Where is the shadow?
The situation shown in the picture is often misinterpreted (Photo taken by Anja Hoff on 22-08-2012). Most people think that the shadow of the plane and the contrail cast on the thin cirrostratus cloud sheet must lay higher than the plane itself. This seems obvious, since the shadows are higher than the objects producing them. The low standing sun leads one to this conclusion – it is shown in the upper sketch:
The sun is perceived as low standing – lower than the clouds. The shadows, necessarily on the other side of the shadowing object, reach higher in the sky, and the illusion is perfect: the shadows must project upwards. But the actual circumstances are quite different. For any observer in the plane, the sun is above the same high over the horizon than it is for the observer on the surface. If he would see the shadow of his own plane, this would be underneath of him and the plane projecting towards the surface of the Earth.
The ground bound observer is a victim of the everyday perception. For him, the atmosphere is a three-dimensional volume, and the sun is located in it. But all the rays of the sun enter and cross the atmosphere parallel. This is shown in the lower sketch. From this it is evident, that the shadows can only be lower than the plane. Even at sunset/sunrise the shadows would not be cast above the plane. The single possibility, which I have had the opportunity to see once, is that the plane heads directly towards the sun eclipsing its own contrail. Another very interesting possibility is the eclipsing of the contrail from one side of the plane by the other, so that the one towards the sun is whitish-bright and the other grayish-dark – indeed a very spectacular view!
The two pictures below are from a series and can be used as a stereoscopic pair. If you look at the pair with crossed view, you will get a 3D impression of the scene – and you will notice that the top of the shadow peaks are much nearer to you than the clouds originating them.
Author: Christoph Gerber, Heidelberg, Germany