# Time of flight detector

A time of flight (TOF) detector is a particle detector which can discriminate between a lighter and a heavier elementary particle of same momentum using their time of flight between two scintillators. The first of the scintillators activates a clock upon being hit while the other stops the clock upon being hit. If the two masses are denoted by ${\displaystyle m_{1}}$and ${\displaystyle m_{2}}$ and have velocities ${\displaystyle v_{1}}$ and ${\displaystyle v_{2}}$ then the time of flight difference is given by
${\displaystyle \Delta t=L\left({\frac {1}{v_{1}}}-{\frac {1}{v_{2}}}\right)\approx {\frac {Lc}{2p^{2}}}(m_{1}^{2}-m_{2}^{2})}$
where ${\displaystyle L}$ is the distance between the scintillators. The approximation is in the relativistic limit at momentum ${\displaystyle p}$ and ${\displaystyle c}$ denotes the speed of light in vacuum.