Electromagnetic radiation (known as Cerenkov radiation) is emitted when a charge

Question

Electromagnetic radiation (known as Cerenkov radiation) is emitted when a charged particle moves through a medium faster then the local speed of light. It should be 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 always less than c).

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 cone angle 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 between the vector of the propagating Cerenkov radiation and the vector in the direction of the propagating particle?

Express your answer in terms of v, c, and n.

Ring-imaging Cerenkov detectors are devices that can accurately measure the velocity of charged particles as they pass through them. They are very useful as subdetectors in large particle detector systems. Let us look at what decisions need to go into designing a Cerenkov detector.

Part B

Suppose 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-imaging Cerenkov detector consisting of a thin slab of material separated from an array of photomultiplier tubes by an arbitrary open space. (Photomultiplier tubes, or PMTs, 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 of light 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 the Cerenkov radiation. (Figure 1) 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 determining particle velocity.

Suppose 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-imaging Cerenkov detector consisting of a thin slab of material separated from an array of photomultiplier tubes by an arbitrary open space. (Photomultiplier tubes, or PMTs, 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 of light 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 the Cerenkov 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 determining particle velocity.

aerogel (n=1.03) anser for part B

Part C

Suppose our detector used aerogel (n=1.03) for the Cerenkov material and the photomultiplier tube array had a resolution of =1.2degrees. This means, for instance, that the detector can distinguish between Cerenkov light emitted at an angle of 15 degrees and that emitted at 13.8 degrees but can't tell the difference between Cerenkov light emitted at 15 degrees and that emitted at 13.9 degrees. What is the highest velocity vmax at which a charged particle can be accurately measured to be below the speed of light in vacuum (c)?

Express your answer as a multiple of c to three significant figures.

vmax = 0.995 c anser for part

Part D

What is the lowest velocity vmin that a charged particle can have and still emit Cerenkov radiation in the aerogel?

Express your answer as a multiple of c to two significant figures.

I just need help with part D

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Explanation / Answer

The refractive index of aerogeo=1.03

lowest velocity vmin=c/n=1/1.03=0.97087 x c

where c is the velocity of light.

Hope this helps. Please rate. Cheers.

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