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In this report, we present our analysis of the relationship between critical power and stimulated Raman scattering in Raman fiber lasers. Through our research, we have established a connection between the R.G. Smith constant at critical power and the necessary pump power required to reach the maximum power delivered by the first Stokes just prior to the generation of the second Stokes. In our experiments, two setups were successful in reaching the second Stokes generation, one utilizing a glass–air interface as the output coupler without HR mirrors and the other using HR-FBGs for both Stokes in conjunction with a glass–air interface. We found that the 1 Km 1060-XP fiber has an R.G. Smith constant of ~4.94 at critical power, which when multiplied by 2 gives ~9.88, a value close to the R.G. Smith constant (9.75) for maximum Stokes corresponding to a pump power of 5.5 W, with an approximation of ~98.6%. Our results demonstrate the importance of knowing the R.G. Smith constant at critical power in estimating the necessary pump power to achieve maximum power delivery in any Stokes component.