Optics for a flat piece of glass 
An object is seen through a flat piece of glass of index of refraction 1.5 and thickness 6 cm. If the object is a distance 10 cm away form the near-surface of the glass, what is the location of the image seen by the observer directly at the other side of the glass?

I'm having trouble figuring out where the rays of light converge. By my count, any ray that goes from the arrow straight through the glass will simply re-emerge at the same angle. Since by geometry the second angle of incidence will be the same as the first angle of refraction.
Therefore, if I draw two rays going straight from the top of the object to the bottom, I will simply get two parallel rays that never converge.
What rays do I draw to correctly find the location of the image? My understanding is that I should generally use a parallel line and one through the focal point, but in this case there is no focal point.
 A: The point here (if I understand the question correctly) is to treat the eye as a point object located exactly at the edge of the glass, as in the added figure, and project the rays that hit the eyes to the adequate distance, provided that the size of the object is known to the observer.
That is to say if the observer is familiar with the object, he will perceive the object as if it is placed somewhere else.

Then it's just a matter of plugging in Snell's law which seems like you know how to apply.
A: You are correct that the emerging rays are parallel to the incoming ones, but sketch the situation. A ray cone $POQ$ converging to point $O$ with no glass plate converges, instead, in the presence of the glass plate to point $O^\prime$ owing to the Snell's-law-induced "kink" through the glass. Indeed, the point $O^\prime$ actually depends on the angle of incidence, so that, strictly speaking, a perfect ray cone no longer converges to a point in the presence of the flat plate. Your question is presumably asking for the small angle limit calculation of $O^\prime$. This nonuniqueness of convergence point is the origin of spherical aberration, and the reason why high NA microscope objectives either have to be used with a known thickness coverslip (the compensation for the spherical aberration from that thickness is built into the design) or else they have a correction collar, allowing the user to impart a variable, compensating spherical aberration to the light field.

