PHYS 1112 In-Class Exam #1, Version D

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1 PHYS 1112 In-Class Exam #1, Version D Tue. Feb. 4, 2014, 11:00am-12:15am This is a closed-book, closed-notes exam, but you are permitted to bring and use a clean copy of the official Formula Sheet for this exam, which you should have printed out from the PHYS1112 web page. The exam consists of 15 multiple-choice questions. Each question is worth one raw score point, without penalty for wrong answers. No partial credit will be given. Read all the questions at the start so that you can allocate your time wisely. (Do easy questions first!) You may use a scientific calculator for arithmetic only; your calculator must be non-graphing, nonprogrammable, and non-algebraic. You are not allowed to share your calculator. The use of cell phones, pagers, PDAs, or any other electronic devices (besides calculators) is forbidden. Do not open the exam until you are told to begin. When told to open the exam, you may tear off the last few sheets, marked WORKSPACE, as scratch paper. Make sure the scantron sheet has your name and your UGA Card ID ( ) number filled in. Make sure you also have entered your name, UGA Card ID number and signature on the exam cover page (this page!) below. Make sure to enter your exam Version ID, A, B, C, D, or E, on your scantron as your answer to Problem 16. Without version ID, your exam can not be graded and you will get a score of zero. At the end of the exam period you must hand in both your scantron sheet and this entire exam paper, except for last few sheets of scratch paper, with cover page signed and with your name and UGA Card ID ( ) number filled-in on both scantron and cover page. Your exam will not be graded, and you will receive a score of zero, if you do not hand in all the foregoing required materials with name and ID information filled in. You will also receive a score of zero if you talk to or otherwise communicate with anyone during the exam, except for attending instructor and teaching assistants. You will also receive a score of zero if you use any unauthorized materials or devices during the exam. You have until the end of the class period (i.e., until 10:45am for Period 2 Class, until 12:15pm for Period 3 Class) to finish the exam and hand in the required exam materials described above. By signing below, you indicate that you understand the instructions for this exam and agree to abide by them. You also certify that you will uphold the university standards of academic honesty for this exam, and will not tolerate any violations of these standards by others. Name (please print): UGACard ID ( ) #: Signature: 1

2 Conceptual Problems Problem 1: Two identically shaped solid blocks, P and Q, made from two different transparent materials, are immersed in the same liquid F. A ray of light strikes each block so that the angle of refraction is the same inside both blocks, as shown. According to the figure below, what is the relative magnitude of the indices of refraction of the solid blocks, n P and n Q, and liquid, n F? F F P Q (A) n Q < n F < n P ; (B) n Q < n P < n F ; (C) n F < n P < n Q ; (D) n P < n Q < n F ; (E) None of the above. Problem 2: If a virtual object (d < 0) is presented to a convex mirror (f < 0), at an absolute distance d less then the absolute focal length f, i.e., d < f, then the image is always (A) real, inverted and enlarged in height relative to the virtual object (B) real, erect and enlarged in height relative to the virtual object (C) virtual, inverted and enlarged in height relative to the virtual object (D) virtual, inverted and reduced in height relative to the virtual object (E) closer to the mirror, in absolute distance, than the object 2

3 Problem 3: A small light source S is placed before a mirror, and a viewer O observes the object s image produced by the mirror, as shown here: O mirror 13 S Where does O perceive the mirror image of S to be located? (A) The image of S cannot be seen by O in the configuration shown above. (B) Position 1. (C) Position 2. (D) Position 3. (E) Position 4. Problem 4: A concave mirror M, a convergent lens L, and two small lightbulbs B and C, are rigidly mounted in two empty tanks, as shown below. From B and C, M and L produce images B and C, respectively. What happens to the locations of B and C when both tanks are completely filled with the liquid benzene, compared to their original locations in the empty tanks? (Hint: The index of refraction of benzene is about 1.50 for visible light.) M L B B C C (A) B does not move; and C moves towards or away from C. (B) B moves towards or away from B; and C does not move. (C) B moves towards B; and C moves towards C. (D) B moves towards B; and C moves away from C. (E) B moves away from B; and C moves towards C. 3

4 Problem 5: Sound waves (including ultrasound) have a speed of wave propagation v Air = 346m/s in air and v Water = 1497m/s in water. Also, note that sin( o ) = 346/1497. A narrow ultrasound beam striking the flat water surface of your swimming pool (A) cannot undergo total internal reflection if incident from above the water surface, regardless of the angle of incidence; (B) will undergo total internal reflection if incident from above the water surface with an angle of incidence of 10 o ; (C) will not undergo total internal reflection if incident from below the water surface with an angle of incidence of 45 o. (D) will have an angle of refraction greater than the angle of incidence if the beam is incident from below the water surface; (E) will always have an angle of refraction not exceeding o if the beam is incident from above the water surface; 4

5 Numerical Problems Problem 6: Two plane mirrors intersect at an angle θ = 68 o, as shown here: β A light ray is incident on the bottom, horizontal mirror at an angle of α = 22 o. What is the angle of reflection, β, for the 2nd reflection, occuring at the slanted mirror, as shown above? (A) 80 o (B) 46 o (C) 69 o (D) 109 o (E) 56 o Problem 7: A very thin, flat circular mirror of 50 cm diameter lies flat on the floor. Hanging from the ceiling and centered above the mirror is a small lamp. The circular spot formed on the flat ceiling 3.5m above the floor, by the reflection of the light from the lamp, has a radius of 1.50 m. How far below the ceiling is the lamp? (A) 1.60 m (B) 1.75 m (C) 2.80 m (D) 1.90 m (E) 0.70 m 5

6 Problem 8: Two laser beams are passing from water through the glass wall of an aquarium tank into air, as shown below. The glass wall is x = 36cm thick and has two parallel planar surfaces. Both beams enter the wall at the same point, beam 1 at normal incidence, beam 2 at an angle α = 55 o to the wall. The two beams points of exit from the wall are y = 15.5cm apart. Air and water have indices of refraction n Air = 1.00 and n Water = 1.333, respectively. At what speed does the light travel through the glass wall? x beam 2 beam 1 α beam 1 y beam 2 (A) m/s (B) m/s (C) m/s (D) m/s (E) m/s Problem 9: In flint glass, red light has an index of refraction (IoR) n R = and violet light has an IoR n V = , while both have an IoR n Air = in air. A beam of white light enters a triangular prism of flint glass from air at normal incidence at the front surface and then stikes the prism s back surface at an angle of incidence φ = 27.0 o as shown here: φ Red Violet The prism is surrounded by air. What is the angle of divergence, enclosed between the red and the violet beam after leaving the prism through the back surface? (A) o (B) o (C) o (D) o (E) o 6

7 Problem 10: If a candle, 12 cm in height, is placed in a dark room, between a flat projection screen and a concave spherical mirror (f > 0) of 60 cm radius, a sharp, upside-down image of the candle, 18 cm in absolute height, is projected onto the screen. How far from the mirror is the candle? How far from the candle is the screen? (A) The candle is 50 cm from the mirror; the screen is 25 cm from the candle. (B) The candle is 100 cm from the mirror; the screen is 50 cm from the candle. (C) The candle is 200 cm from the mirror; the screen is 100 cm from the candle. (D) The candle is 75 cm from the mirror; the screen is 50 cm from the candle. (E) The candle is 50 cm from the mirror; the screen is 75 cm from the candle. Problem 11: Visible light has a range of wavelengths from 400nm (violet) to 700nm (red) in vacuum. A beam of electromagnetic waves with a frequency of THz in air travels from air into water, with indices of refraction n Air = 1.00 and n Water = To an under-water observer, the beam while traveling in water will (A) have a wavelength of nm, the same frequency as in air, and be invisible to the human eye; (B) have a wavelength of 630.1nm, a frequency of THz, and be visible to the human eye; (C) have a wavelength of 839.9nm, the same frequency as in air, and be invisible to the human eye; (D) have a wavelength of 630.1nm, the same frequency as in air, and be invisible to the human eye. (E) have a wavelength of 839.9nm, a frequency of THz, and be visible to the human eye; Problem 12: A convergent lens (Lens1), placed to the right of a small grain of sand, produces an image of the grain 14.00cm to the right of Lens1. If a divergent lens (Lens2) of focal length f 2 = 6.42cm is now placed somewhere to the right of Lens1, the final image produced by Lens2 appears approximately 32.0cm to the left of Lens2. Approximately, how far apart are the two lenses? (A) 22.0 cm (B) 46.0 cm (C) 8.65 cm (D) 5.97 cm (E) 19.3 cm 7

8 Problem 13: A Galilean telecope has been designed to achieve an angular magnification of M θ = 11, with the convergent objective lens (Lens1, f 1 > 0) and the divergent eyepiece lens (Lens2, f 2 < 0) spaced 30cm apart. As in any telescope, the original object of Lens1 is infinitely far away,i.e., d 1. The final image seen though the eyepiece is also very (infinitely) far away from the eyepiece, so approximately d 2 and M θ = f 1 / f 2. Under these assumptions, find the focal length, f 2, of the eyepiece and the focal length, f 1, of the objective lens. (A) f 2 = 6.0 cm and f 1 = cm (B) f 2 = 5.0 cm and f 1 = cm (C) f 2 = 3.0 cm and f 1 = cm (D) f 2 = 2.5 cm and f 1 = cm (E) Cannot be solved based on the information provided. Problem 14: The state highway patrol radar guns send out a a microwave frequency of 7.080GHz. You are approaching a stationary radar speed trap with your car, driving 31.3m/s, and the radar receiver measures the frequency of the microwave reflected from your car. How does the frequency of this reflected microwave, as measured by the stationary receiver mounted on the radar gun, differ from the original frequency sent out by the gun? (A) The reflected is 739Hz higher than the original frequency. (B) The reflected is 1477Hz higher than the original frequency. (C) The reflected is 1477Hz lower than the original frequency. (D) The reflected is 369Hz higher than the original frequency. (E) The reflected is 739Hz lower than the original frequency. Problem 15: A microsope produces a final image of a bacterial cell (as seen through the eyepiece) which appears to be 1.2cm in diameter and located 40.0cm from the eyepiece on the incoming side of the eyepiece lens. If the cell has an actual diameter of 2.8 µm, what is the angular magnification achieved with the microscope, compared to viewing the cell from a 20.0cm nearpoint (reference) distance without instrument? (A) 990 (B) 2140 (C) 3220 (D) 4360 (E) 420 Problem 16: Enter your exam Version, A, B, C, D or E, on your scantron as the answer to Problem 16!! Your exam version is printed in bold face on top of the cover page of this exam paper which you signed. 8

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