Thu, 09 February 2017 Name: Physics 1252 Section 36501 Exam #1E 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 2017 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. Visible light has a range of vacuum wavelengths from 400nm (violet) to 700nm (red). A beam of electromagnetic waves with a frequency of 714.3THz 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 420.0nm, have a frequency of 535.9THz, and be visible to the human eye. B. have a wavelength of 315.1nm, have a frequency of 952.2THz, and be invisible C. have a wavelength of 315.1nm, have the same frequency as in air, and be visible D. have a wavelength of 559.9nm, have the same frequency as in air, and be visible E. have a wavelength of 315.1nm, have the same frequency as in air, and be invisible 2. Which of the following statements best explains why a telescope enables you to see the details of the Moon more clearly? A. The final image formed by the telescope has a larger angular size, subtended at the eye, than the original object. B. The final image formed by the telescope is inverted rather than erect, relative to the original object. C. The final image formed by the telescope is brighter than the original object is. D. The final image formed by the telescope is closer to your eye than the original object is. E. The final image formed by the telescope is virtual rather than real. Copyright c 2017 University of Georgia. 2
3. 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 arcsin(522/2097) = 14.414 o. 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, will... A. undergo total internal reflection if incident from below the interface with an angle of incidence of 8.5 o. B. have an angle of refraction less than the angle of incidence if the beam is incident from above the interface. C. not undergo total internal reflection if incident from below the interface with an angle of incidence of 29.0 o. D. undergo total internal reflection if incident from above the interface with an angle of incidence of 29.0 o. E. always have an angle of refraction not exceeding 14.414 o if the beam is incident from below the interface. 4. An image forming device, either a lens or a mirror, forms an image of a virtual object, as shown by the ray diagram below. Hint: Use the F -ray and the P -ray to first find focal points, F and F. F-ray Lens or Mirror? F -ray P -ray P-ray Q Object Optical Axis A The ray diagram above shows... H A. a divergent mirror forming a real, erect image to the left of the device. B. a convergent lens forming a real, inverted image to the left of the device. C. a divergent lens forming a virtual, inverted image to the right of the device. D. a convergent lens forming a real, erect image to the right of the device. E. a divergent mirror forming a virtual, inverted image to the right of the device. Copyright c 2017 University of Georgia. 3
II: Draw a Ray Diagram (10 points) A real image is generated by a divergent mirror. The image is to the right of the mirror, at an absolute distance from the mirror which is greater than the absolute value of the mirror 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 mirror and both its focal points, the object and the image, all of them clearly labeled. Also answer this: Is the object real or virtual? Hint: You need to construct the object here, given the image. First draw optical axis, mirror and image. Then use sign conventions to find and label incoming and outgoing side of mirror. Then use that to find the location of focal points F and F. Warning: Be very careful if you use the C - and C-ray to construct the object. The C-ray does not pass straight through the mirror to form the C -ray, but rather the C-ray is reflected by the mirror to form the C -ray. Copyright c 2017 University of Georgia. 4
III: Refraction at a Prism Immersed in Air (35 points) Ɣ Surface R Surface L efraction at a prism immersed in air: α Glass n G Surface B Prism surface B and the incident ray (outside the prism) are horizontal. The angle between prism surfaces L and B is α = 32 o. The apex angle between prism surfaces L and R is γ = 104 o. The index of refraction of the glass is n G = 1.75. The refracted ray from rism surface surface B and L inside the incident the prism strikes ray (outside surface R. the prism) are horizontal. The angle between pris nd B is α = 25 o. The index of refraction of the glass is n G = 1.80. The apex angle at the top of pr etween L and (a) R) Find is Ɣ the= angle 100 o of. The incidence refracted and theray angle from of refraction surface atl surface inside L. the prism strikes surface R ) Find the angle of incidence at surface L ) Find the angle of refraction at surface L ) Find the angle ψ at surface R ) Find the angle of incidence at surface R ) Does the ray exit the prism thru surface R? If so, at what angle of refraction? If not, why n (b) Find the angle ψ at surface R. ) What is the maximum value which the apex angle, Ɣ, must not exceed if a refracted ray is t through surface R into air, given α = 25 o and n G = 1.80. ψ (c) Does the ray exit the prism thru surface R? If so, at what angle of refraction? If not, why not? Copyright c 2017 University of Georgia. 5
IV: Galilean Telescope (35 points) In a Galilean telescope, an objective lens (Lens 1) of +120.0cm focal length is placed 117.1cm to the left of an eyepiece lens (Lens 2) of 2.7cm focal length. Your eye is located very close to, and to the right of the eyepiece. You are viewing the planet Jupiter, a very, very distant object, through the telescope. Jupiter has a diameter of 140,000km and its distance from earth is 738,000,000km right now. Make a careful drawing of all this before you start!! (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? [Hint: The distance to Jupiter is much, much larger than the focal length of Lens 1. Hence, 1/d 1 is negligibly small compared to 1/f 1.] (b) At what distance from the eyepiece and to which side of it is Jupiter s final image, produced by the eyepiece? Is this a real or a virtual image? [Hint: The objective lens image found in (a) serves as the object to the eyepiece lens. Use that and the given distance between lenses, to first find the object distance to the eyepiece: it will be a virtual object!] (c) How large, in units of mm, is Jupiter s final image produced by the eyepiece? Is that final image erect or inverted, relative to the original object, planet Jupiter? Copyright c 2017 University of Georgia. 6
V: Telescope 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 telescope, compared to viewing the planet without any optical instrument, from the same, very large distance as in Problem IV. Do not use any memorized angular magnification formula that is not shown in the formula sheet! Copyright c 2017 University of Georgia. 7