I have a question regarding Knott's book on radar cross section (RCS). Specifically, I am interested in the relationship between the 3D RCS, $\sigma_{3D}$, and the scattering width (2D RCS), $\sigma_{2D}$, of an electromagnetically long object. Knott quotes the relationship as $$ \sigma_{3D}=(2\space\sigma_{2D}/\lambda)\left|\frac{l\space sin(k\space l\space sin(\theta))}{k\space l\space sin(\theta)}\right|^{2} $$ where $\lambda$ is wavelength, $k=2\pi/\lambda$ is the wavenumber, $l$ is the length of the object ($l>>\lambda$) and $\theta$ is the angle the incident field makes with the transverse plane through the object (assumed small, $\theta<<1$). Also note the assumption that the induced currents in the confined object are precisely what would be induced in the infinite object i.e. with the effects of the ends ignored.
I would like to see a derivation of this result, particularly as I might get a sense of how quickly it breaks down when the incident angle goes too far off normal incidence, or as the object is very much truncated.
Thanks in advance for any help.