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I believe you actually see the sun "around the corner", due to atmospheric refraction [1].

[1]: http://en.wikipedia.org/wiki/Atmospheric_refraction

That accounts for part of it, but light from different spots on the Sun traces slightly different paths to the Earth. One of the results of that is that shadows cast long distances don't have distinct edges, because there's a zone in which the Sun is partially, but not completely, obscured.

https://en.wikipedia.org/wiki/Umbra

The dark region of the shadow is called the umbra, the partially shaded region is the penumbra. This effect is probably most widely associated with solar eclipses, where the Moon passes in front of the Sun. Where the Sun is only partially obscured, the Earth is in the penumbra. Totality exists within the umbra.

In some orientations of the Moon's orbit, it's further from the Earth (and hence smaller relative the much more distant and constant-sized Sun), and despite the fact that an observer is directly behind the Moon relative to the Sun, totallity isn't observed. This is an annular eclipse, where the Sun forms a ring around the Moon.

https://en.wikipedia.org/wiki/Annular_eclipse#Types

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