Refractive Index is defined as the relative speed at which light moves through a material with respect to its speed in vacuum.
Refractive Index (n) = speed of light in a vacuum (c) /speed of light in a medium (v)
As both the values belong to same quantity (speed), units gets nullified. So Refractive Index is dimensionless quantity.
Dimensional Formula of Refractive Index= M0L0T0.
Refractive Index is dimensionless quantity.