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Not quite parallel. The sun's 0.5° diameter in the sky causes the dark (umbra) of shadows to taper.
      
      A pea casts an umbra about  700 mm long.
      
      A mountain's umbra can extend over 300km when the sun is very low
      
      Earth's umbra is 1,400,000km long, three and a half times the distance of the moon.