There are several ways to derive Snell's Law, and therefore the Angle of Refraction. The first way it was discovered was by an application of Fermat's principle which states that a light wave must take a path that is an extremum in time subject to the constraints present. Normally this is translated into "Light will always take the quickest path it can." From this principle, and using a bit of differential calculus, Snell’s Law can be derived thus leading to the Angle of Refraction. If one looks into the meaning of Fermat’s principle, ot ...
An angle of incidence is the angle between a beam incident on a surface and the normal (line perpendicular to the surface at the point of incidence). The beam can be formed by any wave: optical, acoustical, microwave, X-ray etc. In Fig.1 the red line representing a ray makes an angle θ with the normal (dotted line).
Another common usage is in aviation, where it refers to the angle between the wing's chord (aircraft) and the longitudinal axis of an aircraft (a fixed value). Fig.2 shows a side view of part of an ae ...