Name Final Exam May 1, 2017

Transcription

1 Name Final Exam May 1, 217 This test consists of five parts. Please note that in parts II through V, you can skip one question of those offered. Some possibly useful formulas appear below. Constants, etc. 19 e C 19 ev J k e N m /C Tm/A h J s 15 h ev s 2-Slit Interference sinbright m d 2 d sin I Imax cos Position on a screen x Ltan Lsin I Transformers V1 V2 N1 N2 I V I V Focal Length 1 f 2 R 1 n f n1 R1 R2 Diffraction sin m a dark 2 sin a sin Imax asin Resistors Series: R R1 R Parallel: R R R Magnification M h h q p m Part I: Multiple Choice [2 points] For each question, choose the best answer (2 points each) 1. Suppose light is entering a lens or mirror from the left. If the image distance is positive, so q >, which side will the image be on? A) On the left for a mirror or lens B) On the right for a mirror or lens C) On the left for a mirror and the right for a lens D) On the right for a mirror and the left for a lens E) Insufficient information 2. When light is put through a single slit, how will the central bright spot compare in size with the other bright spots? A) It will be the same size as the other bright spots B) It will be half as wide as the other bright spots C) It will be twice as wide as the other bright spots D) It will be one-fourth as wide as the other bright spots E) It will be four times as wide as the other bright spots 1 2 X-Ray Scattering 2dcos m Compton Scattering h 1cos mc Diffraction Grating sin m d RC Circuits RC t Q Q e Telescope Magnification m f f o Brewster s Angle tan P n n e Thin Film 2t m Weak 2 1

2 3. Geometric optics works best when A) Wavelengths are long and optical components are large B) Wavelengths are short and optical components are large C) Wavelengths are long and optical components are small D) Wavelengths are short and optical components are small E) None of the above 4. If I have a wire with current flowing to the right, which direction will the magnetic field point at the point P above the wire? A) B) C) D) E) P 5. If a convex mirror has a radius of curvature of 4 cm, then its focal length is A) + 8 cm B) +4 cm C) + 2 cm D) 8 cm E) 2 cm 6. Which of the following is not a type of electromagnetic radiation? A) Visible light B) X-rays C) Gamma rays D) Neutrinos E) Microwaves 7. How is most electric current generated for general power consumption? A) Giant strings of chemical batteries B) Rotating loops of wire in magnetic fields (or vice versa) C) Triboelectricity, generated by rubbing materials together to create static electricity D) Forcing materials through small holes that strip off the electrons E) Using sunlight beams to knock electrons into wires 8. The speed of light is approximately 3 8 A) 8 1 m/s B) 3 1 m/s C) m/s D) m/s E) None of these 9. How do rainbows produce the many colors that they have in them? A) Water selectively absorbs different colors at different angles B) Different colors refract by different amounts as they enter and leave the rain drop C) The index of refraction of the water slows the light down, causing it to shift to different wavelengths/colors D) Interference between light bouncing off the front/back end of the raindrop cause some colors to constructively interfere, while others destructively interfere E) The spaces between the water molecules act like a diffraction grating 1. What is the current I in the diagram at right? A) 1 A B) 6 A C) 4 A D) 2 A E) A 11. The device pictured at right does what? A) Allows current through one direction, but not the other B) Resist changes in current C) Resist changes in voltage D) Produce a current proportional to the voltage E) Produces a fixed voltage difference between its two ends 12. A capacitor with capacitance 2 F with a voltage of 5 V across it would have how much charge in it? A).1 C B).4 C C) 1 C D) 2.5 C E) None of these I 2 A 5 A 3 A

3 13. If you have a sketch of equipotential surfaces for the electric potential, how can you tell where the field is strong, and which direction will it point? A) It will be parallel to the equipotential surfaces, pointing the same way they do B) It will be anti-parallel to the equipotential surfaces, pointing the opposite direction C) It will be perpendicular to the surfaces, and pointing uphill (towards higher potential) D) It will be perpendicular to the surfaces, and pointing downhill (towards lower potential) E) None of the above are correct 14. When we say that light has two possible polarizations, what does this mean? A) The light could be moving forwards or backwards B) The light could be made of electric fields or magnetic fields C) The light could be made of short wavelengths or long wavelengths D) There are two independent directions the electric (and magnetic) field could be pointed E) There could either be a photon present or no photon present 15. A photon of wavelength would have momentum given by A) h/ B) /h C) 1/h D) h E) None of these 16. How does the electric force between two protons 1 nm apart differ from the force between two electrons 1 nm apart? A) The electron force is smaller B) The electron force is bigger C) The electron force is the same size, but it is attractive, whereas the protons are repulsive D) The electron force is the same size, but it is repulsive, whereas the protons are attractive E) The forces are the exact same size, and both proton-proton and electron-electron forces are repulsive 17. The energy of a single photon of light is proportional to its A) Frequency B) Period C) Wavelength D) Color E) None of these 18. A capacitor resists changes in, and an inductor resists changes in. A) Current, voltage B) Voltage, current C) Voltage, resistance D) Resistance, voltage E) Resistance, current 19. If a light beam enters water, how would the frequency and wavelength change? A) Frequency increases and wavelength increases B) Frequency decreases and wavelength decreases C) Frequency decreases and wavelength stays the same D) Frequency stays the same and wavelength increases E) Frequency stays the same and wavelength decreases

4 2. For very large and high quality telescopes, one of the advantages of using mirrors instead of lenses is A) Mirrors don t suffer from diffraction B) Mirrors can reflect a wide range of colors C) Mirrors do not suffer from chromatic dispersion D) Mirrors are made of metal, which is cheap, while lenses are made of expensive glass E) Mirrors can reflect light at a wide range of angles, not just perpendicular like glass cam 21. Assuming the lenses below are made of glass and are used in air, which of the following lenses (drawn tilted sideways) would definitely lead to a positive focal length? A) B) C) D) E) Insufficient information 22. The integral of the electric field over the surface sketched at right, if the charges are arranged as shown, would be 2 C 2 C 6 C 4 C 4 C A) B) C) D) E) 23. How does the eye adjust so that it can focus on both nearby and -7 C distant objects? A) It chemically changes the index of refraction of the lens, changing the focal length B) It moves the lens back and forth, so it will focus correctly on the retina C) It moves the retina back and forth, so it will be at the right place D) Special muscles change the shape of the lens E) It changes the fluid inside the eye, so the refraction will change +2 C -6 C +8 C +9 C 24. According to Maxwell s version of Ampere s Law, what are the two ways that magnetic field can be generated? A) Stationary charges and changing currents B) Electric currents and changing charges C) Electric currents and changing electric fields D) Electric currents and constant voltages E) Changing currents and constant voltages 25. If a charge has magnetic forces on it, and it is initially moving perpendicular to a constant magnetic field, the path it will follow will be a A) Circle B) Helix C) Parabola D) Line E) Hyperbola

5 Part II: Short answer, old material: [2 points] Choose two of the following three questions and give a short answer (2-3 sentences) (1 points each) 26. Suppose I have a conducting sphere of radius R, and I place a charge Q on it. Tell me where the charge ends up, and how I could compute the electric field inside the sphere and outside the sphere. 27. Give the formula for the magnetic force on a particle. If a negative charge is moving to the right in a magnetic field that points down, as illustrated at right, what would be the direction of the force on the particle? 28. Describe Lenz s Law. Explain what would happen if the conducting ring illustrated at right were moved to the right, out of the region of magnetic field.

6 Part III: Short answer, new material: [2 points] Choose three of the following four questions and give a short answer (2-3 sentences, or comparable) (1 points each) 29. Since the formula for angle of refraction is just Snell s law, n1sin1 n2sin2, how can a prism bend different colors differently? Also, discuss which visible wavelengths (long or short) bend the most, and which least, in a typical material such as glass. 3. When you look down at a fish underwater from the air, what distortions (if any) in size or distance occur? Assume the surface of the water is flat. 31. One of the main reasons that telescopes have a very large diameter is to gather as much light as possible. Explain another reason they need to have large diameters 32. Explain qualitatively why a very thin layer of oil on top of water often looks colorful.

7 Part IV: Calculation, old material: [4 points] Choose two of the following three questions and perform the indicated calculations (2 points each) 33. A charge Q = 6. C is fixed at the origin. (a) What is the electric field at a point P at position 2. cm to the right of Q? What is the electric potential at this point? Q 2 cm P (b) A second charge of magnitude q = 1.5 C with mass m = kg is now placed at the point P. What is the initial force on this charge? What is its initial potential energy? (c) The small charge q is released and allowed to run off to infinity (while Q remains fixed). What is its initial acceleration?

8 34. A battery of voltage 12. V is connected through a switch S to two resistors of magnitude 16. k and 8. k and a capacitor with capacitance 25. F, as sketched at right. Initially, the switch S is closed, and has been closed for a long time (a) In the steady state, find the current through the two resistors. 8 k + b 12 V 25 F S 16 k (b) In the steady state, find the voltage across the capacitor and the charge on the capacitor (c) At t =, the switch is suddenly opened. What is the time constant for the capacitor to be discharged? (d) Find the charge on the capacitor at t = 1. s.

9 35. A perfect transformer converts a power line with voltage 3, V to household current at 6. V. V rms V rms It then powers the house, which can be treated as a 3. resistor. (a) If the secondary winding, on the house side of the transformer, has 9 turns, how many does the primary have? From power line 3 (b) What is the RMS current through the resistor? Find the power consumed by the resistor. (c) What is the RMS current coming in from the transmission line?

10 Part V: Calculation, new material: [6 points] Choose three of the following four questions and perform the indicated calculations (2 points each) 36. A light beam from air enters a right-isosceles prism of glass with index of refraction n =1.56 at an angle of 14.. After entering the glass, it then reflects off the other side of the prism. It then refracts back out of the prism into air. (a) What is the angle of refraction when it first enters the glass? (b) What is the angle of incidence and the angle of reflection as it passes through this glass prism and bounces off the back?. (c) Assume that the back of the glass has air. Will all of the light be reflected? Suppose instead that some moisture (n = 1.33) has accumulated on the back of the prism. Will it still all be reflected?

11 37. An object denoted by the arrow at right is imaged through the planoconvex lens also sketched at right. The lens is made of glass with index of refraction n = 1.5 and will be used in air. The lens has a focal length of 4. cm. (a) Mark the position of both focal points directly on the diagram. (b) Draw three light rays from the tip of the object, and sketch how they will behave after passing through the lens. You may add dashed lines or whatever if necessary to help guide your lines as accurately as possible. (c) Sketch in the approximate position and size of the image. Is the image upright or inverted? Is it enlarged or reduced? Is it real or virtual? (d) Calculate the radius of curvature R for this lens in cm.

12 38. Light with unknown wavelength is incident on a pair of very narrow slits that are.29 mm apart. The light then lands on a screen at a distance of 4.8 m away. A pattern of light as sketched above then appears on the screen (use your ruler to measure it). (a) Measure the distance between the farthest bright peak on the left and the farthest on the right that you can see. Based on this measurement, deduce the distance between one peak and the next as accurately as possible (b) What is the wavelength of light used to get this interference pattern? (c) What is the intensity of the light 1. cm from the center as a fraction of the intensity at the exact center of the pattern?

13 A hydrogen atom contains an electron with mass m kg moving on a circle of 11 radius a m. (a) Take this to be the uncertainty in the position, x a. Based on this uncertainty, find the minimum uncertainty in the momentum of the electron, p. (b) Assuming this momentum is the momentum of the electron, p p, find the velocity of the electron v in m/s. (c) Find the kinetic energy of the electron. Write your answer in ev.