For Vm1:
Take a unit vector along the mirror m1 and one perpedicular to m1
Now component of velocities along the mirror will be same and same but opposite sign perpendicular to the mirror
It can be easily determined to be
Vm1=v(cos 2θ i +sin 2θ j)
and Vm2=v i
hence,
Vm1/m2=Vm1-Vm2