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

ANS:

Sun being not a point source of light, the shadow of aeroplane cast by the sun consists of a conical region of total darkness (umbra) flanked by regions of part-shadow (penumbra). Since the aeroplane is at a height the apex of the
umbra is unable to reach the earth, so no umbra shadow is formed.

While the penumbra becomes lesser and lesser, dark as the distance goes on increasing. So on reaching the earth penumbra becomes lesser and lesser, dark as the distance goes on increasing. So on reaching the earth penumbra
looses all shades of darkness. Hence no shadow is formed on ground.

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