refractive index is the ratio between the speed of light in medium 1 and medium 2.it does not have any unit as it is a ratio.sin i/sinr=constant for any given 2 mediumsand a given colour of light.if light moves from medium 1 to medium2 this constant=RI in medium2/RI in medium 1.thus sin i/sinr=RI 2/RI1

also sini/sinr=RI of medium 2 /RI of medium 1=c in medium1 /c in medium2=lambda in medium1 / lambda in medium2

as

sini/sinr=u 2/u 1=c / v2 /c / v1=v1 / v2= / = /