Why does an aeroplane flying at a great altitude not cast a shadow on the earth ?

Explanation

If we consider the sun as source and aeroplane as object and the earth as a screen, the aeroplane will cast its shadow on the earth when it is at a lower height. But as the aeroplane moves up the distance of screen from the object increases. As the aeroplane moves further and further away, the umbra becomes smaller and smaller and finally it completely disappears. Thus, an aeroplane or a bird does not cast a shadow when they are at greater heights.