GREPhysics.NET: GR9277 #69

GR9277 #69

Problem

GREPhysics.NET Official Solution

\prob{69}
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

c/3
4c/9
5c/9
2c/3
c

Optics $\Rightarrow$ }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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Comments

dicerandom
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.

Shoshe
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 $v=c/n = c/1.5 = \frac{2}{3}c$ .

Reply to this comment

poop
2005-11-23 15:42:12

FYI, this phenomenon is called "Cherenkov Radiation"

yosun
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.

gt2009
2009-05-20 10:37:56

Why are there so many people named poop on here?

Albert
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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FYI, this phenomenon is called "Cherenkov Radiation"

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