What if the angle of incidence is 90 degrees???

Angle of incidence is described as the angle between the incident ray and the outward-facing normal vector of the surface at the point of incidence.

A 90-degree incidence angle means the ray is parallel to the surface, so it never actually touches the second medium.

Maybe part is reflected and part goes straight in, without being refracted. Perhaps the ray goes both ways a at the angle of refraction determined by snell's law.  If there is uncertainty in the 90 degree angle, it is clear that at the bounds of that uncertainty the ray will be refracted.  

However, this question is only an exercise in theory, as you will never be able to apply the model to a real world situation, there is no such thing as a "ray". Light travels in waves and particles.

I guess I don't really know. I would say that in the ideal model, it goes straight through, in real life, it refracts.