Animate[Show[
Plot[ai*Cos[k1*x-wt],{x,-4Pi,0},PlotStyle->{Blue}],Plot[ar*Cos[-k1*x-wt],{x,-4Pi,0Pi},PlotStyle->{Darker[Green]}],Plot[ai*Cos[k1*x-wt]+ar*Cos[-k1*x-wt],{x,-4Pi,0},PlotStyle->{Red}],
Plot[at*Cos[k2*x-wt],{x,0,4Pi},PlotStyle->{Red}],
PlotRange->{-5,5}],
{wt,0,2Pi},{b,0,Pi/2},AnimationRunning->False]/.{ai->1,ar-> (1-Tan[b])/(1+Tan[b]),at->2/(1+Tan[b]),k1->2,k2->.5}