Please Help me out with all of these! Thanks!!! speed of light in a vacuum. Howe

Question

Please Help me out with all of these! Thanks!!!

speed of light in a vacuum. However particles have been observed that travel in a material medium faster than the speed of light in that medium. When a charged particle moves through a medium faster than light moves in that medium, it radiates coherent light in a cone whose axis lies along the path of the particle. (Note the rough similarity to waves created by a motorboat speeding across calm water and the more exact similarity to the "cone of sonic boom" created by a supersonic aircraft.) This is called Cerenkov radiation (Russian is pronounced as "ch"). Let v be the speed of the particle in the medium and vlight be the speed of light in the medium. From this information use the first figure to show that the half-angle , of the light cone is given by the expression Consider the plastic with the trade name Lucite, for which Vlight = 2/3. What is the minimum velocity that a charged particle can have if it is to produce erenkov radiation in Lucite? What is the maximum angle at which erenkov radiation can be produced in Lucite? Measurement of the angle provides a good way to measure the velocity of the particle. In water the speed of light is approximately Vlight = 0.75. Answer the questions of part b for the case of water. Sec the second figure for an application of erenkov radiation in water. Exercise 3-8, first figure. calculation of Cerenkov angle .

Explanation / Answer

for lucite

Min velocity for radiation = speed of light in that medium = 2/3

Max angle = arccos (2/3) = 48.2 degrees. This will happen when the source is travelling with the speed of light.

for water

Min velocity for radiation = speed of light in that medium = 0.75

Max angle = arccos(2/3) = 41.4 degrees. This will happen when the source is travelling with the speed of light.

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