1 Name: ________________________________________________________ Student ID: ___________________________ Section #: _________ Physics 208 Exam 1 Oct. 3, 2007 Print your name and section clearly above. If you do not know your section number, write your TA’s name. Your final answer must be placed in the box provided. You must show all your work to receive full credit. If you only provide your final answer (in the box), and do not show your work, you will not receive very many points. Problems will be graded on reasoning and intermediate steps as well as on the final answer. Be sure to include units, and also the direction of vectors. You are allowed one 8½ x 11” sheet of notes and no other references. The exam lasts exactly 90 minutes. Problem 1: _______ / 20 Speed of light in vacuum: ! c = 3 "108m / s Problem 2: _______ / 15 Permittivity of free space ! "o= 8.85 #10$12C2/ N % m2 Problem 3: _______ / 15 Coulomb constant ! k = 1/ 4"#o= 9 $109N % m2/C2 Problem 4: _______ / 15 Magnitude of electron charge ! e = 1.6 "10#19C Problem 5: _______ / 15 Problem 6: _______ / 15 TOTAL: _______ / 952 1) [20 points, 4 points each]. i) Two canoes are 10 m apart on a lake. Each bobs up and down with a period T=4.0 s. When one is at the highest point, the other canoe is at its lowest. Both canoes are less than one water wavelength apart. What is the speed of the water wave? a) 2.5 m/s b) 5.0 m/s c) 14 m/s d) 40 m/s e) 80 m/s iii) Total internal reflection occurs a) at angles of incidence greater than that for which the angle of refraction = 90˚ b) at angles of incidence less than that for which the angle of refraction = 90˚ c) at angles of incidence equal to 90˚ d) when the refractive indices of the two media are matched e) none of the above iiii) Below is an electric dipole. What direction is the electric field at the black dot? a) A b) B c) C d) D e) E f) F iv) A 300 nm wavelength laser is shined vertically on a blu-ray disc (similar to a CD or DVD). Aside from the directly reflected beam, the only laser spots detected are at an angle of 70˚ from the incident laser beam. What is the track separation on the blu-ray disc? a) 0.32 microns b) 0.0043 microns c) 0.25 microns d) 0.28 microns e) 0.05 microns v) Which of the following is NOT required of electric field lines a) every field line starts on a positive charge and ends on a negative charge. b) no two field lines cross c) the density of field lines is proportional to the local electric field intensity d) the local electric field is tangent to the electric field line at that point e) all of these are true. + A B C D E F3 2) [15 points total] White light of uniform intensity in the wavelength range 400-690 nm is perpendicularly incident downward on the surface of a suspended water film of thickness L=320 nm and refraction index n2=1.33. The suspended water film is surrounded on all sides by air with index n1=1.0. a) [10 points] What wavelength λ of light reflected by the film appears bright to an observer? b) [5 points] If the water film were on an infinitely thick piece of glass (index n3=1.5), would the bright reflected wavelength be longer or shorter? The light is still shined downward from the air onto the water. Explain. λ = Value Units Answer4 3) [15 points total] Light incident from air (air index of refraction ! nair= 1.0) onto glass (glass index of refraction ! nglass= 1.5) is refracted at an angle of 35˚. Underwater (water index of refraction ! nwater= 1.33), the refracted angle is θ. The light is incident at the same angle in both cases. a) [5 points] Explain in words (no equations) whether the underwater refracted angle θ is greater than, less than, or equal to 35˚. b) [10 points] Calculate the value of the underwater refracted angle θ. 35˚ θ θ = = Value Units5 4) [15 points total] A projector with a single lens is to be used inside a closed room to project an image of a 20 mm X 30mm LCD (liquid crystal display) chip onto the wall of the room. The image needs to be at least 2 m X 3 m. The room is 5 m long. a) [5 points] What is the minimum required magnification? b) [10 points] You have available five different projector lenses, with focal lengths 20mm, 40mm, 80mm, 120mm, 200mm. Which of these can make the required image size in the 5 m long room? Magnification = Possible lenses =6 5) [15 points total] A molecule has a dipole moment of 1.21 Debyes (1 Debye=3.336×10−30 Coulomb-meters). The charge density was displaced 0.0021 nm in order to create this dipole moment. a) [5 points] How many electrons were moved to create this dipole moment (assume they were all moved the same distance)? b) [5 points] Calculate the force on the dipole from an ion 10 nm away as shown below. The ion has a net positive charge of +2e. The dipole vector is as indicated. c) [5 points] Now suppose the ion is directly below the dipole as shown below. Describe in words the force on the dipole and the motion of the dipole as a function of time due to its interaction with the ion. Assume the ion to be fixed in space. Magnitude # electrons = ! r p +2e F= = Magnitude Units Direction ! r p +2e7 6) [15 points total] An insulating sphere of radius 1 cm has a uniform surface charge density of 1 µC/m2. There is charge only on its surface, and nowhere else. Neglect any induced dipoles. a) [5 points] Calculate the magnitude of the electric field at the surface of the sphere. b) [10 points] Calculate the magnitude of the force on a 10 µC charge 2 cm from the center of the sphere. E = = Value Units F = = Value
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