According to Snell's law, the value of the constant(refractive index) depends on:
The pair and order of media (where order implies from where to where )
The constant depends upon the pair of media and from which medium to which medium has the light gone.
For different pairs of media, the value of the constant will be different. Also, the value of the constant will be different depending on whether the light has gone from medium I to medium II or medium II to medium I.