Theory_2_Problem - 39th International Physics Olympiad -...

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39th International Physics Olympiad - Hanoi - Vietnam - 2008 Theoretical Problem No. 2 CHERENKOV LIGHT AND RING IMAGING COUNTER Light propagates in vacuum with the speed . There is no particle which moves with a speed higher than . However, it is possible that in a transparent medium a particle moves with a speed higher than the speed of the light in the same medium c c v c n , where is the refraction index of the medium. Experiment (Cherenkov, 1934) and theory (Tamm and Frank, 1937) showed that a charged particle, moving with a speed in a transparent medium with refractive index such that n v n c n > v , radiates light, called Cherenkov light , in directions forming with the trajectory an angle 1 arccos n θ β = (1) A B where c = v . 1. To establish this fact, consider a particle moving at constant velocity c n > v on a straight line. It passes A at time 0 and B at time . As the problem is symmetric with respect to rotations around AB, it is sufficient to consider light rays in a plane containing AB. 1 t At any point C between A and B, the particle emits a spherical light wave, which propagates with velocity c n . We define the wave front at a given time as the envelope of all these spheres at this time. t 1.1. Determine the wave front at time and draw its intersection with a plane containing the trajectory of the particle. 1 t 1.2. Express the angle ϕ between this intersection and the trajectory of the particle in terms of and n .
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Theory_2_Problem - 39th International Physics Olympiad -...

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