Cherenkov Radiation Ring

In summary, the conversation discusses a theoretical question about a particle beam crossing a concave spherical mirror and creating a ring image in the focal plane. The solution involves considering the geometry of the situation and the two sets of parallel rays to determine the position of the ring's center and radius.
  • #1
ideasrule
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Homework Statement


See here: http://www.jyu.fi/kastdk/olympiads/ [Broken] (year 2008, theoretical question set 2, question 2)

Let us consider a beam of particles moving with velocity v>c/n, such that the angle θ is small, along a straight line IS. The beam crosses a concave spherical mirror of focal length and center C, at point S. SC makes with SI a small angle α. The particle beam creates a ring image in the focal plane of the mirror. Explain why with the help of a sketch illustrating this fact. Give the position of the center O and the radius of the ring image.

Homework Equations


none


The Attempt at a Solution



I'm puzzling over the solutions to no avail. Why is the line from C to the center of the ring parallel to the particles' trajectory? Why is the line from C to the top of the ring, and the line from C to the bottom of the ring, parallel to the Cherenkov radiation's wavefront? I feel like I must be missing something obvious...
 
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  • #2
Does anybody have any idea? I have to figure this out pretty soon.
 
  • #3
I could not find the question using your link. I cannot "see" the diagram from your description. It is too confusing without the diagram. Try to attach the diagram.
 
  • #4
Stupid me; I forgot that "Copy Link Location" gives a direct URL. Here it is:

http://www.jyu.fi/kastdk/olympiads/2008/Theory_2_Problem.pdf [Broken]

And here's the solution:

http://www.jyu.fi/kastdk/olympiads/2008/Theory_2_Solution.pdf [Broken]
 
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  • #5
Consider the situation in 2 dimensions, and consider all of the rays simultaneously. This is a geometry problem. Basically, it is as if the Cherenkov rays are coming in from infinite distance (because they are parallel), and so you just need to figure out where the mirror will focus them. You have two sets of rays to consider: the ones tilted upwards and the ones tilted downwards. The mirror will focus these two sets of rays to two separate points. Those two points are two opposite points on the ring.
 
  • #6
Thanks! I was missing something very simple.
 

1. What is Cherenkov radiation ring?

Cherenkov radiation ring is a phenomenon that occurs when a charged particle travels through a medium at a speed faster than the speed of light in that medium, creating a cone-shaped light emission.

2. How is Cherenkov radiation ring produced?

Cherenkov radiation ring is produced when a charged particle, such as an electron, travels through a medium (such as water) at a speed faster than the speed of light in that medium. This creates a shock wave of light, forming a cone-shaped ring.

3. What is the significance of Cherenkov radiation ring in scientific research?

Cherenkov radiation ring is used in scientific research to detect high-energy particles and to measure their velocities. It is also used in medical imaging, such as in PET scans, to track the movement of radioactive tracers in the body.

4. What are some applications of Cherenkov radiation ring?

Aside from its use in scientific research and medical imaging, Cherenkov radiation ring has also been utilized in nuclear power plants as a safety measure to detect high-energy particles that could potentially damage equipment.

5. Is Cherenkov radiation ring harmful to humans?

Cherenkov radiation ring is not harmful to humans as it is a natural occurrence that happens in small amounts around us all the time. However, exposure to large amounts of Cherenkov radiation can be dangerous, as it indicates the presence of high-energy particles that can be harmful to living organisms.

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