Which is true about refraction from one material into a second material with a greater index of refraction when the incident angle is, say, 30º?

I believe the appropriate answer is that at the interface the ray bends way from the normal. 
When a ray enters a more dense substance or material (with higher refractive index) , it bends more towards the normal. The amount of bending depends on the change in speed such that is a substance causes the light to speed up or slow down more, it will refract more, and the other factor is the angle of incidence such that if the light is entering the substance at a greater angle, the amount of refraction will be more noticeable.