More details on what appears below can be found in these notes: [ scattering.doc] [ scattering.pdf ] and is also illustrated in this Interactive Physics demonstration: IP008.sit.hqx

The relation between the velocities in the CM and LAB for an elastic collision of two particles is shown below.

 

The relationship between the scattering angle for particle 1 in the LAB and CM is given by:

This is plotted below for various mass ratios: