Simple approximate formula for the excitation of an optical fibre by a
plane wave focused through a lens are presented. The formula are vali
d for any mode of a weakly guiding fibre, and depend only on the angle
of incidence of the plane wave striking the lens and a single paramet
er which contains all the waveguide information. The same results appl
y to the case of a uniform beam exciting a fibre. The fraction of powe
r excited in the first two modes is compared with numerical results.