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= / = /

http://www.goiit.com/chapters/tutorial/physics/geometric-optics-2.htm

When you have refractive index of material A with respect to B, that is,n_AB

there are three formulae :

n_AB =n_a / n_b = v_b /  v_a  = sin i / sin r

The second part is not so clear..which rays are you talking about ?

Direction of incident light is at an angular separation of critical angle to the normal...as is obvious from the formula..

Direction of refracted light is perpendicular to the normal...as is obvious,again, from the formula..

Or are you asking about something else?