Question

Why quantity refractive index dooesn't have unit

Answer 1

Refractive Index is a ratio of two similar physical quantity which is dimension less
refractive index = sin I / sin r

therefore it doesn't have a unit.

Answer 2

Refractive index is expressed as a ratio of speed of light in vacuum relative to the speed of considered medium. As it is a ratio and the units m/s or km/h cancel out each other. Therefore, the qauntity refractive index does not have any unit. I hope it will be helpful to you. Thank you