from the second polarizer, which two polarizers should you use, and in what order should the light pass through them? [ ] first through A, then B [ ] first through B, then A [ ] A and B, in either order [ ] first through A, then C [ ] first through C, then A [ ] A and C, in either order [ ] first through B, then C [ ] first through C, then B [ ] B and C, in either order [ points] (d) For the situation in (c), when you minimize the intensity of the light emerging from the second polarizer, what is that intensity? [1 point] (e) Now, you switch the light source to unpolarized light, with an intensity of 800 W/m. To minimize the intensity of the light emerging from the second polarizer, which two polarizers should you select, and in what order should the light pass through them? [ ] first through A, then B [ ] first through B, then A [ ] A and B, in either order [ ] first through A, then C [ ] first through C, then A [ ] A and C, in either order [ ] first through B, then C [ ] first through C, then B [ ] B and C, in either order [ points] (f) For the situation in (e), when you minimize the intensity of the light emerging from the second polarizer, what is that intensity? [1 point] (g) True or false? For the situation in (e), rotating the first polarizer will change the intensity of the light emerging from the second polarizer. [ ] True [ ] False This problem was: 1 very similar to practice problems somewhat similar 3 very different from practice problems 3

4 PROBLEM 10 points (a) A donkey stands at a distance of 1 m from a plane mirror. It is 1.0 m tall and its eyes are 0.6 m above the ground. Suppose it can see its whole self in the mirror. Draw a ray diagram showing the mirror of the minimum size needed so that the donkey can see a full image of itself. State how far above ground level the top and bottom edges of this mirror are, and the height of this mirror. Mirror [1 point] Donkey location Top at (1 point): _ (m) 0.4 m 0.6 m eye Bottom at (1 point): _ (m) [1 point] The height of this mirror is (m) (b) [ points] Suppose the mirror height is now reduced such that it is only 1/ the minimum height you found in (a), and it is mounted such that its bottom edge is at the level you found in part (a) for the bottom edge. With this, the donkey won t be able to see its whole body in the mirror. How much (in meters) does the donkey not see of its body? [ ] 0.9 m [ ] 0.8 m [ ] 0.7 m [ ] 0.6 m [ ] 0.5 m [ ] 0.4 m (c) [ points] For the mirror in part (b), suppose it is mounted such that its upper edge is at the same level as the top of its head. How much (in meters) does the donkey not see of its body? [ ] 0.9 m [ ] 0.8 m [ ] 0.7 m [ ] 0.6 m [ ] 0.5 m [ ] 0.4 m (d) [ points] A spherical mirror is used to produce an image of an object. It is found that the image is half the size of the object. Select from below ALL statements that are true. [ ] The mirror can be a concave mirror. [ ] The mirror can be a convex mirror. [ ] The focal length of the mirror can be 1/3 the distance between the object and the mirror. [ ] The focal length of the mirror can be 3 times the distance between the image and the mirror. This problem was: 1 very similar to practice problems somewhat similar 3 very different from practice problems 4

5 PROBLEM 3 10 points I. A lens forms an image which is three times taller than the object. [1 point] (a) Draw below a ray diagram to show the formation of such an image. Clearly indicate the lens, the object, and the image. [1 point] (b) Select from below ALL statements that may be true in this situation. [ ] this is a converging lens [ ] this is a diverging lens [ ] the magnification is 1/3 [ ] the magnification is -1/3 [ ] the magnification is 3 [ ] the magnification is -3 [ points] (c) If the image is 1.6 m away from the object, use your ray diagram and find the object distance d 0, and focal distance of the lens f. II. The picture at right shows two transparent 30 o 60 o 90 o prisms made of material with index of refraction n, and immersed in a transparent medium with index of refraction n m. The bold arrow shows a beam of light entering the first prism. [1 point] (a) After entering the first prism, the beam travels along path [ ] I [ ] II [ ] III [ ] none of the above [1 point] (b) Suppose after traveling through the first prism, light enters the second prism through side DE and subsequently leaves the second prism through side FE. In the picture above, draw a possible path taken by the beam from where it enters the first prism until it leaves the second one. Complete the following sentence: The angle between side FE and the light emerging from the second prism at side FE is _ degrees. [1 point] (c) If we want to replace the medium around the prism by another one such that the beam does not emerge from the first prism any more, the new medium should have its index of refraction [ ] greater than the old medium [ ] less than the old medium [1 point] (d) If we want to replace the medium around the prism with another one such that the light does not emerge from the first prism any more, the new medium should have its index of refraction n m [ ] > n [ ] = n [ ] < n [ points] (e) Suppose the index of refraction of the two prisms is n = 3. Find the maximum value for the index of refraction n m of the medium so that the beam experiences total internal reflection at side AC. This problem was: 1 very similar to practice problems somewhat similar 3 very different from practice problems 5

6 PROBLEM 4 10 points (a) [ points] The picture on the right shows a profile of a string at two consecutive times; t = 0 s, and t = 1 s. Draw the string profile at t = 4 s (you can use two extra grids for your work and the last extra grid for your final answer) The picture on the right shows a pattern formed as a result of interference between two wave sources (which are in phase and have the same frequency). Black corresponds to zero displacement, and white to maximum displacement. (b) [ points] Select all the points at which constructive interference occurs, and explain your choice. [ ] A [ ] B [ ] C [ ] D (c) [ points] Suppose the picture provided in part (b) illustrates the Young s double slit experiment with the following parameters: the distance from the slits to the screen is 4.0 m; the distance between the slits is 40 μm; the distance between the two first-order maxima is 0 cm. Find the wavelength of the light (you can treat the angles as small). This problem was: 1 very similar to practice problems somewhat similar 3 very different from practice problems 6

7 (d) [ points] In order to investigate diffractive properties of light, you cover one of the slits with a non-transparent material. If w = 40 μm is the width of each slit, find the width of the central maximum for the pattern you observe on the screen now (you can treat the angles as small). (e) [ points] Suppose, in the experiment described in part (d), you increase the distance between the slits and the screen. What change will happen to the pattern of light and dark fringes you observe on the screen? [ ] no change happens [ ] the fringes get closer together [ ] the fringes get farther apart [ ] not enough information This problem was: 1 very similar to practice problems somewhat similar 3 very different from practice problems 7

8 PROBLEM 5 10 points [1 point] (a) In the visible spectrum, photon energies range from about 1.8 ev to 3.1 ev. Photons with energies near 1.8 ev correspond to which color? [ ] blue [ ] green [ ] red [1 point] (b) In a particular photo-electric effect experiment, ultraviolet light causes electrons to be emitted from the surface of a particular metal. Will violet light also causes electrons to be emitted? [ ] Definitely Yes [ ] Definitely No [ ] It is possible, but we need more information to say. [ points] (c) The data table shows the maximum kinetic energy of electrons emitted from a metal surface by photons of different energies. Plot these points on the graph, and draw the most appropriate line(s) through the points. Photon energy (ev) Electron KE max (ev) [ points] (d) Determine the work function of the metal in (c). [ points] (e) First, determine the photon energy needed to produce electrons with a maximum kinetic energy of 4.0 ev, for the metal in (c). Then, using the approximation h = ev s, calculate the corresponding frequency for photons of this energy. [ points] (f) Imagine that you repeat the experiment in part (c), but for a different metal, which has a different work function than the metal in (c). Comparing the parts of the graphs for which the photon energies exceed the work function (i) the slopes of the lines should be [ ] the same [ ] different (ii) the x-intercepts of the lines should be [ ] the same [ ] different This problem was: 1 very similar to practice problems somewhat similar 3 very different from practice problems 8

9 PROBLEM 6 10 points [ points] (a) In a transmission electron microscope, electrons are accelerated from rest through a potential difference. Find the de Broglie wavelength of the electrons if the accelerating potential is 3.0 kv. Use Planck s constant h = Js, electron mass m e = kg, e = C. [1 point] (b) Find the energy of the electron in ev. [4 points] (c) The chart shows the existing nuclides and their lifetime, where a darker shade represents nuclides with a longer half-life. In particular, the nuclides shaded in black have half-life > 30 million years and are regarded as stable. The chart also shows that for atomic number 0 Z 7, the stable nuclides always have the neutron number, N = Z and/or Z+1 (except for hydrogen whose stable nuclides are 1 H and 1 1H ). For Z > 7, most of the stable nuclides have N increasingly bigger than Z as Z increases. Based on the above information, select ALL the following statements that are correct. [ ] 4 He is a stable isotope of helium (He). [ ] 17 B is an unstable isotope of boron (B) and would likely decay by the 5 β+ decay. [ ] 50 Co is an unstable isotope of cobalt (Co) and would likely decay by the 7 β- decay. [ ] H would likely undergo the following nuclear reaction: 1H+ 1H He+ 0n A specimen of a radioactive isotope that undergoes β decay has a mass of 56 g, an activity of 640,000 Bq and a half-life of.5 hours. [1 points] (d) Which of the following choices is the closest to the mass of the specimen 10 hours later? [ ] 8 g [ ] 16 g [ ] 3 g [ ] 64 g [ ] 18 g [ ] 56 g [ ] none of these [ points] (e) Suppose, after 10 hours, a 4 g sample is taken out of the specimen. Find the activity of the 4 g sample. This problem was: 1 very similar to practice problems somewhat similar 3 very different from practice problems 9

10 Feedback page optional (but very appreciated!) I. If you would like, in addition to the absolute ranking you have provided at the end of each problem, you can rank the problems relative to each other from easiest (1) to most difficult (6). Problem 1: Problem : Problem 3: Problem 4: Problem 5: Problem 6: Rank Also optional, and anonymous, feel free to use this space to give us comments about this test (for example, its overall difficulty, length, and/or familiarity), and/or about the course in general (for example, comparing to other courses you have been taking). You can tear this sheet off and give it back to us without your name on it. II. We are seeking opinions from you on the following two questions about test arrangements for this course. Your input will help us make plans for this course and for future courses as well. Would you prefer that each lecture section has its own grading scale and/or a test, or should all students take the same test and have the same grading scale? [ ] each lecture section has its own test and its own grading scale [ ] students from different sections should take the same test but the grading scales should be different (depending on the section) [ ] students from different sections should take different tests but the grading scales should be the same for the whole class [ ] it does not matter how tests are taken but the grading scale has to be the same for the whole class [ ] all students have to take the same test, the grading scales do not mater [ ] everything should be the same for all sections [ ] it does not matter to me, any system is OK Comments: B. What works better for you: having no class on the days of the tests but losing the review sessions, or having classes on the test days and also having review sessions for test? [ ] no review classes, and no classes on test days [ ] keep the current system Comments: This problem was: 1 very similar to practice problems somewhat similar 3 very different from practice problems 10

11 PY106 Equation Sheet III Values of some constants: e = 1.6 x C ε 0 = 8.85 x 10-1 C /(Nm ) μ 0 = 4π x 10-7 Tm/A 1 9 k = = Nm /C c = 3.00 x 10 8 m/s = 1/(ε 0 μ 0 ) 1/ 4 πε 0 Waves: v = fλ k = π/λ ω = π/t Constructive interference: ΔL = mλ Destructive interference: ΔL = (m + ½) λ EM waves: v = c = ± rel f ' f 1 B c E Average Intensity: max B I = max μ 0 Malus Law: I 1 = I 0 cos (Δθ) Lenses and mirrors: = +. This can be rewritten as: d f d o d i i d o f = d f o Magnification, m = h h i o d i = Index of refraction, n = c/v = λ/λ d o Snell s Law: n 1 sinθ 1 = n sinθ Critical angle, θ c = sin -1 (n /n 1 ) Interference and diffraction of light: Constructive interference, n > 1 slits: dsinθ = mλ Destructive interference, double slit: dsinθ = (m + ½) λ Destructive interference, single slit: Wsinθ = mλ Photon energy: E ph = hf Photo-electric effect: K max = hf W 0 Particle waves: λ = h / p E = mc 1 u = MeV/c Planck s constant: h = Js 1 ev = J Radioactivity, R = ΔN = λ N N = N o e λ t Δt T 1/ = ln = λ λ This problem was: 1 very similar to practice problems somewhat similar 3 very different from practice problems 11