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Cherenkov radiation is a type of electromagnetic radiation which is observed when a charged particle moves with a faster speed than the speed of light in that medium in which charged particle is moving. Speed of the particle should be faster than the phase velocity of light instead of overall velocity.

## Cherenkov Effect

Cherenkov Effect is observed when a charged particle moves in a medium with high speed faster than the speed of light. This effect can be observed in a dielectric medium with refractive index greater than 1.
Speed of the charged particle should be such that it is greater than the phase velocity of light in that medium as follows:

$v$ $>$ $\frac{c}{n}$

$v$ is velocity if charged particle, c (3 $\times$ 10m/s)is speed of light and $n$ is refractive index of the medium.

The radiations are emitted as a result of asymmetric polarization of the atoms of the medium in front and at the back of the moving charged particle. This results in a changing electric dipole momentum. A portion of the energy of charged particle is converted into Cherenkov light. A coherent wave front is produced of velocity v i.e. equal to the velocity of moving charged particle at an angle ?°c. this angle remains fixed for ultra relativistic particles. The value of angle is maximum in water i.e. 43o. Cherenkov light can be detected in transparent medium like water.

## Cerenkov Light

If we drop a pebble into a pond, a circular ripple will spread out on the surface of water. If we continue dropping pebbles at regular intervals then a series of concentric rings all moving outwards with the same speed will be formed. But what happens if we drop pebbles by moving our hand linearly in one direction or horizontal direction? A series of circular waves will be produced that are no longer concentric but rather crowded in the direction where hand is moving. If we move the hand with the speed with which the rings move then all the rings will touch at a point. What happens if we move the source of the ripples faster than the speed of rings with which they spread.

Consider a case of a bird or duck moving on the surface of water, we will see a v – shaped waves behind the bird. This is what happens. The bird when swims faster than the speed of the ripples it creates, individual waves that it creates never comes in front of it. The angle of the v depends on how faster than the waves the bird is moving. This is an example of a shock wave in two dimensions. The object that is creating the waves is moving faster than the speed of the waves.

Now consider a three dimensional case: the jet aircraft moves not only on the surface but through a medium of atmosphere. Pressure waves due to the aircraft moving in three dimensions are called sound waves and the speed with which they travel is called the speed of sound. Just as the case of swimming bird if the jet is moving faster than the speed of sound waves then the sound waves cannot propagate ahead of the jet and becomes attached and travels along with the object spreading out a three dimensional form of a ‘v’ i.e. a cone. This is the sonic boom observed by supersonic aircraft.

Just as the jet aircraft creates a pressure disturbance while travelling through the air an electrically charged particle traveling through any medium creates an electromagnetic disturbance and as a pressure or sound waves were created in the former case, electromagnetic or light waves are created in the later case. If a charged particle is moving faster than the speed of light in that medium than a cone shaped shock wave will travel along the particle. But now this is a cone of light not of pressure waves. Light produced in this way is called Cherenkov Light in honor of the Russian physicist Pavel Cherenkov who first explained it. This light plays a large role in search of the neutrino oscillations and detection of high energy charged particles.

## Cherenkov Detector

$\cos \theta$= $\frac{c}{v.n}$
where $c$ is the speed of light, and n is the refractive index of the medium.