What is the general trend of the angle of refraction at a given angle of incidence, as the refractive index increases?

Answer 1

since the sines are directly proportional, with the index as the constant of variation, as the index increases, so does the angle of refraction. Take a look at Snell's Law and it should be clear.

Answer 2

see Snell's Law

increasing the refractive index would decrease the angle of refraction

Answer 3

the angles are measured relative to the normal to the interface

as the index increases, the ray is refracted more towards the normal , lessening the angle of refraction

sorry, Steve

Answer 4

Clearly I was not thinking clearly.
As usual, Scott is correct.