Why do the edges of glass blocks create a shadow? I have always observed that the shadow of glass blocks becomes darker as the glass is moved away from the surface where the shadow falls. And I know this is because refracted light rays from the glass block leave the block at an angle which creates the shadow of the glass block in the first place. However, whenever I try to observe the shadow of a glass block I can clearly see a dark outline of the block formed by its edges, irrespective of the distance from the surface where the shadow falls. And it is this outline, I seek an explanation for. Why is it that no matter how the glass block is oriented or how far it is from the surface where its shadow falls, its edges always form a distinct shadow?

 A: Not all the light shining on the top surface of your glass block can pass straight through the block.
Inside the block, total internal reflection occurs at the side faces. The light which was "supposed" to exit through the sides is refracted to the inside. This causes the shadow you observe and a slighly brighter middle section, which is hard to see. 
In fact, you might be able to see a brighter rim on the inside of the side's shadows if you move the block very close to the table.
A: Some sources say that about 6-7% of light gets reflected on hitting a glass.A glass seems to be transparent, but it not. Actually we cannot create a completely transparent solid body.
At molecular level:
When light encounters a material, it can interact with it in several different ways. These interactions depend on the wavelength of the light and the nature of the material. Photons interact with an object by some combination of reflection, absorption and transmission. Some materials, such as plate glass and clean water, transmit much of the light that falls on them and reflect little of it.
Regarding thicker shadows at edge
If you see the mirror sideways, you will find that its green in color. The green color is due to presence of impurities like iron. With naked eyes you cannot see through the mirror in side ways orientation, thus the incident light are obstructed to pass completely through the edges, hence the shadows at edge are thicker
I hope that I was able to answer your question, Comment if you have any doubt or query :) 
A: [This was an answer to an earlier version of the question, and doesn't address the band-of-shadow thing at all.]
I think the answer is that glass isn't that transparent, and in particular there are fairly significant losses at the surfaces (this is why camera lenses have fancy coatings which attempt to reduce the loss at the air-glass surfaces).
So, while there are effects due to refraction there is also the blunt effect that, if there's a bit of glass between you and a source of light -- and particularly if there are air-glass or glass-air surfaces -- then not all the light reaches you.  The result of this is shadows with fairly hard edges.
A: It appears to me that your piece of glass is beveled on the edges. When I place a beveled and non beveled piece of glass side by side directly under a light only the beveled one has the shadow.The angled edges are reflecting and refracting the light away from the area directly below.
