Determine whether the light will reach certain points or not I've got an interesting question which goes like that: suppose we have a long cylindrical rod made of a transparent material (see illustration below). A point source $O$ which sits on rod's axis emits light in all directions. The light is partially reflected and partially refracted (i.e. goes to the air). The question is - which points will the light rays reach? (1) A only, (2) A and B only (3) All the four points (4) Not enough information

According to the book the right answer is (3), but I'm not so sure that this is correct - one the one hand, the light is emitted in all possible directions but on the other hand, my friend thinks there could be a total internal reflection at some point. In both cases there's no strict proof for either answer.
By the way, there's no information about positions, indices of refractions and so on.
 A: This is a cross section of the rod:

Snell's law tells us that the angle $r$ is given by:
$$ \sin r = n \sin i $$
where $n$ is the refractive index of the rod ($n \gt 1$). No matter how far down the rod $D$ is there will be a value for $i$ that allows the light to reach $D$. The total internal reflection angle is the limiting value for $i$ as the distance to $D$ goes to infinity and $r \rightarrow \pi/2$.
A: There could be a point where we have total internal reflection, in that case the light trying to leave the rod at that particular 'critical angle' will be totally reflected.  So you are saying if this is the case, then there will be a point outside the rod where the light doesn't reach?
This wouldn't be the case, the light will be partially reflected from the both sides of the rod many times meaning that there will be more than one way for the light to reach each point outside the rod.
So if point A, B, C or D was at a position where the light coming straight from the source was totally internally reflected and couldn't reach the point, there would still be ways for light which had been partially reflected from the other side of the rod to reach it.
Also, if the light is not monochromatic the different frequencies will be refracted by different amounts and we wouldn't require the light to have been partially reflected from the other side of the rod at all.  The refraction would provide many other routes for the light to travel to each point outside the rod. 
