Question

*I need help with Part C. Thanks!

Electromagnetic radiation (known as Cerenkov radiation) is emitted when a charged particle moves through a medium faster then the local speed of light. It shouldbe stressed that the particle is never going faster then the speed of light in vacuum (or c), just faster than the speed of light in the material (which is alwaysless than c).

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When a charged particle passes straight through a medium faster than the local speed of light, it will emit Cerenkov radiation in a cone. Let's see how the coneangle is correlated to the speed of the particle.

Part A
If a particle is traveling straight through a material with index of refraction n at a speed v, what is the angle θ between the vector of the propagatingCerenkov radiation and the vector in the direction of the propagating particle?
Express your answer in terms of v, c, and n.
θ= cos^-1(c/(nv))
Correct

Part BSuppose you wish to accurately measure the speed of high-energy particles with velocities greater than 98% the speed of light in vacuum. You can use a ring-imagingCerenkov detector consisting of a thin slab of material separated from an array of photomultiplier tubes by an arbitrary open space. (Photomultiplier tubes, orPMTs, are devices used to detect weak light signals.) The detector works on the principle that the Cerenkov radiation emitted in the thin slab will be a cone oflight that can be measured with the array of PMTs. The PMTs, having a finite width, can only resolve a finite change in the angle of the ring created by theCerenkov radiation. Use these constraints and the equation for from Part A to determine which of the following substrate materials is best suited to giving you the greatest precision in determiningparticle velocity.

	diamond () crown glass () ice ( aerogel () vacuum ()
Correct

Part CSuppose our detector used aerogel () for the Cerenkov materialand the photomultiplier tube array had a resolution of .This means, for instance, that the detector can distinguish between Cerenkov light emitted at an angle of 15 and that emitted at 13.8 but can't tell the difference between Cerenkov lightemitted at 15 and that emitted at13.9 What is the highestvelocity $v_max$ at which a charged particle can beaccurately measured to be below the speed of light in vacuum ()?Express your answer as a multiple of to three significantfigures.

$v_max$ =

Answer 1

Arc cos (c/(nv))

Aerogel

Answer 2

v max = 0.995 c

Answer 3

ok, so the highest angle that we can go is 13.9
subtract 1.2 from that and rework the problem with 12.7 degrees and you will get 0.995 c