Let
be the successive radii, each having its own
proper sign as well as magnitude.
the indices of refraction at the several surfaces.
the original focal distance.
those after one, two, three, refractions.
Then, if only we neglect the distances between the surfaces along the axis, we shall have
and so on.
When the surfaces are those of lenses,
and the equations are reducible to those we have already seen.