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CERENKOV RADIATION question

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A charged particle travelling in empty space at uniform velocity cannot emit electromagnetic radiations. This is not allowed from the point of view of conservation of energy and momentum.

Investigate if a charge particle inside a dielectric moving at a uniform speed greater than the speed of light can emit photons. It has been found that it does. The emitted radiation is called CERENKOV-RADIATION. the emitted photons emerge at certain angle with respect to the direction of the charged particle. Find this angle, assuming that the refractive index is 1.5; the particle is a pion of energy 5BeV and the photon is in the optical range. The mass of a pion is 140MeV. Such detectors are commonly employed in high-energy physics.
 

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