Teaching Modern Physics - QuarkNet - Fermilab

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4. A common particle detector technique involves optical scintillating fiber, which emits light when crossed by a charged particle. If the fiber consists of a core with index of refraction 1.59 and a cladding of index of refraction 1.49, what fraction of the light is trapped in the fiber and transported to an end? Assume all light is emitted at the center of the fiber (i.e., on the fiber axis) and that the light emission is isotropic. This problem is fairly tricky, as it involves light emission into three dimensions. Thus, one must use calculus and solid-angle calculations. First, one must find the critical angle of reflection, then convert that to limits of integration. Finally, the integrated solid angle must be divided by the total solid angle. sin θc = 1.49/1.59 → θc = 69.6° θ = 90° – θc = 20.43° Light is emitted into all solid angles. 2π π Ω = ∫∫ sinθ dθ dφ = 4π 0 0 Only the light emitted with angle smaller than 20.43° (= 0.36 radians) will be trapped. Thus, 2π 0. 36 Ωtrapped = ∫ ∫ sinθ dθ dφ = 0. 396 0 0 The fraction trapped is Ωtrapped/Ω = 3.15%. A common error is to ignore the azimuthal angle and use a simple proportion. This error yields 11.3%. 5. Cerenkov light is a form of light emitted when a charged particle travels in a transparent medium faster than light travels in the same medium. Calculate the minimum velocity an electron must have to emit Cerenkov light in water. This is a simple problem. Use n = c/v. The index of refraction of water is 1.33. So v = 2.26 × 10 8 m/s. 53 θc θ
6. Cerenkov light is a form of light emitted when a charged particle travels in a transparent medium faster than light travels in the same medium. An imaginative experiment called ICE-CUBE plans to use a cubic kilometer of ice (which becomes clear at great depths) in Antarctica to detect charged particles from outer space called muons. Calculate the minimum velocity a muon must have to emit Cerenkov light in the ICE-CUBE experiment. This is a simple problem. Use n = c/v. The index of refraction of ice is 1.31. So v = 2.29 × 10 8 m/s. 54
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Materials for Teaching Modern Physi
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Which activities did you use in you
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Materials for Teaching Modern Physi
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QuarkNet is a nationwide program th
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Radioactivity PowerPoint Presentati
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Problems & Worksheets * This activi
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The Cloud Chamber: In the Nobel Pri
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Draw Geiger, Marsden, and Rutherfor
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10. Describe how particle physics a
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Particle Acceleration (Principles)
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Electric Field and Acceleration +
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Multistage Accelerators (LINAC) 1 2
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Particle Accelerators Why were they
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Cyclotrons are constructed as two
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QUIZ ON PARTICLE ACCELERATORS 1. De
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Z Boson Mass Reconstruction for DØ
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1 Z Boson Mass Reconstruction for D
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d.) energy / a silicon detector and
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Anticharm ( c ) Antimatter Quark Ch
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Gluon Gauge boson Force carrier: St
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Standard Model Review - Answer Key
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Newton’s Universal Law of Gravita
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II. Intended Activities and Approxi
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All questions from project written
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periodicals and newsletters. The co
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Fermilab’s Accelerators This is a
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A Game for Building a Detector http
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us. An alternate “radiation” so
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Day 4: 1. Question of the Day: A ha
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Teaching Modern Physics - QuarkNet - Fermilab

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