The effect of refractive index dip an splice loss in arbilrarily graded-index singlemode jiber has been studied lIIilising the four-term polynomial fonnula and the injinite sum representation for power transmission coefficient. In the fanner case, we have used a highly accurale single parameter variational approximation, whereas ill the latter, we have used infinite slim of {he Lagllerre-Gaussian functions for the representation of the LPm mode. The results obtained by the infinite slim representation represent the exact results.