1. A semiconductor light emitting element, comprising: a substrate including GaN; a first cladding layer of a first conductivity type provided over the substrate and including In 1-n1-n2 Al n2 Ga n1 N (where 0<n1<1, 0≦n2<1, and n1+n2≦1); a quantum well active layer provided over the first cladding layer; a second cladding layer of a second conductivity type provided over the quantum well active layer and including In 1-m1-m2 Al m2 Ga m1 N (where 0<m1<1, 0<m2<1, and m1+m2≦1); and a first refractive index correction layer of the first conductivity type provided between the substrate and the first cladding layer, wherein the first refractive index correction layer includes a layer of In 1-x-y Al y Ga x N (where x+y<1), x and y satisfy the relations x/1.05+y/0.69>1, x/0.91+y/0.75≧1, and x/1.08+y/0.91≦1, and the quantum well active layer has an emission wavelength of equal to or greater than 430 nm.