Optics Total Internal Reflection Critical Angle

When a ray of light coming from the medium $$n_1$$

$$\mbox{ has an incident angle } \theta_1 = \theta_c$$

where $$\theta_c = \mbox{critical angle}$$

what phenomenon are we observing? Is it called a partial internal reflection? In others, is only some of the light reflected back into the medium? What about the rest?

It's an evanescent wave. Because that surface path is neither in medium $$n_2$$ nor medium $$n_1$$, it has neither propagating-wave character. It will exist as a kind of ripple, not truly a "ray", and because internal reflection is total, it doesn't carry energy away as a true refracted beam might.