A solution of the electromagnetic scattering problem for confocal coat
ed spheroids has been obtained by the method of separation of variable
s in a spheroidal coordinate system. The main features of the solution
are (i) the incident, scattered, and internal radiation fields are di
vided into two parts: an axisymmetric part independent of the azimutha
l angle phi and a nonaxisymmetric part that with integration over ip g
ives zero; the diffraction problems for each part are solved separatel
y; (ii) the scalar potentials of the solution are chosen in a special
way: Abraham's potentials (for the axisymmetric part) and a superposit
ion of the potentials used for spheres and infinitely long cylinders (
for the nonaxisymmetric part). Such a procedure has been applied to ho
mogeneous spheroids [Differential Equations 19, 1765 (1983); Astrophys
. Space Sci. 204, 19, (1993)] and allows us to solve the light scatter
ing problem for confocal spheroids with an arbitrary refractive index,
size, and shape of the core or mantle. Numerical tests are described
in detail. The efficiency factors have been calculated for prolate and
oblate spheroids with refractive indices of 1.5 +/- 0.0i, 1.5 + 0.05i
for the core and refractive indices of 1.3 + 0.0i, 1.3 + 0.05i for th
e mantle. The effects of the core size and particle shape as well as t
hose of absorption in the core or mantle are examined. It is found tha
t the efficiency factors of the coated and homogeneous spheroids with
the volume-averaged refractive index are similar to first maximum.