Shadow

I saw an airplane's shadow as it flew by.   I wonder if the shadow gets bigger as the plane flies higher and closer to the light source?  The light source (sun) is so far away and the relative distance between it and the plane doesn't really change to any great degree.  I don't think the shadow would get much bigger than, say, a millimeter.  Then I thought about how you see those huge 747's flying really high up.  Those plane's look like specks in the sky.  The sun, on the other hand, appears to dwarf those planes.  Would they even have a shadow then?  I wouldn't think they would, only because the part of the visible sun that the plane takes up would only be fractional and the rest of the sun would fill in whatever shadow would be there.  Does that make any sense?  Maybe not.  I don't care.  Maybe I didn't want this to make any sense.  Ever think of that?  Hmph!