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A fast charged particle passes perpendicularly through a thin glass sheet of index of refraction 1.5. The particle emits light in the glass. The minimum speed of the particle is

  1. c/3
  2. 4c/9
  3. 5c/9
  4. 2c/3
  5. c

Optics}Speed of Light

The speed of light is related to the index of refraction by n=c/v. Thus, the minimal velocity the particle must have is v=c/n=2/3c, since n=3/2.

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2018-10-25 12:05:41
My half-BS solution: I tried to figure out which of the answers could reasonably come from 1.5. I thought 1.5 = 3/2, saw 2/3, and then picked it. A guessing strategy for if you know zero Physics.NEC
2013-09-03 10:52:30
when I first read this problem, I thought the particle was entering the glass. The word perpendicular lead me to that assumption. I guess the particle was already in the glass and emitting the Cherenkov Radiation. Since I thought the particle was entering the glass, I thought this was a question about Bremsstrahlung (breaking) radiation.Common Pitfalls
2012-10-02 23:16:55
Seems that I misunderstood this question at first, wondering the relation of the initial speed of particle and the energy of the emitted light. After reading your notes, I think what matters is that the particle has to be moving in a velocity bigger than the medium speed in order to emit. This speed is a minimal and we need not consider any rigid conservation here.NEC
2010-09-19 21:50:13
It seem like this question is improperly formed. The question states only that a fast particle travels through a medium with an index of refraction n = 1.5 and emits light. Why must the particle's MINIMUM speed equal the speed of light in the medium (c/n = 0.67c)? What is to prevent the particle from traveling at half the speed of light, while emitting light that travels within the medium at the speed c/n = 0.67c? This question would make sense if it said the particle emits a CONE of light. Then we would know the particle was giving off Cerenkov radiation, and must be traveling faster than c/n. Am I misunderstanding the question?NEC
2006-10-25 18:19:22
Wait... what? The minimum speed the particle can have is the maximum speed it could possibly obtain? And it emits light because it actually went faster than that?

When I read this I figured light was emitted because the thing knocked into an atom and excited an electron which then dropped down a level or two and radiated.
2006-11-03 15:33:19
Your assumption of "The minimum speed the particle can have is the maximum speed it could possibly obtain" isn't right. The maximum speed the particle could possibly obtain is c, the speed of light in a vacuum. Nothing prevents a particle traveling through a medium from going faster than the {\it speed of light in that medium}\ (v=c/n). Cherenkov radiation is emitted when a charged particle's velocity in a medium is greater than the speed of light in that medium. So the charged particle in this question must be going faster than v=c/n = c/1.5 = \frac{2}{3}c.
Answered Question!
2005-11-23 15:42:12
FYI, this phenomenon is called "Cherenkov Radiation"
2005-11-23 15:56:55
FYI: Cherenkov Radiation occurs when the particle travels faster than the speed of light in the medium. A particle emits light when it makes transitions from level to level, but since this is a free particle, the only way it can emit light is through Cherenkov Radiation.
2009-05-20 10:37:56
Why are there so many people named poop on here?
2009-10-21 08:05:09
Did you not think that there could be just one person named poop who is writing all those posts?

Use it, its more than just a hat rack :)
his dudeness
2010-09-04 19:17:48
my personal favorite is "poop loops"

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