Contrails are clouds with relatively sharp boundaries and hence may cast a sharp shadow on lower-altitude clouds. This shadow is then visible from the underside of the cloud, if the optical thickess of the cloud (the opacity) is not too large. If the lower-altitude cloud is cirrostratus, which is translucent, a three-dimensional shadow will form. This shadow is a plane defined by the sun and the (line-shaped) contrail. As a result, such a shadow is usually only visible if the contrail is in front of the sun for the observer. It is remarkable to see that a contrail shadow usually appears in an odd direction with respect to the sun and realizing that it is being cast on a lower-level cloud: perspective can be really deceptive.
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