A charged particle moving with speed υ through a medium of refractive index n emits C̆erenkov radiation at an angle θ to the direction of the particles.

(a) What is the maximum angle of emission and to what limit does it correspond?

(b) If the momentum p of the particle is known, show that the mass squared x of the particle is given by 

x = (mc²)² = p²c² (n² cos² θ ˆ’ 1).

(c) If the error on the momentum is negligible, show, by taking derivatives of this expression, that for highly relativistic particles, the standard error σ_x on x is approximately

where σ_θ is the standard error on θ.

= 2pc /[n 1) 0o,