oops sorry it is 1/2.... because if the ray shown in figure undergoes TIR then all other rays incident undergoes TIR ........so if we go on increasing r/R .....means we are decreasing R ...which also decreases @...so at some value of R this @ equals the critical angle and at that point we'll have max. value of r/R for which all rays undergo TIR.....so R/R+r = 2/3 => r/R = 1/2
this is my answer if wrong tell me where i've gone wrong.........