Question

How Sin i/sinr derived geometrical ?

Answer 1

The equations are equivalent - the angle through which the light will bend will depend on the relative speeds in the two media.

Explanation:
The more the light slows down the greater the angle it turns through i.e the greater the difference between sin i and sin r and therefore the greater the refractive index. Think of a car going from a motorway into a level field at an angle. The wheel that enters the filed first will slow down and the faster movement of the rest of the wheels will make the car turn - the greater the difference in speed, the more it will turn