\subsection{Principles of a RICH detector}
``RICH'' stands for \textit{Ring Imaging \v{C}erenkov} detector. This device is based on the \v{C}erenkov emission of light by a charged particle going through a medium at a speed $\beta > 1/n$, where $n$ is the refractive index of the medium. Light is emitted at an angle $\theta_C$ relative to the particle direction, defined by
\begin{align*}
\cos{\theta_C} = \dfrac{1}{n \, \beta}
\end{align*}
The light cone is projected on a focal plane, perpendiculr to the beam direction, by a system of mirrors of focal lenght $f$. For particles travelling parallel to the beam line, the image on the focal plane is a circle of radius
\begin{align*}
r_C = f \, \tan {\theta_C}
\end{align*}
while for particles travelling at an angle $\theta$ relative to the beam line the image is shifted from the focus of a distance
\begin{align*}
d = f \, \tan {\theta}
\end{align*}
\figurename~\vref{img:rich} shows a draft of a basic RICH detector.\\

Given the momentum of a particle, %by means of a RICH detector it is possible 
a RICH detector allows 
to compute its mass, and thus to identify it. In fact, the aims of this device in the frame of the NA62 experiment are:
\begin{itemize}
\item separating muons from pions: in the momentum range from 15 GeV to 35 GeV the separation is achieved with a precision of $10^{-2}$;
\item generating a level 0 trigger for charged particles;
\end{itemize}

DA FINIRE - DA RIFARE

\begin{figure}
	\centering
	\includegraphics[width=0.8\textwidth]{Images/pdf/rich}
	\caption{Draft of a simple RICH detector. The radius of the circle in the focal plane is determined by the speed of the particle, while the position of its center depends on the particle direction.}\label{img:rich}
\end{figure}