In the above, impedance of free space is the intrinsic impedance of free space. The second major result of Babinet's/Booker's principle is that the fields of the dual antenna are almost the same as the slot antenna (the fields components are interchanged, and called "duals"). That is, the fields of the slot antenna (given with a subscript S) are related to the fields of it's complement (given with a subscript C) by:
dual fields for slot antennas
Hence, if we know the fields from one antenna we know the fields of the other antenna. Hence, since it is easy to visualize the fields from a dipole antenna, the fields and impedance from a slot antenna can become intuitive if Babinet's principle is understood.
Note that the polarization of the two antennas are reversed. That is, since the dipole antenna on the right in Figure 2 is vertically polarized, the slot antenna on the left will be horizontally polarized.