Physics 1252 Sec.A Exam #1A Instructions: This is a closed-book, closed-notes exam. You are allowed to use a clean print-out of your formula sheet, any scientific calculator, and a ruler. Do not write on your formula sheet There is space after each question to show your work; if you need more space, you may use the back of the page, or request more paper. Please clearly indicate where your work for each problem is. Underline or draw a box around your final answer. The exam consists of four sections. Read all the questions at the start so that you can allocate your time wisely. Do easy ones first! You may not share your calculator. The use of cell phones or any other electronic devices (besides calculators) is prohibited. All such gadgets must be turned off and put away throughout the exam. Do not open the exam until told to begin. You have the entire lab/class period to finish the exam. Put your last name on every page of the exam. You must provide explanations and/or show work legibly to receive full credit for Sections III and IV. Make sure that your answers include appropriate units and significant digits. (Note: For intermediate steps in your calculation, it s best to carry around more significant digits.) Assume that the index of refraction of air is the same as for a vacuum, unless otherwise stated. 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 personally uphold the university s standards of academic honesty for this exam, and will not tolerate any violations of these standards by others. Unsigned exams will not be graded. Signature: UGACard #: Copyright c 2016 University of Georgia. Unauthorized duplication or distribution prohibited.
Section I II III IV V (Bonus) Score /20 /10 /35 /35 /10 I: Multiple-Choice Questions (20 points) For each question below, choose the single best response and write the corresponding capital letter in the box provided. There is no penalty for guessing the wrong answer. 1. UGA waves weren t covered in class, but they do obey Snell s law! They have a speed of wave propagation v A = 2097m/s in apple juice and v B = 522m/s in butter milk. Also, assume that sin(14.414 o ) = 522/2097. A narrow beam of UGA waves striking a flat horizontal interface between apple juice and butter milk, with the apple juice above and the butter milk below the interface A. will undergo total internal reflection if incident from below the interface with an angle of incidence of 8.5 o. B. will have an angle of refraction greater than the angle of incidence if the beam is incident from above the interface without total internal reflection. C. will undergo total internal reflection if incident from below the interface with an angle of incidence of 29.0 o. D. will undergo total internal reflection if incident from above the interface with an angle of incidence of 29.0 o. E. will always have an angle of refraction not exceeding 14.414 o if the beam is incident from below the interface. 2. A real object is placed in front of a converging mirror, at a distance smaller than the focal length. When the object is moved slightly away from the mirror, without crossing the focal point, in which direction does the image move or change its size? A. The image moves closer to the mirror. B. The image (lateral) size grows. C. The image position doesn t change. D. The image (lateral) size shrinks. E. Not enough information is given. Copyright c 2016 University of Georgia. 2
3. Visible light has a range of wavelengths from 400nm (violet) to 700nm (red) in vacuum. A beam of electromagnetic waves with a frequency of 357.2 THz in air travels from air into water, with indices of refraction n Air = 1.00 and n Water = 1.333. To an under-water observer, the beam while traveling in water will A. have a wavelength of 839.9nm, a frequency of 268.0 THz, and be visible to the human eye; B. have a wavelength of 1119.5nm, the same frequency as in air, and be invisible to the human eye; C. have a wavelength of 630.1nm, a frequency of 476.1 THz, and be visible to the human eye; D. have a wavelength of 839.9nm, the same frequency as in air, and be invisible to the human eye; E. have a wavelength of 630.1nm, the same frequency as in air, and be invisible to the human eye. 4. Two identically shaped solid blocks, S and T, made from two different transparent materials, are immersed in the same liquid L. A ray of light strikes each block at a different angle of incidence, as shown. According to the figure below, what is the relative magnitude of the indices of refraction of the solid blocks, n S and n T, and liquid, n L? L L S T A. n S < n T < n L ; B. n T < n L < n S ; C. n T < n S < n L ; D. n S < n L < n T. E. n L < n S < n T ; Copyright c 2016 University of Georgia. 3
II: Draw a Ray Diagram (10 points) A virtual image is generated by a divergent lens. The image is to the left of the lens, at an absolute distance from the lens which is greater than the absolute value of the lens s focal length. Use a ruler to draw a clean ray diagram for the formation of the image, showing at least two of the principal rays, the lens and both its focal points, the object and the image, all of them clearly labeled. Is the object real or virtual? Hint: You need to construct the object here, given the image. First draw optical axis, lens and image. Then use sign conventions to find and label incoming and outgoing side of lens. Then use that to find the location of focal points F and F. Copyright c 2016 University of Georgia. 4
III: Refraction at a Glass Wall (35 points) 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, vertical planar surfaces. Both beams enter the wall at the same point, beam 1 at normal incidence, beam 2 at an angle α = 59 o to the wall. The two beams points of exit from the wall are y = 12.5cm apart. Air and water have indices of refraction n Air = 1.00 and n Water = 1.333, respectively. beam 2 beam 1 α x beam 1 y beam 2 (a) What is the index of refraction of the glass in the wall? (b) Does beam 2 undergo total internal reflection (TIR) at the right-hand surface of the wall? If so: What is the maximum allowed value of α for beam 2 to undergo TIR at the right-hand surface of the wall? If not: What is the angle of refraction of beam 2 at the right-hand surface of the wall? (c) How long does it take for a wave crest or trough in laser beam 2 to travel through the glass wall? Copyright c 2016 University of Georgia. 5
IV: A Microscope Image (35 points) In a microscope, an objective lens (Lens 1) of +1.00cm focal length is placed to the left of an eyepiece lens (Lens 2) of +2.00cm focal length. Your eye is located very close to, and to the right, of the eyepiece. A neuron is placed as the original object 1.05cm to the left of the objective lens. The final image produced by the eyepiece appears 30cm to the left of the eyepiece. (a) How far from the objective lens and to which side of it is the image produced by the objective lens? Is this image real or virtual? Is it erect or inverted relative to the original object. (b) Is the final image produced by the eyepiece real or virtual and, therefore, what is its image distance relative to the eyepiece? How far from the eyepiece is the eyepiece s object (=object from which the final image is produced)? How far apart are the two lenses? [Hint: The objective lens image found in (a) serves as the object to the eyepiece lens.] (c) If the original neuron object is 0.12mm in diameter what is the diameter of its final image, as seen through the eyepiece of the microscope? Is this final image erect or inverted relative to the original object? Copyright c 2016 University of Georgia. 6
V: Microscope Angular Magnification (10 extra points bonus, if correct numerical answer is obtained) From the results in Problem IV calculate the angular magnification achieved with the microscope, compared to viewing the neuron without any optical instrument, held at the near-point distance, 20.0cm from the eye. Copyright c 2016 University of Georgia. 7