title: Time-of-flight detector
text: # 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 $m_{1}$and $m_{2}$ and have velocities $v_{1}$ and $v_{2}$ then the time of flight difference is given by
  
      $\Delta t=L\left({\frac {1}{v_{1}}}-{\frac {1}{v_{2}}}\right)\approx {\frac {Lc}{2p^{2}}}(m_{1}^{2}-m_{2}^{2})$
  
  where $L$ is the distance between the scintillators. The approximation is in the relativistic limit at momentum $p$ and $c$ denotes the speed of light in vacuum.
  
  