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MasteringPhysics: Print View with Answers http://session.masteringphysics.com/myct/assignmentPrin... Part B Part C "extra" distance it travels is twice the thickness of the slick (once as it moves toward the oil-water interface, and once as it reflects back, out into the air). Hint 3. Phase shift due to reflections Recall that when light reflects off a surface with a higher index of refraction, it gains an extra phase shift of radians. What used to be a maximum is now a minimum! Be careful, though; if two beams each reflect off a surface with a higher index of refraction, they will both get a phase shift, canceling out that effect. ANSWER: = 313 Suppose the oil had an index of refraction of 1.50. What would the minimum thickness be now? Express your answer in nanometers, to three significant figures. Hint 1. Phase shift due to reflections Keep in mind that when light reflects off a surface with a higher index of refraction, it gains an extra phase shift. What used to be a maximum is now a minimum! Be careful, though; if two beams reflect, they will both get a phase shift, canceling out that effect. Also, reflection off a surface with a lower index of refraction yields no reflection phase shift. ANSWER: = 125 Now assume that the oil had a thickness of 200 and an index of refraction of . A diver swimming underneath the oil slick is looking at the same spot as the scientist with the spectromenter. What is the longest wavelength of the light in water that is transmitted most easily to the diver? Express your answer in nanometers, to three significant figures. Hint 1. How to approach this part For transmission of light, the same rules hold as before, only now one beam travels straight through the oil slick and into the water, while the other beam reflects twice; once off the oil-water interface, once again off of the oil-air interface, before being finally transmitted to the water. Hint 2. Wavelength of light in air Find the wavelength of the required light, in air. Express your answer numerically in nanometers. ANSWER: Hint 3. The wavelength of light in water There is a simple relationship between the wavelength of light in one medium (with one index of refraction) and the wavelength in another medium (with a different index of refraction). ANSWER: = 600 = 451 4 of 11 2/7/13 1:01 PM
MasteringPhysics: Print View with Answers http://session.masteringphysics.com/myct/assignmentPrin... This problem can also be approached by finding the wavelength with the minimum reflection. Conservation of energy ensures that maximum transmission and minimum reflection occur at the same time (i.e., if the energy did not reflect, then it must have have been transmitted in order to conserve energy), so finding the wavelength of minimum reflection must give the same answer as finding the wavelength of maximum transmission. In some cases, working the problem one of these ways may be substantially easier than the other, so you should keep both approaches in mind. Using a Michelson Interferometer Description: A Michelson interferometer is used to find the wavelength of a laser and then the index of refraction for an unknown fluid. You are asked to find the index of refraction for an unknown fluid, using only a laser and a Michelson interferometer. A Michelson interferometer consists of two arms--paths that light travels down, which end in mirrors-- attached around a beam splitter. The beam splitter separates the incoming light into two separate beams and then recombines them once they return from the ends of the arms. The recombined beams are sent to a telescope, where their interference pattern may be observed in detail. Part A Part B First, you must find the wavelength of the laser. You shine the laser into the interferometer and then move one of the mirrors until you have counted fringes passing the crosshairs of the telescope. The extremely accurate micrometer shows that you have moved the mirror by millimeters. What is the wavelength of the laser? Express your answer in nanometers, to four significant figures. Hint 1. Relating wavelength and distance in a Michelson interferometer Since the change in path difference for a Michelson interferometer comes from both the increased distance that light travels to the moving mirror and the distance traveled back from it, the equation for how far the mirror has moved takes the form , where is the distance traveled by the mirror, is the number of fringes that have moved past the crosshairs, and is the wavelength of the light. ANSWER: = 632.8 You now immerse the interferometer in a tank filled with some unknown liquid and carefully align the laser into the interferometer. You move the mirror until you count 100.0 fringes passing the crosshairs of the telescope. The micrometer indicates that the mirror has moved millimeters. What is the mystery fluid? Hint 1. Find the index of refraction What is the index of refraction for this liquid? Express your answer to four significant figures. Hint 1. Find the wavelength of the light in the fluid 5 of 11 2/7/13 1:01 PM
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