My thanks to Alan Gibson, author of the Urbane Forager blog and book, for sending me these great images of a contrail shadow.
(Contrails are the long thin clouds that can form behind high jet aircrafts’ engines.)
These shadows form when a contrail casts a shadow on clouds below them. They are not especially rare, but images as good as this are.
There is a common but interesting optical illusion in these photos. Notice how the clouds that have the shadow cast on them appear to be higher than the contrail, but the shadow proves they must be lower.
For more on contrails see this page.