Why is it that the angle of incidence and angle of refraction are not directly proportional?

Question

(For example... once the angle of incidence is greater than 40 degrees, the bend is much more visible.)

Answer 1

It can not be, given that both angles fall in the range between 0 and π /2 (measured in radians).  For example, suppose that you have as law θ2=k θ1, where k is some function of the refractive indices.  If k>1, then θ2>π /2 whenever θ1>π /2k, which is impossible.  Likewise if k<1, then, reversing the direction of the ray so that  ÃŽÂ¸2 is the incident angle and θ1 the refracted angle, then θ1> π /2 when θ2>k π /2, which is again impossible.

Answer 2

It is measured by the Refractive Index of the substance. The RI is determined by just such disproportionality. Different materials have different RIs. Once you know the RI you can use it to figure the change in the angle. Rainbows are produced at 42°, but if they were made of diamonds the angle would be closer to 46°.

Answer 3

It is due to  the nature of the substance,which is chosen  as medium.

It also  matters  with  the different  nature and  refractive index

  being  unique  for individual medium.Primary and Secondary

medium in the  process of  refraction,determine the  variation

for the angle of  incidence with  respect  to  angle of  refraction.